September 2008 Technical Report 

 NREL/TP-550-43388

International Energy Agency Building Energy Simulation Test 

and Diagnostic Method (IEA BESTEST) 

In-Depth Diagnostic Cases for Ground Coupled Heat Transfer 

Related to Slab-On-Grade Construction 

(Revised Cover) 

By 

J. Neymark 

J. Neymark & Associates, Wheat Ridge, Colorado, U.S. 

R. Judkoff 

National Renewable Energy Laboratory, Golden, Colorado, U.S. 

With 

I. Beausoleil-Morrison 

Natural Resources Canada, Ottawa, Canada 

A. Ben-Nakhi 

Public Authority for Applied Education and Training, Kuwait, State of Kuwait 

M. Crowley 

Dublin Institute of Technology, Dublin, Ireland 

M. Deru 

National Renewable Energy Laboratory, Golden, Colorado, U.S. 

R. Henninger 

GARD Analytics, Park Ridge, Illinois, U.S. 

H. Ribberink 

Natural Resources Canada, Ottawa, Canada 

J. Thornton 

Thermal Energy System Specialists, Madison, Wisconsin, U.S. 

A. Wijsman 

VABI Software BV, Delft, The Netherlands 

M. Witte 

GARD Analytics, Park Ridge, Illinois, U.S. 

Link to Required Zipped Data Files (6MB)

Link to IEA Participant Zipped Simulation Input File Archive (100MB)

National Renewable Energy Laboratory 

1617 Cole Boulevard 

Golden, Colorado 80401-3393
International Energy Agency Building 

Energy Simulation Test and 

Diagnostic Method (IEA BESTEST) 

In-Depth Diagnostic Cases for Ground 

Coupled Heat Transfer Related to 

Slab-on-Grade Construction 

J. Neymark

J. Neymark & Associates 

R. Judkoff 

National Renewable Energy Laboratory

Contributors: 

I. Beausoleil-Morrison Natural Resources Canada 

A. Ben-Nakhi Public Authority for Applied Education and 

Training

M. Crowley Dublin Institute of Technology

M. Deru National Renewable Energy Laboratory

R. Henninger GARD Analytics

H. Ribberink Natural Resources Canada

J. Thornton Thermal Energy System Specialists

A. Wijsman VABI Software 

M. Witte GARD Analytics

Prepared under Task No. BEC7.6051 

Technical Report 

NREL/TP-550-43388 

September 2008 

National Renewable Energy Laboratory

1617 Cole Boulevard, Golden, Colorado 80401-3393 

303-275-3000 • www.nrel.gov 

Operated for the U.S. Department of Energy 

Office of Energy Efficiency and Renewable Energy 

by Midwest Research Institute • Battelle 

Contract No. DE-AC36-99-GO10337
NOTICE

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Acknowledgments 

The work described in this report was a cooperative effort involving the members of the International 

Energy Agency (IEA) Testing and Validation of Building Energy Simulation Tools Experts Group. The 

group was composed of experts from the IEA Solar Heating and Cooling (SHC) Programme, Task 34, 

and Energy Conservation in Buildings and Community Systems (ECBCS) Programme Annex 43. 

For assistance with interpreting the analytical solution that provides the mathematical foundation of the 

analytical verification methodology used here, we wish to thank one of its authors, A. Delsante of 

Commonwealth Scientific and Industrial Research Organisation (CSIRO), Australia. P. Hollmuller of 

Université de Genève, Switzerland, provided an early review of the applicability of CSIRO’s analytical 

solution and a preliminary comparative analysis. 

We appreciate the support and guidance of D. Crawley, U.S. Department of Energy (DOE) program 

manager for this IEA research task and DOE representative to the IEA SHC Programme Executive 

Committee; and R. Karney, DOE representative to the IEA ECBCS Programme Executive Committee. 

iii 
Preface 

This report is a product of a joint effort between the International Energy Agency (IEA) Solar Heating 

and Cooling (SHC) and Energy Conservation in Buildings and Community Systems (ECBCS) 

Programmes. SHC monitors this work as Task 34 and ECBCS monitors this work as Annex 43. Ron 

Judkoff of the National Renewable Energy Laboratory (NREL) was the Operating Agent for IEA SHC 

34/ECBCS 43 on behalf of the United States Department of Energy. 

International Energy Agency 

The International Energy Agency (IEA) was established in 1974 within the framework of the 

Organisation for Economic Co-operation and Development (OECD) to implement an international energy 

programme. A basic aim of the IEA is to foster co-operation among the twenty-four IEA participating 

countries and to increase energy security through energy conservation, development of alternative energy 

sources and energy research, development and demonstration (RD&D). 

Solar Heating and Cooling Programme 

The Solar Heating and Cooling Programme was one of the first IEA Implementing Agreements to be 

established. Since 1977, its members have been collaborating to advance active solar and passive solar 

technologies and their application in buildings and other areas, such as agriculture and industry. Current 

members are: 

Australia Finland Portugal 

Austria France Spain 

Belgium Italy Sweden 

Canada Mexico Switzerland 

Denmark Netherlands United States 

European Commission New Zealand 

Germany Norway 

A total of 39 Tasks have been initiated, 30 of which have been completed. Each Task is managed by an 

Operating Agent from one of the participating countries. Overall control of the program rests with an 

Executive Committee comprised of one representative from each contracting party to the Implementing 

Agreement. In addition to the Task work, a number of special activities—Memorandum of 

Understanding with solar thermal trade organizations, statistics collection and analysis, conferences and 

workshops—have been undertaken. 

The Tasks of the IEA Solar Heating and Cooling Programme, both underway and completed are as 

follows: 

Current Tasks: 

Task 36 Solar Resource Knowledge Management 

Task 37 Advanced Housing Renovation with Solar & Conservation 

Task 38 Solar Assisted Cooling Systems 

Task 39 Polymeric Materials for Solar Thermal Applications 

Completed Tasks: 

Task 1 Investigation of the Performance of Solar Heating and Cooling Systems 

Task 2 Coordination of Solar Heating and Cooling R&D 

iv 
Task 3 Performance Testing of Solar Collectors 

Task 4 Development of an Insolation Handbook and Instrument Package 

Task 5 Use of Existing Meteorological Information for Solar Energy Application 

Task 6 Performance of Solar Systems Using Evacuated Collectors 

Task 7 Central Solar Heating Plants with Seasonal Storage 

Task 8 Passive and Hybrid Solar Low Energy Buildings 

Task 9 Solar Radiation and Pyranometry Studies 

Task 10 Solar Materials R&D 

Task 11 Passive and Hybrid Solar Commercial Buildings 

Task 12 Building Energy Analysis and Design Tools for Solar Applications 

Task 13 Advance Solar Low Energy Buildings 

Task 14 Advance Active Solar Energy Systems 

Task 16 Photovoltaics in Buildings 

Task 17 Measuring and Modeling Spectral Radiation 

Task 18 Advanced Glazing and Associated Materials for Solar and Building Applications 

Task 19 Solar Air Systems 

Task 20 Solar Energy in Building Renovation 

Task 21 Daylight in Buildings 

Task 23 Optimization of Solar Energy Use in Large Buildings 

Task 22 Building Energy Analysis Tools 

Task 24 Solar Procurement 

Task 25 Solar Assisted Air Conditioning of Buildings 

Task 26 Solar Combisystems 

Task 28 Solar Sustainable Housing 

Task 27 Performance of Solar Facade Components 

Task 29 Solar Crop Drying 

Task 31 Daylighting Buildings in the 21st Century 

Task 32 Advanced Storage Concepts for Solar and Low Energy Buildings 

Task 33 Solar Heat for Industrial Processes 

Task 34 Testing and Validation of Building Energy Simulation Tools 

Task 35 PV/Thermal Solar Systems 

Completed Working Groups: 

 CSHPSS, ISOLDE, Materials in Solar Thermal Collectors, and the Evaluation of Task 13 Houses 

To find more IEA Solar Heating and Cooling Programme publications or learn about the Programme visit 

our Internet site at www.iea-shc.org or contact the SHC Executive Secretary, Pamela Murphy, e-mail: 

pmurphy@MorseAssociatesInc.com. 

Energy Conservation in Buildings and Community Systems 

The IEA sponsors research and development in a number of areas related to energy. The mission of one 

of those areas, the ECBCS - Energy Conservation for Building and Community Systems Programme, is to 

facilitate and accelerate the introduction of energy conservation, and environmentally sustainable 

technologies into healthy buildings and community systems, through innovation and research in decisionmaking, building assemblies and systems, and commercialisation. The objectives of collaborative work 

within the ECBCS R&D program are directly derived from the on-going energy and environmental 

challenges facing IEA countries in the area of construction, energy market and research. ECBCS 

addresses major challenges and takes advantage of opportunities in the following areas: 

v 
• exploitation of innovation and information technology; 

• impact of energy measures on indoor health and usability; 

• integration of building energy measures and tools to changes in lifestyles, work environment 

alternatives, and business environment. 

The Executive Committee 

Overall control of the program is maintained by an Executive Committee, which not only monitors 

existing projects but also identifies new areas where collaborative effort may be beneficial. To date the 

following projects have been initiated by the executive committee on Energy Conservation in Buildings 

and Community Systems (completed projects are identified by (*) ): 

Annex 1: Load Energy Determination of Buildings (*) 

Annex 2: Ekistics and Advanced Community Energy Systems (*) 

Annex 3: Energy Conservation in Residential Buildings (*) 

Annex 4: Glasgow Commercial Building Monitoring (*) 

Annex 5: Air Infiltration and Ventilation Centre 

Annex 6: Energy Systems and Design of Communities (*) 

Annex 7: Local Government Energy Planning (*) 

Annex 8: Inhabitants Behaviour with Regard to Ventilation (*) 

Annex 9: Minimum Ventilation Rates (*) 

Annex 10: Building HVAC System Simulation (*) 

Annex 11: Energy Auditing (*) 

Annex 12: Windows and Fenestration (*) 

Annex 13: Energy Management in Hospitals (*) 

Annex 14: Condensation and Energy (*) 

Annex 15: Energy Efficiency in Schools (*) 

Annex 16: BEMS 1- User Interfaces and System Integration (*) 

Annex 17: BEMS 2- Evaluation and Emulation Techniques (*) 

Annex 18: Demand Controlled Ventilation Systems (*) 

Annex 19: Low Slope Roof Systems (*) 

Annex 20: Air Flow Patterns within Buildings (*) 

Annex 21: Thermal Modelling (*) 

Annex 22: Energy Efficient Communities (*) 

Annex 23: Multi Zone Air Flow Modelling (COMIS) (*) 

Annex 24: Heat, Air and Moisture Transfer in Envelopes (*) 

Annex 25: Real time HEVAC Simulation (*) 

Annex 26: Energy Efficient Ventilation of Large Enclosures (*) 

Annex 27: Evaluation and Demonstration of Domestic Ventilation Systems (*) 

Annex 28: Low Energy Cooling Systems (*) 

Annex 29: Daylight in Buildings (*) 

Annex 30: Bringing Simulation to Application (*) 

Annex 31: Energy-Related Environmental Impact of Buildings (*) 

Annex 32: Integral Building Envelope Performance Assessment (*) 

Annex 33: Advanced Local Energy Planning (*) 

Annex 34: Computer-Aided Evaluation of HVAC System Performance (*) 

Annex 35: Design of Energy Efficient Hybrid Ventilation (HYBVENT) (*) 

Annex 36: Retrofitting of Educational Buildings (*) 

Annex 37: Low Exergy Systems for Heating and Cooling of Buildings (LowEx) (*) 

Annex 38: Solar Sustainable Housing (*) 

Annex 39: High Performance Insulation Systems (*) 

vi 
Annex 40: Building Commissioning to Improve Energy Performance (*) 

Annex 41: Whole Building Heat, Air and Moisture Response (MOIST-ENG) 

Annex 42: The Simulation of Building-Integrated Fuel Cell and Other Cogeneration Systems 

(FC+COGEN-SIM) 

Annex 43: Testing and Validation of Building Energy Simulation Tools 

Annex 44: Integrating Environmentally Responsive Elements in Buildings 

Annex 45: Energy Efficient Electric Lighting for Buildings 

Annex 46: Holistic Assessment Tool-kit on Energy Efficient Retrofit Measures for Government 

Buildings (EnERGo) 

Annex 47: Cost-Effective Commissioning for Existing and Low Energy Buildings 

Annex 48: Heat Pumping and Reversible Air Conditioning 

Annex 49: Low Exergy Systems for High Performance Built Environments and Communities 

Annex 50: Prefabricated Systems for Low Energy / High Comfort Building Renewal 

Working Group - Energy Efficiency in Educational Buildings (*) 

Working Group - Indicators of Energy Efficiency in Cold Climate Buildings (*) 

Working Group - Annex 36 Extension: The Energy Concept Adviser (*) 

(*) – Completed 

Participating countries in ECBCS: 

Australia, Belgium, CEC, Canada, Czech Republic, Denmark, Finland, France, Germany, Greece, Israel, 

Italy, Japan, the Netherlands, New Zealand, Norway, Poland, Portugal, Sweden, Switzerland, Turkey, 

United Kingdom and the United States of America. 

SHC Task 34/ECBCS Annex 43: Testing and Validation of Building Energy 

Simulation Tools 

Goal and Objectives 

The goal of this Task/Annex is to undertake pre-normative research to develop a comprehensive and 

integrated suite of building energy analysis tool tests involving analytical, comparative, and empirical 

methods. These methods will provide for quality assurance of software, and some of the methods will be 

enacted by codes and standards bodies to certify software used for showing compliance to building 

energy standards. This goal will be pursued by accomplishing the following objectives: 

• Create and make widely available a comprehensive and integrated suite of IEA Building Energy 

Simulation Test (BESTEST) cases for evaluating, diagnosing, and correcting building energy 

simulation software. Tests will address modeling of the building thermal fabric and building 

mechanical equipment systems in the context of innovative low energy buildings. 

• Maintain and expand analytical solutions for building energy analysis tool evaluation. 

• Create and make widely available high-quality empirical validation data sets, including detailed and 

unambiguous documentation of the input data required for validating software, for a selected number 

of representative design conditions. 

Scope 

This Task/Annex investigates the availability and accuracy of building energy analysis tools and 

engineering models to evaluate the performance of innovative low-energy buildings. Innovative lowenergy buildings attempt to be highly energy efficient by using advanced energy efficiency technologies 

or a combination of energy efficiency and solar energy technologies. To be useful in a practical sense, 

such tools must also be capable of modeling conventional buildings. The scope of the Task is limited to 

building energy simulation tools, including emerging modular type tools, and to widely used innovative 

vii 
low-energy design concepts. Activities will include development of analytical, comparative and 

empirical methods for evaluating, diagnosing, and correcting errors in building energy simulation 

software. 

The audience for the results of the Task/Annex is building energy simulation tool developers, and codes 

and standards (normes) organizations that need methods for certifying software. However, tool users 

such as architects, engineers, energy consultants, product manufacturers, and building owners and 

managers are the ultimate beneficiaries of the research, and will be informed through targeted reports and 

articles. 

Means 

The objectives are to be achieved by the participants in the following projects. 

 Comparative and Analytical Verification Tests: 

Project A: Ground-Coupled Heat Transfer with Respect to Floor Slab and Basement Constructions 

Project B: Multi-Zone Buildings and Air Flow 

 Empirical Validation and Comparative Tests: 

Project C: Shading/Daylighting/Load Interaction 

Project D: Mechanical Equipment and Controls 

Project E: Buildings with Double-Skin Facades 

 Other: 

Project G: Web Site for Consolidation of Tool Evaluation Tests 

Participants 

The participants in the Task are Australia, Belgium, Canada, Czech Republic, Denmark, France, 

Germany, Japan, The Netherlands, Spain, Sweden, Switzerland, the United Kingdom, and the United 

States. The United States served as the Operating Agent for this Task; Ron Judkoff of National 

Renewable Energy Laboratory provided Operating Agent services on behalf of the U.S. Department of 

Energy. 

This report documents work carried out under Project A: Ground-Coupled Heat Transfer with Respect to 

Floor Slab and Basement Constructions. 

viii 
Table of Contents

Page

Acknowledgments................................................................................................................................ iii 

Preface ............................................................................................................................................... iv 

Electronic Media Contents .................................................................................................................. xi 

Executive Summary ............................................................................................................................. xii 

 References for Executive Summary .............................................................................................. xxii 

Introduction ........................................................................................................................................ xxvi 

 References for Introduction .......................................................................................................... xxviii 

1.0 Part I: User's Manual: Procedure and Specification....................................................................... 1 

 1.1 General Description of the Test Cases ..................................................................................... 1 

 1.1.1 Accompanying Electronic Files ..................................................................................... 4 

 1.2 Performing the Tests ................................................................................................................ 5 

 1.2.1 Modeling Rules .............................................................................................................. 5 

1.2.2 Comparing Your Output to the Analytical Solution, Verified Numerical-Model 

Results, and Other Example Simulation Results ................................................................. 6 

 1.3 Test Specifications ................................................................................................................ 7 

 1.3.1 “b”-Series Cases ............................................................................................................... 7 

 1.3.1.1 Case GC30b – Steady-State Comparative Test Base Case ................................... 7 

 1.3.1.1.1 Objective ................................................................................................... 7 

 1.3.1.1.2 Method ...................................................................................................... 7 

 1.3.1.1.3 Input Specification .................................................................................... 8 

 1.3.1.1.4 Output Requirements ................................................................................ 13 

 1.3.1.2 Case GC40b – Harmonic Variation of Ambient Temperature ............................. 15 

 1.3.1.3 Case GC45b – Aspect Ratio ............................................................................... 17 

 1.3.1.4 Case GC50b – Large Slab ............................................................................... 18 

 1.3.1.5 Case GC55b – Shallow Deep Ground Temperature ............................................. 19 

 1.3.1.6 Case GC60b – Steady State with Typical Interior Convective Surface Coefficient 19 

 1.3.1.7 Case GC65b – Steady State with Typical Interior and Exterior Convective 

Surface Coefficients................................................................................................... 20 

 1.3.1.8 Case GC70b – Harmonic Variation of Ambient Temperature with Typical 

Interior and Exterior Convective Surface Coefficients.............................................. 21 

 1.3.1.9 Case GC80b – Reduced Slab and Ground Conductivity ...................................... 21 

 1.3.2 “a”-Series Cases ................................................................................................................ 22 

 1.3.2.1 Case GC10a – Steady-State Analytical Verification Base Case ........................... 22 

 1.3.2.1.1 Objective ................................................................................................... 22 

 1.3.2.1.2 Method ...................................................................................................... 22 

 1.3.2.1.3 Input Specification .................................................................................... 22 

 1.3.2.1.4 Output Requirements ................................................................................ 24 

 1.3.2.1.5 Analytical Solution for Steady-State Heat Flow through the Floor Slab .. 24 

 1.3.2.2 Case GC30a – Steady-State Comparative Test Base Case with Direct Input of 

 Surface Temperatures .............................................................................................. 26 

 1.3.2.3 Case GC40a – Harmonic Variation of Direct-Input Exterior Surface Temperature 27 

 1.3.3 “c”-Series Cases ................................................................................................................ 28 

 1.3.3.1 Case GC30c – Steady-State Comparative Test Base Case with BASESIMP 

Boundary Conditions ................................................................................................. 28 

 1.3.3.2 Case GC40c – Harmonic Variation of Direct-Input Exterior Surface Temperature 

with BASESIMP Boundary Conditions .................................................................... 29 

 1.3.3.3 Case GC45c – Aspect Ratio with BASESIMP Boundary Conditions ................ 30 

ix 
Page

 1.3.3.4 Case GC55c – Shallow Deep Ground Temperature with BASESIMP Boundary 

Conditions ............................................................................................................... 31 

 1.3.3.5 Case GC80c – Reduced Slab and Ground Conductivity with BASESIMP 

Boundary Conditions ................................................................................................. 31 

Appendix A: TMY2 File Format ......................................................................................................... 32 

Appendix B: Output Spreadsheet Instructions..................................................................................... 37 

Appendix C: Abbreviations and Acronyms ......................................................................................... 38 

Appendix D: Glossary ...................................................................................................................... 39 

Appendix E: Remarks About The Test Cases .................................................................................... 41 

Appendix F: Diagnosing the Results Using the Flow Diagrams ......................................................... 43 

References for Part I ...................................................................................................................... 48 

2.0 Part II: Production of Simulation Results ................................................................................... 49 

 2.1 Introduction ...................................................................................................................... 49 

 2.2 Selection of Simulation Programs and Modeling Rules for Simulations ............................... 50 

 2.3 Improvements to the Test Specification as a Result of the Field Trials.................................. 51 

 2.4 Examples of Error Trapping with BESTEST Diagnostics...................................................... 56 

 2.4.1 TRNSYS Version 16.1.................................................................................................. 56 

 2.4.2 DIT 3-D Numerical Model using MATLAB Version 7.0............................................. 59 

 2.4.3 PAAET 3-D Numerical Model using FLUENT 6.0 ..................................................... 61 

 2.4.4 EnergyPlus ................................................................................................................ 62 

 2.4.5 VA114 Version 2.20 with ISO 13370 Ground Heat Transfer Model ........................... 68 

 2.4.6 BASESIMP/ESP-r and BASECALC............................................................................ 71 

 2.4.7 GHT/SUNREL-GC....................................................................................................... 74

 2.5 Interpretation of Results.......................................................................................................... 79 

 2.5.1 Developing a Secondary Mathematical Truth Standard Based on an Analytical 

Solution and Verified Numerical Models .................................................................. 79 

 2.5.2 Comparing Typical Simulation Model Results to Verified Numerical-Model Results 82 

 2.5.3 Improvements to Simulations during the Field Trials................................................... 82 

 2.5.4 Test Cases for Future Work .......................................................................................... 88

 2.6 Conclusions and Recommendations ....................................................................................... 91 

 2.6.1 Conclusions ................................................................................................................ 91 

 2.6.2 Recommendations......................................................................................................... 95 

 2.7 Abbreviations and Acronyms for Parts II and III .................................................................. 98 

 2.8 References for Parts II and III ................................................................................................ 100 

 2.9 Appendix II: Simulation Modeler Reports.............................................................................. 106 

 Appendix II-A: TRNSYS, Thermal Energy System Specialists, United States ................ 107 

 Appendix II-B: FLUENT, Public Authority of Applied Education and Training, Kuwait 125 

 Appendix II-C: MATLAB, Dublin Institute of Technology, Ireland ................................ 136 

 Appendix II-D: EnergyPlus, GARD Analytics, United States .......................................... 148 

 Appendix II-E: BASECALC and BASESIMP/ESP-r, CETC/NRCan, Canada ............... 163 

 Appendix II-F: VA114/ISO-13370, VABI Software, The Netherlands ........................... 178 

 Appendix II-G: GHT/SUNREL-GC, National Renewable Energy Laboratory, US ........ 197 

3.0 Part III: Simulation Field Trial Results.......................................................................................... 201 

 Graphs ................................................................................................................................... 204 

 Tables ................................................................................................................................... 221 

x 
Electronic Media Contents 

The following files apply as they are called out in the test procedure; these are included in the .zip file 

link on the cover page of the posted electronic version of this document; click on “Link to Required 

Zipped Data Files (6 MB)”: 

• README-GC-InDepth.DOC: Electronic media contents 

• GCSS-W40.TM2: TMY2 weather data for 10°C constant ODB, 40.0 m/s wind speed 

• GCSS-W20.TM2: TMY2 weather data for 10°C constant ODB, 19.9 m/s wind speed 

• GCSS-W01.TM2: TMY2 weather data for 10°C constant ODB, 1.0 m/s wind speed 

• GCSP-W40.TM2: TMY2 data for harmonically varying (10°C mean) ODB, 40.0 m/s wind speed 

• GCSP-W20.TM2: TMY2 data for harmonically varying (10°C mean) ODB, 19.9 m/s wind speed 

• GCSP-W01.TM2: TMY2 data for harmonically varying (10°C mean) ODB, 1.0 m/s wind speed 

• GC-InDepth-Out.XLS: Raw output data spreadsheet 

• GC-InDepth-Results.XLS: Results spreadsheet to assist users with plotting their results versus the 

example simulation results 

• GC-InDepth-Results.DOC: Documentation for navigating GC-InDepth-Results.XLS. 

The IEA SHC Task 34/ECBCS Annex 43 participant simulation input files are included in the .zip file link 

on the cover page of the posted electronic version of this document; click on “Link to IEA Participant 

Zipped Simulation Input File Archive (100 MB).” These files are not necessary to run the test cases. The 

.zip file will unzip to the folder structure shown below. Each subfolder contains files used to develop the 

results for the listed programs provided in Part III. 

\InpFiles-GC-InDepth 

 \BASECALC 

 \BASESIMP 

 \DIT-MATLAB 

 \EnergyPlus 

 \GHT 

 \PAAET-FLUENT 

 \SUNREL-GC 

 \TRNSYS 

 \VA114-ISO13370 

xi 
Executive Summary 

This report documents a set of idealized in-depth diagnostic test cases for use in validating groundcoupled floor slab heat transfer models. These test cases represent an extension to IEA BESTEST,1

 which 

originally focused on testing and validation of building thermal fabric models, but addressed only 

cursorily the modeling of heat transfer between the building and the ground. This new work was 

conducted by the National Renewable Energy Laboratory (NREL), United States in collaboration with a 

working group of international experts under International Energy Agency (IEA) Solar Heating and 

Cooling (SHC) Programme Task 34 and IEA Energy Conservation in Buildings and Community Systems 

(ECBCS) Programme Annex 43. Ron Judkoff of NREL was the operating agent for IEA 34/43. 

Background 

The development of practical procedures and data for tool evaluation and improvement is part of an 

overall IEA validation methodology that NREL2,3,4 and the IEA5,6 have been developing for many years. 

The methodology combines empirical validation, analytical verification, and comparative analysis 

techniques; details are discussed in the Background Section of HVAC BESTEST Volume 1;7

 updates are 

published in the 2005 ASHRAE Handbook of Fundamentals8

 and elsewhere.4 NREL originally developed 

the BESTEST method in IEA SHC Task 12 to test building thermal fabric (envelope) models, and to 

diagnose sources of predictive disagreements.1

 This method of test was adopted with some refinements by 

the American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE) in 

accordance with procedures of the American National Standards Institute (ANSI), and now forms the 

basis for ANSI/ASHRAE Standard 140, Method of Test for the Evaluation of Building Energy Analysis 

Computer Programs.9,10,11 Since Standard 140 was first published, three HVAC BESTEST test suites 

developed within IEA SHC Task 22 have been added: two that address unitary space cooling 

equipment,7,12 and one that addresses fuel-fired furnaces.13

Importance of the Ground Heat Transfer Problem

As above-grade components of the building thermal fabric become more energy efficient, the heat 

transfer between the building and the ground becomes relatively more important. Ground-coupled heat 

transfer is a complex phenomenon that involves three-dimensional (3-D) thermal conduction, moisture 

transport, long time constants, and the heat storage properties of the ground. Based on simulations by 

NREL discussed in the Introduction of this report, typical slab-on-grade floor heat loss can range from 

15% to 45% of the annual heating load. This result depends on a wide variety of parameters, including 

climate, above-grade thermal properties of the building, presence of slab and/or perimeter insulation, and 

the ground heat transfer model used for the calculation. Estimates of the range of disagreement among 

models used for calculating uninsulated slab-on-grade heat transfer are 25% to 60% or higher for 

simplified models versus detailed models, depending on the models being compared, building 

construction characteristics, and climate. 

Brief History of Ground Heat Transfer Model Development

During the early 1990s computers were substantially less powerful than they are today; such computers 

typically allowed only the use of simplified models for calculating ground heat transfer. A common 

simplified model is ASHRAE’s slab-on-grade perimeter heat-loss calculation, which uses perimeter 

length (m) and an F-factor heat loss coefficient (W/(m⋅K)) to assimilate a typical steady-state thermal 

conductance (UA-value [W/K]).14,15 For basement heat loss ASHRAE provides a simplified steady-state 

calculation method based on heat transfer path lengths that occur at given increments of basement wall 

depth.15,16,17 These models can be modified to include one-dimensional (1-D) dynamic conduction 

xii 
modeling of a limited amount of ground, including thermal mass storage,18 but addressing further detail 

was typically beyond the capability of most computers. 

Because of recent improvements to computers, the state-of-the-art in ground heat transfer modeling has 

improved. Consequently, a number of mid-level detailed models have been developed and applied to 

building energy simulation software, including the following examples of models tested in this work: 

• BASECALC – produces quasi-3-D analysis by combining two dimensional (2-D) finite element 

simulations with corner correction factors19

• BASESIMP – correlation method based on more than 100,000 BASECALC simulations20 

• EnergyPlus – monthly 3-D numerical analysis in a preprocessor21,22,23 

• EN ISO 13370 – European standard below-grade heat transfer calculation methodology applying 

a 3-D heat loss component varied monthly and a 1-D heat loss component varied hourly; VA114 

applies this method; however, the 3-D heat loss component is varied daily.24,25

Recent ground heat transfer simulation improvements include the development of stand-alone 3-D 

detailed numerical models that have also been integrated with whole-building energy simulation 

programs. Such models used in this work include TRNSYS’s 3-D finite difference model26 and the GHT 

3-D finite element model that interfaces with SUNREL-GC.27 Two detailed models not linked to wholebuilding simulation programs, but used as stand-alone models in this project, were developed using 

FLUENT28,29 and MATLAB.30,31

Evolution of BESTEST Ground-Coupled Heat Transfer Test Cases

The BESTEST ground-coupled heat transfer test cases have evolved in parallel with model development. 

The initial IEA BESTEST1

 ground-coupled heat transfer test case published in 1995 was developed when 

simplified tools were predominant. This test case included a half basement, did not define all boundary 

conditions that would be required for use by detailed models, and had a wide range of disagreement 

among the results. Because of its cursory nature, this was the only case from IEA BESTEST excluded 

from ASHRAE Standard 140. 

HERS BESTEST,18 also published in 1995, is designed to test simplified tools commonly used with 

residential modeling, and includes cases designed to test simplified ground heat transfer models for slabon-grade and basement configurations. The ground coupling results set within HERS BESTEST also 

displayed a wide range of disagreement among the simplified models that were tested. Because of the 

simplified nature of the tests, running HERS BESTEST with detailed models would require modeling 

assumptions not documented in the test specification, which would cause variations among results. 

Several building energy software producers are developing relatively detailed ground-coupled heat 

transfer models and integrating them with whole-building energy simulation computer programs. 

However, there is little to no quantitative information about the accuracy of these new models, or about 

how well they compare to each other or to previously developed, simpler models. Furthermore, it is 

extremely difficult and expensive to collect good empirical data on ground-coupled heat transfer 

phenomena because of the disturbance to the earth and to temperature profiles resulting from the 

construction of a building and placement of sensors, the long time constants associated with large ground 

mass, and the variability in field conditions. For these reasons, NREL collaborated with the previous IEA 

SHC Task 22 to develop a BESTEST-type method to test and diagnose the more advanced groundcoupled heat transfer models. The SHC Task 22 cases tested various relatively realistic slab-on-grade and 

basement constructions.32 The cases were defined to test the following aspects of ground-coupled heat 

transfer models: (1) interaction of the building with the atmosphere through the ground; (2) effects of 

solar radiation on ground-coupled surfaces; (3) effects of calculated versus constant surface heat transfer 

xiii 
coefficients; (4) slab-on-grade geometries with and without insulation; (5) basement geometries with and 

without insulation; (6) interaction of the building with the deep ground conditions; and (7) walkout 

basement construction. Preliminary results from the Task 22 project for cases that isolated the effects of 

the ground heat transfer models (e.g., no windows, near-adiabatic above-grade construction) are shown in 

Figure ES-1. The results indicate some large disagreements among the detailed ground-coupled heat 

transfer models linked to whole-building energy simulation software, even after a major algorithmic 

limitation was fixed in one of the programs. However, the sources of these disagreements could not be 

readily determined because the cases were designed to be relatively realistic, not diagnostic, and there 

was no mathematical or empirical truth standard. 

IEA BESTEST Ground Coupling

Heating Loads

0

2

4

6

8

10

12

14

16

18

GC100: Pure Slab

GC180: Pure Slab, 12x16

GC180-100: Slab Area

GC200: Pure Bsmt.

GC100: Pure Slab

GC180: Pure Slab, 12x16

GC180-100: Slab Area

GC200: Pure Bsmt.

HOT3000

Annual Heating Load (MWh) Peak Heating Load * 5 (kW)

SUNREL VA114 EnergyPlus

Figure ES-1. Results from IEA SHC Task 22 test cases isolating ground-coupled 

heat transfer effects32

Based on these unresolved disagreements, NREL concluded, and the participants agreed, that before 

proceeding with other realistic test cases in-depth diagnostics had to be developed to resolve or better 

understand the causes of differences found during the SHC Task 22 work. The participants also agreed 

that after the in-depth test cases were completed, the past Task 22 tests should be revised and rerun, and 

that other realistic tests should be considered for development. 

In parallel with the Task 22 work, ASHRAE published a compilation of analytical solutions33 that 

included a 3-D steady-state analytical solution for a slab-on-grade related heat transfer problem with 

rectangular geometry originally developed by Commonwealth Scientific and Industrial Research 

Organization (CSIRO), Australia.34 This spawned the idea to design a test suite beginning with the 

CSIRO analytical solution, which would then step methodically toward more realistic boundary 

conditions and parametric assumptions. Furthermore, if detailed stand-alone 3-D numerical models were 

applied to the test cases using a solution process that demonstrates convergence, and good agreement was 

verified, those numerical models could be established as quasi-analytical solutions. Such solutions would 

provide a powerful secondary mathematical truth standard, based on their range of disagreement, for 

checking other ground-coupling models typically used with whole-building energy simulation programs. 

(Definitions of the following terms are provided in the glossary of Part I, Appendix D: “analytical 

xiv 
solution,” “quasi-analytical solution,” “verified numerical model,” “mathematical truth standard,” and 

“secondary mathematical truth standard.”) 

The Current IEA 34/43 In-Depth Diagnostic Analytical Verification Test Cases

This report documents a set of idealized in-depth diagnostic analytical verification test cases for use in 

validating ground-coupled floor slab heat transfer models. The logic for the cases may be summarized as 

follows: 

• Identify or develop exact analytical solutions that may be used as mathematical truth standards 

for testing detailed numerical models using parameters and simplifying assumptions of the 

analytical solution. 

• Apply a numerical solution process that demonstrates convergence in the space and time domains 

for the analytical-solution test cases and additional test cases where numerical models are applied. 

• Once validated against the analytical solutions, use the numerical models to develop reference 

results for test cases that progress toward more realistic (less idealized) conditions, and that do 

not have exact analytical solutions. 

• Check the numerical models by carefully comparing their results to each other while developing 

the more realistic cases, and make corrections as needed. 

• Good agreement for the set of numerical models versus the analytical solution – and versus each 

other for subsequent test cases – verifies them as a secondary mathematical truth standard based 

on the range of disagreement among their results. 

• Use the verified numerical-model results as reference results for testing other models that have 

been incorporated into whole-building simulation computer programs. 

This approach represents an important methodological advance to extend the analytical verification 

method beyond the constraints inherent in classical analytical solutions. It allows a secondary 

mathematical truth standard to be developed in the form of a set of stand-alone detailed numerical models 

(quasi-analytical solutions). Once verified against all available classical analytical solutions, and 

compared with each other for cases that do not have exact analytical solutions, the set of verified 

numerical models can be used together to test other models as implemented in whole-building simulation 

programs. This allows for much greater enhanced diagnostic capability than the purely comparative 

method, and it allows somewhat more realistic boundary conditions to be used in the test cases than are 

possible with pure analytical solutions. A more detailed description of the new methodology is given in 

Part II, Section 2.5.1. 

The CSIRO analytical solution34 was the only 3-D analytical solution with rectangular surface geometry 

we found, and formed the basis for the test cases included in Part I. This analytical solution is for a 

steady-state condition. We investigated the possibility of finding or developing a comparable 3-D solution 

for a harmonic boundary condition. However, we did not find a ready-made solution, and several applied 

mathematicians advised that such a solution would be difficult, if not impossible, to derive. 

The new test cases use an idealized uninsulated slab-in-grade configuration. This simplified configuration 

is required by the CSIRO analytical solution, is appropriate for developing robust ground-coupling test 

cases, is compatible with the tested programs, and facilitated the development of accurate model results 

by minimizing chances for input errors. These cases, as they step away from the analytical solution, also 

test parametric sensitivities to variation of floor-slab aspect ratio, slab area, water table depth (constant 

deep ground temperature depth), slab-interior and ground-exterior surface heat transfer coefficients, and 

slab and ground thermal conductivity. The cases use steady-state and harmonic boundary conditions as 

applied within artificially constructed annual weather data, along with an adiabatic above-grade building 

xv 
envelope to isolate the effects of ground-coupled heat transfer. Because the zone heating load is driven 

exclusively by the slab heat losses, it is equal to the slab conduction heat loss. This is convenient for 

testing programs that may not readily disaggregate floor conduction losses in their output. Various output 

values – including steady-state, annual total steady-periodic, and annual peak-hour steady-periodic results 

for floor conduction and zone heating load, along with time of occurrence of peak-hour loads and other 

supporting output – are compared and used in conjunction with a formal diagnostic method to determine 

algorithms responsible for predictive differences. 

Results 

Field trials of the new IEA BESTEST cases were conducted with a number of detailed state-of-the-art 

numerical models and state-of-the art whole-building energy simulation programs, which contained a 

variety of ground-coupled heat transfer models from around the world (see Table ES-1). The field-trial 

process was iterative in that executing the simulations led to refinement of the BESTEST cases, and the 

results of the tests led to improving and debugging the ground-coupled heat transfer models. 

Table ES-1. Participating Organizations and Models 

Analytical Solution, 

Case GC10a Authoring Organization Implemented by

Delsante, Stokes, and 

Walsh34

Commonwealth Scientific and Industrial 

Research Organisation, Australia NREL/JNA, a,b United States 

Verified Numerical 

Model Authoring Organization Implemented by

FLUENT 6.0.20 Fluent, Incorporated, United States PAAET,c Kuwait 

MATLAB 7.0.4.365 (R14) The MathWorks, Inc., United States Dublin Institute of Technology, Ireland 

TRNSYS 16.1 University of Wisconsin/TESS,d United States TESS,d United States 

Simulation Program Authoring Organization Implemented by

BASECALC V1.0e CETC,e

 Canada CETC,e Canada 

EnergyPlus 2.0.0.025 LBNL/UIUC/DOE-BT,f,g,h United States GARD Analytics, Inc., United States 

ESP-r/BASESIMP CETC/ESRU,e,i Canada/United Kingdom CETC,e

 Canada 

GHT NREL,a

 United States NREL,a United States 

SUNREL-GC 1.14.01 NREL,a

 United States NREL,a United States 

VA114 2.20/ISO-13370 VABI Software BV, The Netherlands; 

CEN/ISOj,k VABI Software BV, The Netherlands 

a

NREL: National Renewable Energy Laboratory, United States 

b

JNA: J. Neymark & Associates, United States 

c

PAAET: Public Authority for Applied Education and Training, Kuwait 

d

TESS: Thermal Energy Systems Specialists, United States 

e

CETC: CANMET Energy Technology Centre, Natural Resources Canada, Canada 

f

LBNL: Lawrence Berkeley National Laboratory, United States 

g

UIUC: University of Illinois Urbana/Champaign, United States h

DOE-BT: U.S. Department of Energy, Office of Building Technologies, Energy Efficiency and Renewable Energy, United States 

i

ESRU: Energy Systems Research Unit, University of Strathclyde, United Kingdom 

j

CEN: European Committee for Standardisation, Belgium 

k

ISO: International Organization for Standardization, Switzerland 

xvi 
The agreement among simulation results improved with each iteration of the field trials. Improvements to 

the simulation programs are evident when the initial results set (see Figure ES-2 for the steady-state cases 

and Figure ES-4 for the steady-periodic cases) is compared to the final results set (see Figure ES-3 for the 

steady-state cases and Figure ES-5 for the steady-periodic cases). (In these figures verified numericalmodel results are shown with blue shaded background and the analytical solution result [Case GC10a] is 

shown with magenta background.) Improvements to simulation programs or simulation inputs made by 

participants were required to have a mathematical and a physical basis, and to be applied consistently 

across tests. Arbitrary modification of a simulation program’s input or internal code to more closely 

match a given set of results was not allowed. All improvements were required to be documented and 

justified in the modeler reports. 

These results indicate that there was initially a 9%–55% disagreement among the cases for the simulated 

energy consumption results, with substantial scatter among the programs. Here disagreement is the 

difference between the maximum and minimum results for each case, divided by the mean of the results 

for each case ((max-min)/mean). These results include two estimates for results that would have occurred 

before fixes were made during preliminary work of IEA SHC Task 22 documented in Section 2.4, which 

were not previously published; see Figure ES-2 results for Case GC60b and Figure ES-4 results for Case 

GC70b. After correcting software errors using BESTEST diagnostics – 24 disagreements were found 

among the programs, which resulted in 19 fixes so far – the remaining disagreements for the models are 

1%–24% with reduced scatter among results. This may be a reasonable range of disagreement, given the 

complexity of the modeling problem, although a few remaining disagreements identified in Section 2.4 

could be addressed later. Agreement is also improved among the detailed numerical models (results 

shown with blue shaded background), where initial disagreements up to 12% were reduced to 0%–4% for 

the verified numerical-model results over the course of the project. 

Findings 

Several important technology advances were made as a result of running the test cases: 

• The detailed numerical-methods modelers used the analytical solution to improve their models – 

e.g., a TRNSYS node meshing refinement (finer mesh near perimeter boundaries) resulted in a 

10% results improvement versus the analytical solution; compare results for Case GC10a in 

Figures ES-2 and ES-3. 

• There were three participating stand-alone 3-D numerical models with excellent agreement with 

the analytical solution and with each other for the remaining cases (see results with blue 

background in Figures ES-3 and ES-5 and the GC10a result with magenta background in Figure 

ES-3). These verified numerical-model results form a secondary mathematical truth standard 

based on their range of disagreement. 

• The high level of agreement among the verified numerical models allowed diagnosis of errors in 

other mid-level detailed models integrated with whole-building energy simulation software; some 

may have been missed without the secondary mathematical truth standard. 

• Of 24 found disagreements, 19 were diagnosed and fixed, 3 are planned for investigation by the 

software authors, and 2 were judged as acceptable by the authors of mid-level detailed models 

(after they had fixed previous disagreements). Several of the found errors affected some 

individual results by more than 20%; this was after two major problems were fixed as a result of 

the Task 22 work. A listing of the problems found among the tested models appears in Table 2-8 

(see Section 2.6.1 of Part II), with supporting details included in Section 2.4 of Part II. 

• Based on this work and previous work of IEA SHC Task 22, there are a number of recommended 

areas for further investigation with respect to developing additional validation test cases for 

modeling ground-coupled heat transfer. These are described in detail in Section 2.5.4 of Part II. 

xvii 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-State Floor Conduction

0

500

1000

1500

2000

2500

3000

GC10a 

linear dT

GC30a 

adiab. wall, 

ideal films

GC30b 

adiab. wall, 

h = 100 

GC30c 

h,int = 7.95; 

h,ext = ideal

GC60b 

h,int = 7.95; 

h,ext = 100

GC65b 

h,int = 7.95; 

h,ext = 11.95

Floor Heat Flow (W or Wh/h)

Analytical Solution/CSIRO TRNSYS/TESS FLUENT/PAAET

MATLAB/DIT GHT/NREL SUNREL-GC/NREL

EnergyPlus/GARD VA114-ISO13370/VABI ESP-r-BASESIMP/NRCan

BASECALC/NRCan

 

Figure ES-2. BESTEST slab/ground heat transfer steady-state cases – floor conduction, before 

BESTESTing (Abbreviations along the x-axis are shorthand for the case descriptions; see Part I for full 

case descriptions.) 

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-State Floor Conduction

0

500

1000

1500

2000

2500

3000

GC10a 

linear dT

GC30a 

adiab. wall, 

ideal films

GC30b 

adiab. wall, 

h = 100 

GC30c 

h,int = 7.95; 

h,ext = ideal

GC60b 

h,int = 7.95; 

h,ext = 100

GC65b 

h,int = 7.95; 

h,ext = 11.95

Floor Heat Flow (W or Wh/h)

Analytical Solution/CSIRO TRNSYS/TESS FLUENT/PAAET

MATLAB/DIT GHT/NREL SUNREL-GC/NREL

EnergyPlus/GARD VA114-ISO13370/VABI ESP-r-BASESIMP/NRCan

BASECALC/NRCan

Figure ES-3. BESTEST slab/ground heat transfer steady-state cases – floor conduction, after 

BESTESTing (Abbreviations along the x-axis are shorthand for the case descriptions; see Part I for full 

case descriptions.)

xviii 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Floor Conduction

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

GC40a

ideal films

GC40b

h=100

GC45b

AR=36x4

GC50b

large

slab/10

GC55b 

2m depth

GC70b

hint=7.95,

hext=11.95

GC80b 

k=0.5

GC40c

hint=7.95,

hext=ideal

GC45c

AR=36x4

GC55c 

5m depth

GC80c

k=0.85

Floor Heat Flow (kWh)

TRNSYS/TESS FLUENT/PAAET MATLAB/DIT

GHT/NREL SUNREL-GC/NREL EnergyPlus/GARD

VA114-ISO13370/VABI ESP-r-BASESIMP/NRCan BASECALC/NRCan

Figure ES-4. BESTEST slab/ground heat transfer state-periodic cases – floor conduction, before 

BESTESTing (Abbreviations along the x-axis are shorthand for the case descriptions; see Part I for full 

case descriptions.)

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Floor Conduction

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

GC40a

ideal films

GC40b

h=100

GC45b

AR=36x4

GC50b

large

slab/10

GC55b 

2m depth

GC70b

hint=7.95,

hext=11.95

GC80b 

k=0.5

GC40c

hint=7.95,

hext=ideal

GC45c

AR=36x4

GC55c 

5m depth

GC80c

k=0.85

Floor Heat Flow (kWh)

TRNSYS/TESS FLUENT/PAAET MATLAB/DIT

GHT/NREL SUNREL-GC/NREL EnergyPlus/GARD

VA114-ISO13370/VABI ESP-r-BASESIMP/NRCan BASECALC/NRCan

Figure ES-5. BESTEST slab/ground heat transfer steady-periodic cases – floor conduction, after 

BESTESTing (Abbreviations along the x-axis are shorthand for the case descriptions; see Part I for full 

case descriptions.) 

xix 
Based on results after several iterations of BESTESTing, and resulting model improvements, all tested 

programs now appear to be generally reliable for modeling ground-coupled heat transfer related to slabon-grade construction, although some remaining disagreements should be addressed. The verified 

numerical-model results may be used as a reference or benchmark against which other software can be 

tested. For applications where ground-coupled heat transfer is a major component of a given simulation 

problem, the superior accuracy of the verified numerical models may justify adapting highly detailed 

models to more whole-building energy simulation programs, especially as computer hardware continues 

to improve and the detailed models become more user friendly. 

Conclusions 

Major Accomplishments 

The major accomplishments of this project were: 

• The IEA BESTEST building thermal fabric envelope tests were expanded to include in-depth 

diagnostic analytical verification test cases for ground-coupled heat transfer related to slab-ongrade construction. 

• A formal methodology was developed to facilitate using and verifying numerical models to 

establish a secondary mathematical truth standard. This method applies to the test case 

development and to numerical model implementation, and allows quasi-analytical solutions to be 

developed for more realistic (less constrained) cases than exact analytical solutions allow. 

• A set of verified numerical-model results was developed for all test cases, using the newly 

developed methodology. This represents a secondary mathematical truth standard founded on the 

range of disagreement of the numerical-model results. 

• The accuracy of all models that participated in the field trials of the test cases was improved: 19 

errors were diagnosed and fixed; initial disagreement ranges of 9%–55% for the test cases were 

reduced to 1%–24% by applying the diagnostic logic of the test cases to expose problems with the 

models; initial disagreement ranges for only the numerical models were narrower (up to 12%), 

and were similarly reduced to 0%–4% for the verified numerical-model results over the course of 

the project. 

With respect to the value of the test cases to software developers, one software developer/vendor 

participant made the following comment about this project: 

Without this IEA subtask for ground coupling, we would have had no means to check the 

results from our model, nor had a reason to make improvements to our model. There should be 

no question that the IEA subtask has improved the TRNSYS ground coupling model and, in 

doing so, has also provided energy modelers a greatly increased sense of confidence when 

modeling heat transfer to the ground.26

Closing Remarks 

The work presented in this report, other work of IEA SHC Task 34/ECBCS Annex 43, and the work that has 

preceded it in IEA SHC Tasks 8, 12, and 22 is important for two reasons: (1) the methods have been 

extremely successful at correcting software errors in advanced building energy simulation programs 

throughout the world; and (2) the methods are finding their way into industry by being adopted as the 

theoretical basis for formalized standard methods of test and software certification procedures; in this sense 

the work may be thought of as pre-normative research. 

xx 
Along with the overall validation methodology that has recently been added to the ASHRAE Handbook of 

Fundamentals,

2,3,4,8 the following test suites developed in conjunction with the IEA have been codelanguage adapted and formally approved as a standard method of test, ANSI/ASHRAE Standard 140-

2007:11

• IEA BESTEST, building thermal fabric comparative tests1

• HVAC BESTEST Volume 1, unitary cooling equipment analytical verification tests7

• HVAC BESTEST Volume 2, unitary cooling equipment comparative tests12

• HVAC BESTEST fuel-fired furnace analytical verification and comparative tests.13

The new in-depth slab-on-grade ground heat transfer test cases described in this report are also planned for 

inclusion in Standard 140. 

Standard 140 and the reports that comprise the test suites contained therein are being referenced and used 

by a growing number of code promulgation authorities worldwide. ASHRAE Standard 90.1,35,36 which is 

ASHRAE’s consensus energy code for commercial buildings and for non-low-rise residential buildings, 

requires that software used for demonstrating performance compliance with Standard 90.1 be tested using 

ASHRAE Standard 140-2004.10 Software used to calculate energy savings for the energy-efficient 

commercial building tax deductions in the United States must be tested with Standard 140-2007.37 As part 

of building energy performance assessments under the European Community’s Energy Performance 

Directive,38 several countries are using software tools that have been checked with BESTEST. Further 

details of international use of BESTEST, along with growing evidence that the BESTEST procedures are 

becoming part of software developers’ normal in-house quality control efforts, are included in Section 

2.6.2 of this report and elsewhere.4

Computer scientists universally accept the merits of software testing. A well-known rule of thumb is that 

in a typical programming project more than 50% of the total cost is expended in testing the program or 

system being developed.39 Of this, about 20% of development time goes toward system testing.40 Because 

new energy-related technologies are continually being introduced into the buildings market, there will 

always be a need to further develop simulation models, combined with a substantial program of testing and 

validation. Such an effort should contain all the elements of an overall validation methodology,4,8 including: 

• Analytical verification 

• Comparative testing and diagnostics 

• Empirical validation. 

Future work should therefore encompass: 

• Continued production of a standard set of analytical tests 

• Development of a set of diagnostic comparative tests that emphasize the modeling issues important 

in large commercial buildings, including more tests for heating, ventilating, and air-conditioning 

systems, and other mechanical equipment, including on-site power generation equipment 

• Development of a sequentially ordered series of high-quality data sets for empirical validation. 

Finally, the authors wish to acknowledge that the expertise available through the IEA and the dedication 

of the participants were essential to the success of this project. Over the 4-year field trial effort, there were 

several revisions to the BESTEST specifications and subsequent re-executions of the computer 

simulations. This iterative process led to the refining of the new BESTEST cases, and the results of the 

tests led to improving and debugging of the simulation models. The process underscores the leveraging of 

resources for the IEA countries participating in this project. Such extensive field trials, and resulting 

xxi 
enhancements to the tests, were much more cost effective with the participation of the IEA SHC Task 

34/Annex 43 experts. 

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Huang, Y.J.; Henninger, R.; Glazer, J.; Fisher, D.; Shirey, D.; Griffith, B.; Ellis, P.; Gu, L. (2004). 

“EnergyPlus: New Capable and Linked,” in Proceedings of the SimBuild 2004 Conference, August 2004, 

Boulder, Colorado, US: IBPSA-USA. 

24ISO 13370. (1998). Thermal Performance of Buildings – Heat Transfer via the Ground – Calculation 

Methods. European Committee for Standardization. Brussels, Belgium. 

xxiii 
25VABI Software BV. (2007). VA114, the Dutch Building Performance Simulation tool. Delft, The 

Netherlands. Initial development by TNO, further development, distribution, maintenance, and support by 

Vabi Software BV. 

26Thornton, J. (2007). Modeler Report for BESTEST Cases GC10a-GC80c, TRNSYS Version 16.1.

Madison Wisconsin, US: Thermal Energy System Specialists. Included with Section 2.9, Appendix II-A, 

of this final report. 

27Deru, M. (2003). A Model for Ground-Coupled Heat and Moisture Transfer from Buildings. NREL/TP550-33954. Golden, CO: National Renewable Energy Laboratory. www.nrel.gov/docs/fy03osti/33954.pdf 

28Nakhi, A. (2007). Modeler Report for BESTEST Cases GC10a-GC80c, FLUENT Version 6.0.20.

Kuwait, State of Kuwait: Public Authority for Applied Education and Training. Included with Section 

2.9, Appendix II-B, of this final report. 

29Fluent 6.3 User’s Guide. (2007). Lebanon, New Hampshire, US: Fluent Incorporated. 

30Crowley, M. (2007). Modeler Report for BESTEST Cases GC10a-GC80c, MATLAB 7.0.4.365 (R14) 

Service Pack 2. Dublin, Ireland: Dublin Institute of Technology. Included with Section 2.9, Appendix IIC, of this final report. 

31The MathWorks, Inc. (2007). Getting Started with MATLAB. Natick, Massachusetts, US: The MathWorks, 

Inc. 

32Deru, M.; Judkoff, R.; Neymark, J. (2003). Proposed IEA BESTEST Ground-Coupled Cases. Golden, 

CO: National Renewable Energy Laboratory. In conjunction with International Energy Agency, Solar 

Heating and Cooling Programme, Task 22. IEA Working Document. Draft, September 19, 2003. 

33Spitler, S.; Rees, S.; Xiao, D. (2001). Development of An Analytical Verification Test Suite for Whole 

Building Energy Simulation Programs – Building Fabric. Final Report for ASHRAE 1052-RP. Stillwater, 

OK: Oklahoma State University School of Mechanical and Aerospace Engineering. 

34Delsante A.E., A.N. Stokes, P.J. Walsh. (1983). Application of Fourier Transforms to Periodic Heat 

Flow into the Ground under a Building. International Journal of Heat Mass Transfer, 26(1): 121-132. 

35ANSI/ASHRAE/IESNA Standard 90.1-2007. (2007). Energy Standard for Buildings Except Low-Rise 

Residential Buildings. Atlanta, Georgia, US: American Society of Heating, Refrigerating and AirConditioning Engineers. References ANSI/ASHRAE Standard 140-2004. 

36ANSI/ASHRAE/IESNA Standard 90.1-2004, Addendum L, Energy Standard for Buildings Except LowRise Residential Buildings. (2005). Atlanta, Georgia, US: American Society of Heating, Refrigerating and 

Air-Conditioning Engineers. References ANSI/ASHRAE Standard 140-2004. 

37U.S. Internal Revenue Service. (2008). Amplification of Notice 2006-52, Deduction for Energy Efficient 

Commercial Buildings. IRS Notice 2008-40. Appears in Internal Revenue Bulletin (IRB) No. 2008-14, 

April 7, 2008. Washington, DC, US: U.S. Department of Treasury, Internal Revenue Service. 

38European Union. (2002). On the Energy Performance of Buildings. Directive 2002/91/EC of the 

European Parliament and of the Council, Official Journal of the European Communities, December. 

xxiv 
39Myers, G. (2004). The Art of Software Testing. Hoboken, New Jersey, US: John Wiley & Sons. See p. 

xiii. 

40McConnell, S. (2004). Code Complete: A Practical Handbook of Software Construction. Microsoft 

Press, p. 502. 

xxv 
Introduction 

A method of test for evaluating building energy simulation computer programs – International Energy 

Agency Building Energy Simulation Test and Diagnostic Method (IEA BESTEST) - was developed by the 

National Renewable Energy Laboratory (NREL) in collaboration with IEA SHC Task 12 and ECBCS 

Annex 21 (Judkoff and Neymark 1995a). During follow-on IEA SHC Task 22, preliminary test cases 

were developed to extend the capabilities of IEA BESTEST for testing detailed models of ground-coupled 

heat transfer with respect to various slab-on-grade and basement constructions. (Deru, Judkoff, and 

Neymark 2003). Results of the Task 22 project indicated substantial disagreements among detailed 

ground-coupled heat transfer models linked to whole-building energy simulation software, where the 

sources of such disagreements could not be readily determined. New work presented herein, which 

follows up Task 22, was conducted by NREL in collaboration with the participants of IEA SHC Task 34/ 

ECBCS Annex 43, Project A (Ground-Coupled Heat Transfer with respect to Floor Slab and Basement 

Constructions). The objective of Project A is to develop in-depth diagnostic test cases for ground-coupled 

heat transfer models that can identify the causes of differences in results found during the Task 22 work, 

so they can be corrected. 

Background 

As above-grade components of the building thermal fabric become more energy efficient, the heat 

transfer between the building and the ground becomes relatively more important. Ground-coupled heat 

transfer is a complex phenomenon that involves three-dimensional thermal conduction, moisture 

transport, long time constants, and the heat storage properties of the ground. To estimate the importance 

of ground-coupled heat transfer, we reviewed SERIRES/SUNCODE simulations for Colorado Springs 

Colorado (6415 HDD65) for the Home Energy Rating Systems (HERS) BESTEST (Judkoff and Neymark 

1995b) uninsulated and insulated slab-on-grade test cases. These HERS BESTEST cases use a singlestory house with typical roof and wall insulation characteristics, and specify slab-on-grade soil geometry 

and material property characteristics consistent with the ASHRAE perimeter method simplified ground 

heat transfer model (ASHRAE 2001; Wang 1979). SERIRES/SUNCODE simulation results for an 

uninsulated slab-on-grade, using two simplified ground heat transfer models, indicate that 41%–45% of 

building heating load is generated by heat transfer through the floor, depending on the model. These 

simulation results also indicate that the type of ground heat transfer model applied in the HERS 

BESTEST uninsulated slab-on-grade case causes a variation in the calculated floor heat flow of 25%, and 

variation in the overall building heating load of 13%. Similarly, for the HERS BESTEST insulated slab 

case SERIRES/SUNCODE indicates 25%–28% of heating load is caused by heat transfer through the 

floor. These simulation results further indicate that the type of simplified ground heat transfer model 

applied in the HERS BESTEST insulated slab case causes a variation in the calculated floor heat flow of 

26%, and variation in the overall building heating load of 12%. Simulations of the HERS-BESTEST 

house for five California (generally milder) climates indicate heat flow through an uninsulated slab-ongrade floor (with carpet) represents 17%–45% of annual heating loads and 4%–22% of peak-hour heating 

load, depending on climate and ground modeling technique (Neymark 2007). Furthermore, the range of 

disagreement of floor conduction heating loads varied 60%–300% for a given climate depending on the 

models. This is consistent with work by Beausoleil-Morrison (2006) who presented study results 

indicating a 40%–55% uninsulated slab-on-grade heat loss difference for ASHRAE’s simplified method 

versus more advanced methods. These estimates indicate a high degree of uncertainty, especially for 

simplified ground heat transfer models typically applied in building energy simulations. 

A brief history of ground heat transfer model development, evolution of the BESTEST ground-coupled 

heat transfer cases, and summary discussion of the new in-depth diagnostic cases for ground-coupled heat 

transfer related to slab-on-grade construction, are provided in the Executive Summary. 

xxvi 
Advantages of BESTEST Methodology

An advantage of the BESTEST methodology is that a program is examined over a broad range of 

parametric interactions based on a variety of output types. This minimizes the possibility that 

compensating errors will conceal problems. The tests resulted in quality improvements to all slab-ongrade heat transfer models and building energy simulation programs used in the field trials. Although the 

advancement of the state-of-the-art in ground heat transfer modeling is relatively recent, some of the bugs 

that were found may well have been present for several years. The fact that they have just now been 

uncovered shows the power of BESTEST and suggests the importance of continuing to develop 

formalized validation and diagnostic methods. Only after coding bugs have been eliminated can the 

assumptions and approximations in the algorithms be evaluated. 

Checking a building energy simulation program for the first time with the BESTEST in-depth slab-ongrade heat transfer cases requires about one person-week for an experienced simulation user, not 

including improvements to software if necessary. Subsequent program checks are faster because input 

files may be reused. Because the simulation programs have taken many years to produce, the new 

BESTEST cases provide a very cost-effective way of testing them. As we continue to develop new test 

cases, we will adhere to the principle of parsimony so the entire suite of BESTEST cases may be 

implemented by users with a reasonable time commitment. 

Software developers, architects, engineers, and researchers can use these new BESTEST cases to: 

 

• Compare output from building energy simulation programs to a set of analytical and quasianalytical solutions that constitute a reliable set of theoretical results given the underlying physical 

assumptions in the case definitions. 

• Compare several building energy simulation programs to determine the degree of disagreement 

among them. 

• Diagnose the algorithmic sources of prediction differences among several building energy 

simulation programs. 

• Compare predictions from other building energy simulation programs to the analytical solution, 

verified numerical-model results, and simulation results in this report. 

• Check a program against a previous version of itself after internal code modifications to ensure 

only the intended changes resulted. 

• Check a program against itself after a single algorithmic change to understand the sensitivity 

among algorithms. 

Other BESTEST Procedures 

As a BESTEST user, if you have not already tested your software with previously developed BESTEST 

procedures, we strongly recommend that you run all the building thermal fabric and mechanical 

equipment cases currently included in ANSI/ASHRAE Standard 140-2007. (ANSI/ASHRAE 2007; 

Judkoff and Neymark 1995a; Neymark and Judkoff 2002, 2004; Purdy and Beausoleil-Morrison 2003.) 

Another set of building thermal fabric test cases, which were designed to test simplified tools such as 

those currently used for home energy rating systems, is included in HERS BESTEST (Judkoff and 

Neymark 1995b; Judkoff and Neymark 1997). HERS BESTEST, which is being adapted for Standard 

140, has a more realistic base building than the IEA BESTEST building thermal fabric test cases that are 

currently included with Standard 140; however, its ability to diagnose sources of results differences is less 

robust (Neymark and Judkoff 1997). 

xxvii 
Report Structure 

This report is divided into three parts. Part I is a user’s manual that furnishes instructions on how to apply 

this BESTEST procedure. Part II describes the development, field-testing, and production of results data 

for the procedure. Part III presents the simulation program example results in tables and graphs along 

with disagreement statistics that compare the simulation programs to each other; these data can be used to 

compare results from other programs to Part III results. 

References for Introduction 

ANSI/ASHRAE Standard 140-2007. (2007). Standard Method of Test for the Evaluation of Building 

Energy Analysis Computer Programs. Atlanta, Georgia, US: American Society of Heating, Refrigerating 

and Air-Conditioning Engineers. 

ASHRAE. (2001). 2001 ASHRAE Handbook Fundamentals. Atlanta, Georgia, US: American Society of 

Heating, Refrigerating and Air-Conditioning Engineers. See pp. 28.12-13. 

Beausoleil-Morrison, I. (2006). “Heat Losses through Basement and Slab-On-Grade Foundations.” 

ASHRAE Annual Meeting, Seminar 45. June 24-28, 2006. Quebec City, Quebec, Canada. 

Deru, M.; Judkoff, R.; Neymark, J. (2003). Proposed IEA BESTEST Ground-Coupled Cases. Golden, 

CO: National Renewable Energy Laboratory. In conjunction with IEA SHC Programme, Task 22. IEA 

Working Document. Draft, September 19, 2003. 

Judkoff, R.; Neymark, J. (1995a). International Energy Agency Building Energy Simulation Test 

(BESTEST) and Diagnostic Method. Golden, Colorado, US: National Renewable Energy Laboratory, 

NREL/TP-472-6231, www.nrel.gov/docs/legosti/old/6231.pdf. 

 

Judkoff, R.; Neymark, J. (1995b). Home Energy Rating System Building Energy Simulation Test (HERS 

BESTEST). Golden, Colorado, US: National Renewable Energy Laboratory, NREL/TP-472-7332. 

Volume 1: Tier 1 and Tier 2 Tests User’s Manual, NREL/TP-472-7332a, 

www.nrel.gov/docs/legosti/fy96/7332a.pdf; 

Volume 2: Tier 1 and Tier 2 Tests Reference Results, NREL/TP-472-7332b, 

www.nrel.gov/docs/legosti/fy96/7332b.pdf. 

Judkoff, R.; Neymark, J. (1997). Home Energy Rating System Building Energy Simulation Test for 

Florida (Florida-HERS BESTEST). Golden, Colorado, US: National Renewable Energy Laboratory, 

NREL/TP-550-23124, www.nrel.gov/docs/legosti/fy97/23124a.pdf. 

Neymark J. (2007). Uncertainty in Ground Heat Transfer Based on Modeling Method and California 

Climate. Wheat Ridge, CO: J. Neymark & Associates. Draft. 

Neymark, J.; Judkoff, R. (1997). “A Comparative Validation Based Certification Test for Home Energy 

Rating System Software.” Proceedings of Building Simulation ’97. September 8–10, Prague, Czech 

Republic. International Building Performance Simulation Association. 

Neymark J.; Judkoff, R. (2002). International Energy Agency Building Energy Simulation Test and 

Diagnostic Method for Heating, Ventilating, and Air-Conditioning Equipment Models (HVAC BESTEST), 

Volume 1: Cases E100–E200. NREL/TP-550-30152. Golden, Colorado, US: National Renewable Energy 

Laboratory. www.nrel.gov/docs/fy02osti/30152.pdf. 

xxviii 
Neymark, J.; Judkoff, R. (2004). International Energy Agency Building Energy Simulation Test and 

Diagnostic Method for Heating, Ventilating, and Air-Conditioning Equipment Models (HVAC BESTEST), 

Vol. 2: Cases E300-E545. Golden, Colorado, US: National Renewable Energy Laboratory, NREL/TP550-36754, www.nrel.gov/docs/fy05osti/36754.pdf. 

Purdy, J.; Beausoleil-Morrison, I. (2003). Building Energy Simulation Test and Diagnostic Method for 

Heating, Ventilating, and Air-Conditioning Equipment Models (HVAC BESTEST): Fuel-Fired Furnace 

Test Cases. Ottawa, Canada: Natural Resources Canada, CANMET Energy Technology Centre. www.ieashc.org/task22/deliverables.htm. 

Wang, F.S. (1979). “Mathematical Modeling and Computer Simulation of Insulation Systems in Below 

Grade Applications.” ASHRAE/DOE Conference on Thermal Performance of the Exterior Envelopes of 

Buildings. December 3-5, 1979, Kissimmee, FL. 

xxix 
1 

1.0 Part I: BESTEST User’s Manual: Procedure and Specification 

Cases GC10a – GC80c 

1.1 General Description of the Test Cases 

Seventeen test cases are summarized in Tables 1-1 and 1-2. The test cases are designed to use the results 

of verified detailed numerical ground-coupled heat transfer models as a secondary mathematical truth 

standard for comparing the results of simplified and mid-level detailed ground-coupled heat transfer 

models typically used with whole-building energy simulation software. The new test cases use an 

idealized uninsulated slab-in-grade configuration. This simplified configuration is required by the 

analytical solution of Case GC10a, is appropriate for developing robust ground-coupling test cases, is 

compatible with all of the programs run in field trials of the test procedure, and facilitated development of 

accurate model results by minimizing chances for input errors. Parametric variations versus a steady-state 

base case (Case GC30b) include periodic ground surface temperature variation, floor slab aspect ratio, 

slab area, deep ground temperature depth (water table depth), slab and ground thermal conductivity, and 

slab-interior and ground-exterior surface heat transfer coefficients (realistic versus high values to test the 

effect of surface temperature uniformity). The cases use both steady-state and harmonic boundary 

conditions applied with artificially constructed annual weather data, along with an adiabatic above-grade 

building envelope to isolate the effects of ground-coupled heat transfer. Because the zone-heating load is 

driven exclusively by the slab heat losses, it is equal to the slab conduction heat loss. This is convenient 

for testing programs that may not readily disaggregate floor conduction losses in their output. Various 

output values – including steady-state, annual total steady-periodic, and annual peak hour steady-periodic 

results for floor conduction and zone heating load, along with time of occurrence of peak-hour loads and 

other supporting output – are compared and used in conjunction with a formal diagnostic method to 

determine algorithms responsible for predictive differences. The test cases are divided into three 

categories: 

• “a”-series cases are for the most detailed numerical-methods programs (e.g., three-dimensional 

[3-D] numerical models that have been developed for whole-building energy simulation programs 

such as TRNSYS and SUNREL-GC, and similarly detailed models developed using FLUENT 

and MATLAB); the intent of these cases is to demonstrate that the numerical models have been 

properly applied. 

• “b”-series cases are for more constrained models used in whole-building simulation programs 

(e.g. EnergyPlus and the ISO 13370 calculation method), allowing comparison with the more 

detailed/flexible models. 

• “c”-series cases apply boundary conditions that are compatible with BASESIMP, allowing 

comparison of BASESIMP with the other models. 

A preliminary analytical verification case (Case GC10a) is included for comparing detailed 3-D 

numerical models to a 3-D steady-state analytical solution (Delsante, Stokes, and Walsh 1983) that 

incorporates boundary conditions that may be difficult to model in the context of a whole-building 

simulation. Case GC10a provides an analytical solution reference result for checking detailed numerical 

models for overall correctness and proper application in this context. 

The test specification is structured such that the “b”-series cases, which are likely to be possible for more 

programs than the “a”- or “c”-series cases, are presented first. The “a”- and “c”-series cases, which are 

derived from the “b”-series cases, are presented in later sections. If the program being tested can run the 

“a”-series cases as they are described, run the “a”-series cases before running any of the other cases. 
Table 1-1. Ground Coupling In-Depth Diagnostic “a”-Series and “b”-Series Cases 

Slab Ground Far-Field

Dimen. h,int h,ext Depth Boundb Cond.

Case Description/Test Dynamic (m x m) (W/m2K) (W/m2K) (m) (m) (W/mK) Comments

Analytical Verification TestsGC10a Analytical Base Case steady state 12 x 12 const Ta const Ta infinite infinite 1.9 Analytical verification of detailed numerical-m

Original Delsante et al. (1983) set up of node meshing and boundary co

Boundary Conditions: constant temperature 

Rectangular floor slab, (To) surfaces; linear dT across slab perime steady-state, 3-d conduction Other Inputs: 24 cm perimeter boundary wid

 suppress all other modes of heat transfer.

Comparative TestsGC30a Comparative Base Case steady state 12 x 12 const Ta const Ta 30 20 1.9 Boundary Conditions: slab perimeter surface 

for "a"-series GC30a-GC10a tests adiabatic versus linear 

GC30b Comparative Base Case steady state 12 x 12 100 100 15 15 1.9 Most robust version of GC30a possible for E

 for "b"-series Inputs: To,a = 10°C, Ti,a = 30°C.

GC30b-GC30a tests h = 100 versus direct Tc 

GC40a Harmonic Variation harmonic 12 x 12 direct Ta direct Ta 30 20 1.9 Annual "harmonic" variation of To or To,a: m

GC40 tests phase shift of varying q versus va

GC40b Harmonic Variation harmonic 12 x 12 100 100 15 15 1.9 GC40-GC30 tests annual mean q for varying GC45b Aspect Ratio (AR) harmonic 36 x 4 100 100 15 15 1.9 GC45b-GC40b tests aspect ratio, high perimGC50b Large Slab harmonic 80 x 80 100 100 15 15 1.9 GC50b-GC40b tests large slab, high core heGC55b Shallow Deep Ground Temp. harmonic 12 x 12 100 100 2 15 1.9 GC55b-GC40b tests shallow deep ground te

 transfer fraction

GC60b h,int steady state 12 x 12 7.95 100 15 15 1.9 GC60b-GC30b tests h,int and resulting floor GC65b h,int and h,ext steady state 12 x 12 7.95 11.95 15 15 1.9 GC65b-GC60b tests h,ext and resulting grou

GC65b-GC30b tests combined effects of h,in

GC70b Harmonic h,int and h,ext harmonic 12 x 12 7.95 11.95 15 15 1.9 GC70b-GC40b tests combined effects of h,in

GC70b-GC65b tests annual mean q for vary

GC80b Ground Conductivity harmonic 12 x 12 100 100 15 15 0.5 GC80b-GC40b tests ground conductivityAbbreviations: "direct T" = direct input temperature (varies hourly) "Temp." = temperature "b.c." = boundary condition "dT" = temperature variation "Ti" = slab interior surface temperature

 "Cond." = slab & soil conductivity "h,ext" = exterior surface convective coefficient "Ti,a" = zone air temperature

 "const T" = direct input constant temperature "h,int" = interior surface convective coefficient "To" = exterior ground surface temperature "Dimen." = dimension "q" = heat flow through floor slab "To,a" = outdoor dry-bulb temperatureNotes: a For models that require air temperature inputs (i.e., that do not allow direct input of surface temperatures), convective surface coefficients are effectively 

b Distance from slab edge.c GC30c-GC30a also includes minor difference in amount of soil modeled.

2 
3 

Cas

Slab Ground Far-Field

Dimen. h,int h,ext Depth Boundb Cond.

e Description/Test Dynamic (m x m) (W/m2K) (W/m2K) (m) (m) (W/mK) Comments

c Comparative Base Case steady state 12 x 12 7.95 const Ta 15 8 1.9 Most robust version of GC30 that can be don

 for "c"-series Inputs: To = 10°C, Ti,a = 30°C.

GC30c-GC30a tests reduced h,int = versus d

c Harmonic Variation harmonic 12 x 12 7.95 direct Ta 15 8 1.9 GC40c tests phase shift of varying q versus v

GC40c-GC30c tests annual mean q for varyi

c Aspect Ratio (AR) harmonic 36 x 4 7.95 direct Ta 15 8 1.9 GC45c-GC40c tests aspect ratio, high perimc Shallow Deep Ground Temp. harmonic 12 x 12 7.95 direct Ta 5 8 1.9 GC55c-GC40c tests shallow deep ground te

 transfer fraction

c Ground Conductivity harmonic 12 x 12 7.95 direct Ta 15 8 0.85 GC80c-GC40c tests ground conductivity

"Cond." = slab and soil conductivity "h,ext" = exterior surface convective coefficient "Ti,a" = zone air temperature"const T" = direct input constant temperature "h,int" = interior surface convective coefficient "To" = exterior ground surface temperature"Dimen." = dimension "q" = heat flow through floor slab"direct T" = direct input temperature (varies hourly) "Temp." = temperature

s: a For models that require air temperature inputs (which do not allow direct input of surface temperatures), convective surface coefficients are effectively i

b Distance from slab edge.c GC30c-GC30a also includes minor difference in amount of soil modeled.

GC30GC40GC45GC55GC80Abbreviations:Note

Table 1-2. Ground Coupling In-Depth Diagnostic “c”-Series Cases
1.1.1 Accompanying Electronic Files 

The files described below are included in the .zip file link on the cover page of the posted electronic 

version of this document; click on “Link to Required Zipped Data Files (6 MB).” 

1.1.1.1 Weather Data Files 

The following TMY2-format weather data files are included with the accompanying electronic media: 

GCSS-W40.TM2, GCSS-W20.TM2, GCSS-W01.TM2, GCSP-W40.TM2, GCSP-W20.TM2, 

GCSP-W01.TM2. 

A summary of site and weather parameters is given in Table 1-3. These apply to the test cases as follows: 

Case Weather Data Case Weather Data 

GC10a none GC65b GCSS-W01.TM2 

GC30a GCSS-W40.TM2 GC70b GCSP-W01.TM2 

GC30b GCSS-W20.TM2 GC80b GCSP-W20.TM2 

GC40a GCSP-W40.TM2 GC30c GCSS-W40.TM2 

GC40b GCSP-W20.TM2 GC40c GCSP-W40.TM2 

GC45b GCSP-W20.TM2 GC45c GCSP-W40.TM2 

GC50b GCSP-W20.TM2 GC55c GCSP-W40.TM2 

GC55b GCSP-W20.TM2 GC80c GCSP-W40.TM2 

GC60b GCSS-W20.TM2 

Table 1-3. Site and Weather Summary for Ground-Coupled Heat Transfer Tests—TMY2 Data 

Weather Type Artificial Conditions 

Weather Format TMY2 

Latitude 25.8° North 

Longitude (local site) 80.3° West 

Altitude 2 m (6.6 ft) 

Time Zone (Standard Meridian Longitude) 5 (75° West) 

Site Flat, unobstructed, located 

exactly at weather station 

Dew Point Temperature (constant) -56.6°C (-69.9°F) 

Humidity Ratio (constant) 0.000007 kg moisture/kg dry air 

(0.000007 lb moisture/lb dry air) 

Global Horizontal Solar Radiation Annual Total 0 MJ/m2 (0 kBtu/ft2) 

Direct Normal Solar Radiation Annual Total 0 MJ/m2 (0 kBtu/ft2) 

Diffuse Horizontal Solar Radiation Annual Total 0 MJ/m2 (0 kBtu/ft2) 

Quantities That Vary 

between Data Sets 

Mean Ambient DryBulb Temperature Mean Ambient 

Relative Humidity 

Constant Annual Wind Speed 

GCSS-W40.TM2 10°C (50.0°F), 

constant 

0.09%, constant 40.0 m/s (89.48 miles/h) 

GCSS-W20.TM2 10°C (50.0°F), 

constant 

0.09%, constant 19.9 m/s (44.52 miles/h) 

GCSS-W01.TM2 10°C (50.0°F), 

constant 

0.09%, constant 1.0 m/s (2.24 miles/h) 

GCSP-W40.TM2 10°C (50.0°F), 

harmonically varying 

0.09%, harmonically 

varying 

40.0 m/s (89.48 miles/h) 

GCSP-W20.TM2 10°C (50.0°F), 

harmonically varying 

0.09%, harmonically 

varying 

19.9 m/s (44.52 miles/h) 

GCSP-W01.TM2 10°C (50.0°F), 

harmonically varying 

0.09%, harmonically 

varying 

1.0 m/s (2.24 miles/h) 

4 
1.1.1.2 Other Accompanying Electronic Files 

For reporting output use the following file provided with the accompanying electronic media: 

GC-InDepth-Output.XLS. 

1.2 Performing the Tests 

1.2.1 Modeling Rules 

1.2.1.1 Consistent Modeling Methods 

If a simulation program has options for modeling a specific thermal behavior, consistent modeling methods 

shall be used for all cases. For example, if the program being tested gives the user a choice of methods for 

modeling floor slabs, the same floor slab modeling method shall be used for all cases. To generate the 

example results, the IEA SHC Task 34/ECBCS Annex 43 (IEA 34/43) participants used the most detailed 

level of modeling that was allowed by their simulation programs and that was consistent with the level of 

detail provided in this test specification; more discussion about this is included in Part II (Section 2.2). 

When a program has options for modeling this specification, these were discussed in the IEA 34/43 

participant modeler reports included in Part II (Section 2.9). 

1.2.1.2 Equivalent Modeling Methods 

If a program or specific model within a program does not allow direct input of specified values, or if input 

of specified values causes instabilities in a program’s calculations, modelers should develop equivalent 

inputs that match the intent of the test specification as nearly as the software being tested allows. Such 

equivalent inputs shall be developed based on the data provided in the test specification, shall have a 

mathematical, physical, or logical basis, and shall be applied consistently throughout the test cases.

Document the equivalent modeling method in the modeler report for the tested program. 

1.2.1.3 Nonapplicable Inputs 

Some specifications include input values that do not apply to the input structure of the program being tested. 

When nonapplicable input values are found, either use approximation methods suggested in the user’s 

manual of the program being tested, or disregard the nonapplicable inputs and continue. Such inputs are in 

the specification for programs that may need them. 

1.2.1.4 Time Convention 

References to time in this specification are to local standard time. Assume that hour 1 = 0:00–1:00 (the 

interval from midnight to 1:00 A.M.). Do not use daylight saving time or holidays for scheduling. The 

required typical meteorological year 2 (TMY2) data are in hourly bins corresponding to standard time, 

consistent with all other schedules. 

1.2.1.5 Geometry Convention 

If the program being tested includes the thickness of walls in a 3-D definition of the building geometry, the 

wall, roof, and floor thicknesses should be defined such that the interior air volume of each zone remains as 

specified (e.g., 12 m × 12 m × 2.7 m = 388.8 m3

). 

5 
1.2.1.6 Simulation Preconditioning 

If the program being tested allows for preconditioning (iterative simulation of an initial time period until 

temperatures or fluxes, or both, stabilize at initial values), use that capability. 

1.2.1.7 Simulation Duration 

Use the weather data provided to run the full annual simulation; some models may need to run for a 

number of years to satisfy the requirements of specific test cases. Give outputs as required per the test 

case descriptions. 

1.2.1.8 Simulation Input Files 

All supporting data required for generating results with the tested software shall be saved, including: 

• Input files 

• Processed weather data 

• Intermediate files containing calculations used for developing inputs 

• A “Readme-softwarename-yymmdd.pdf” file that briefly describes the contents of the files 

according to their file type (their “.xyz” file extension). 

1.2.1.9 Omitted Test Cases 

If a program being tested omits a test case, provide an explanation in the modeler report. 

1.2.1.10 Modeler Reports 

The IEA-34/43 participants submitted modeler reports along with their simulation results (see Part II, 

Section 2.9). Users developing modeler reports may consider using the structure of any of those modeler 

reports as a template. 

1.2.2 Comparing Your Output to the Analytical Solution, Verified Numerical-Model 

Results, and Other Example Simulation Results 

 

For detailed numerical models that can do Case GC10a, output should be compared with the Case GC10a 

analytical solution. For all cases that the program being tested can do, output may also be compared with the 

verified numerical-model results and other example simulation results provided in Part III, or with other 

results that were generated using this test procedure. 

1.2.2.1 Criteria for Determining Agreement between Results 

There are no formal criteria for when results agree or disagree. Determination of when results agree or 

disagree is left to the user. In making this determination the user should consider: 

 

• Magnitude of results for individual cases 

• Magnitude of difference in results between certain cases (e.g., Case GC45b–Case GC40b) 

• Same direction of sensitivity (positive or negative) for differences in results between certain cases 

(e.g., Case GC45b–Case GC40b) 

• If results are logically counterintuitive with respect to known or expected physical behavior 

6 
• Availability of analytical or verified numerical-model results (mathematical truth standard or 

secondary mathematical truth standard as described in Sections 2.5.1 and 2.5.2) 

• If a mathematical or secondary mathematical truth standard is provided, the degree of 

disagreement that occurred for other simulation results versus such an analytical verification truth 

standard 

• Example simulation results – other than the verified numerical-model results – do not represent a 

truth standard. 

For any given case, a tested program may fall outside the range of example results without necessarily 

being incorrect. However, it is worthwhile to investigate the source of significant differences, as the 

collective experience of the authors of this test procedure is that such differences often indicate problems 

with the software or its usage, including, but not limited to: 

• User input error, where the user misinterpreted or incorrectly entered one or more program inputs 

• A problem with a particular algorithm in the program 

• One or more program algorithms used outside their intended range. 

Also, for any given case, a program that yields values in the middle of the range established by the 

example results should not be perceived as better or worse than a program that yields values at the borders 

of the range. 

1.2.2.2 Diagnostic Logic for Determining Causes of Differences among Results 

To help you identify which algorithm in the tested program is causing specific differences between 

programs, we have included diagnostic flow charts in Appendix F. 

1.2.2.3 Rules for Modifying Simulation Programs or Simulation Inputs 

Modifications to simulation programs or simulation inputs shall have a mathematical, physical, or logical 

basis, and shall be applied consistently across tests. Such improvements must be documented in modeler 

reports. Arbitrary modification of a simulation program’s input or internal code to more closely match a 

given set of results shall not be allowed. 

1.3 Test Case Specifications 

1.3.1 “b”-Series Cases 

1.3.1.1 Case GC30b – Steady-State Comparative Test Base Case 

1.3.1.1.1 Objective. Compare steady-state heat flow results from whole-building simulation programs to 

the verified numerical-model results (secondary mathematical truth standard). 

1.3.1.1.2 Method. This case drives floor conduction based on the temperature difference between zone air 

and ambient air (and deep ground boundary condition) using an adiabatic zone except for the floor, with 

an adiabatic wall/ground interface boundary (see Figure 1-1), and interior and exterior air temperatures 

with high convective surface coefficients. High convective surface coefficients facilitate robust floor 

conduction, and establish somewhat uniform temperatures for the interior slab surface and exterior ground 

surfaces. Soil and far-field boundary conditions are also described. These boundary conditions are 

allowed by more whole-building simulation programs than those of Case GC10a or Case GC30a. Hourly 

7 
TMY2-format weather data with constant ambient temperature are provided. Comparison of GC30b 

versus GC30a (GC30b–GC30a) checks the sensitivity to high convective surface coefficients versus 

direct-input constant and uniform surface temperature boundary conditions. Note: Previous sensitivity 

tests of 60 m ground depth (40 m far field) versus 15 m deep ground boundary depth (15 m far field) 

indicate a 1% effect for the given slab geometry, so the effect of decreased boundary depth between the 

“b”- and “a”-series cases should be smaller than that of varying the surface boundary condition. 

1.3.1.1.3.1 Geometry and General Description. Geometry and location of boundary conditions are 

described in Figures 1-1 and 1-2. Interior edges of zone walls begin at the edges of the surface defined by 

the area B × L in Figure 1-2. The slab edge detail is described in Figure 1-3. Parameters related to these 

figures and other input parameters are described in Table 1-4 and the accompanying text (following 

sections). 

Assumptions and boundary conditions are applied as described in the following sections; any variations 

from the given specifications are to be noted in the modeler’s report. 

F

Soil

E

Tdg

q = 0 q = 0

To,a

h,ext

q = 0 Conditioned 

Zone

Ti,a h,int

Floor Slab

Elevation Section

Figure 1-1. Case GC30b conceptual schematic diagram including boundary conditions 

 and soil dimensions 

8 

1.3.1.1.3 Input Specification. The bulk of the work for implementing the test cases is assembling an 

accurate base case model. Thoroughly checking the Case GC30b inputs before going on to the other cases 

is recommended. 
B = 12 m

W = 0.24 m

Adiabatic 

Walls

North

Conditioned 

Zone

L = 12 m

Floor Slab

Not to 

Scale

W = 0.24 m

Plan View

Adiabatic Walls

h,ext h,ext

0.24 m

h,int

12 m 2.7 m

Floor Slab

Elevation Section

Figure 1-2. Case GC30b floor slab and conditioned zone adiabatic wall dimensions

9 
Figure 1-3. Case GC30b slab edge detail 

Table 1-4. Input parameters 

Test parameters SI Units IP Units 

Slab length (L) 12 m 39.37 ft 

Slab width (B) 12 m 39.37 ft 

Wall thickness (W) 0.24 m 0.7874 ft 

Inside zone air temperature (Ti,a) 30°C 86°F 

Outside air temperature (To,a) 10°C 50°F 

Deep ground temperature (Tdg) 10°C 50°F 

Deep ground boundary depth (E) 15 m 49.21 ft 

Far field boundary distance (F) 15 m 49.21 ft 

1.3.1.1.3.2 Soil and Slab Thermal Properties and Boundary Conditions 

• For these test cases, the soil and floor slab properties are constant and equal to: 

Thermal conductivity = 1.9 W/(m⋅K) (1.098 Btu/(h⋅ft⋅°F)) 

Density = 1490 kg/m3 (93.125 lb/ft3

) 

Specific heat = 1800 J/(kg⋅K) (0.4302 Btu/(lb⋅°F)). 

• Initially (time < 0) the ground and slab are at 10°C (50°F) throughout; at the beginning of the 

simulation (time = 0) the zone air temperature steps to 30°C (86°F) and slab and soil temperatures 

begin to change accordingly. 

Grade

Above Grade Wall 

(UA = 0)

Foundation Wall

Soil

(no scale)

0.24 m

Slab In Grade

(slab has same properties 

as soil; slab thickness as 

thin as the model being 

tested allows for stable 

calculation)

(foundation wall has same 

properties as soil; belowgrade wall dimensions as 

small as the model being 

tested allows for stable 

calculation)

10 
• No surface radiation exchange; one possible method to disable radiation exchange is to set 

exterior solar absorptances and infrared emittances to 0, or as low as the program being tested 

allows (e.g., 0.000001). 

• The ground is not shaded except by the building (if the program accounts for this); shading and 

orientation are not relevant with radiative exchange disabled. 

• The ground surface is assumed to be uniform and flat. 

• Interior floor slab and outside ground surfaces are level with each other. 

• For models requiring input of slab thickness, use the least thickness that the software allows for a 

stable calculation. 

• For models requiring input for below-grade foundation walls, use the same thermal properties as 

soil, with foundation wall dimensions as small as the model being tested allows for a stable 

calculation. 

• Deep ground temperature is constant and uniform at the given depth. 

• Far-field ground conditions are adiabatic for vertical planes penetrating the ground at the given 

far-field distance from the surface. 

• Ambient air temperature is uniform (well mixed air). 

• If the program being tested can model evapotranspiration, it should be turned off or reduced to its 

lowest level. 

1.3.1.1.3.3 Above-Grade Construction 

• Building height = 2.7 m (8.858 ft). 

• Zone air volume = 388.8 m3

 (13730 ft3). 

• All surfaces of the zone except the floor are adiabatic (thermal conductance = 0 W/(m2

⋅K)). If the 

program being tested does not allow adiabatic surfaces, use the lowest thermal conductance the 

program allows (e.g., 0.000001 W/(m2

⋅K)) and document those values in your modeler report. 

• All surfaces except the floor are massless. If the program being tested does not allow massless 

surfaces, use the lowest density or thermal capacitance, or both, that the program allows (e.g., 

0.000001 kg/m3

 or J/(kg⋅K), or both) and document those values in your modeler report. 

• The adiabatic walls contact, but do not penetrate, the ground. Heat may flow within the ground 

just below the adiabatic walls; heat cannot flow from the ground into the adiabatic walls (or out 

of the adiabatic walls into the ground). 

• No surface radiation exchange occurs. One possible method to disable radiation exchange is to set 

interior and exterior solar absorptances and infrared emittances to 0, or as low as the program 

being tested allows (e.g., 0.000001). 

• No windows. 

• No infiltration or ventilation. 

• No internal gains. 

1.3.1.1.3.4 Convective Surface Coefficients 

• Interior convective surface coefficients (h,int) = 100 W/(m2

⋅K) (17.61 Btu/(h⋅ft2⋅°F)) 

• Exterior convective surface coefficients (h,ext) = 100 W/(m2

⋅K) (17.61 Btu/(h⋅ft2⋅°F)). 

These values apply to surface coefficients for the floor, adiabatic surfaces, and exterior ground surface as 

appropriate. If the program being tested cannot model these convective surface coefficients, use the 

largest value the program allows. Document values for convective surface coefficients in your modeler 

report. 

11 
If the program being tested allows direct user input of convective surface coefficients and surface infrared 

(IR) emittances, ignore the remainder of this paragraph. If the program being tested allows only direct 

user input of combined surface coefficients, set that value to 100 W/(m2

⋅K) (17.61 Btu/(h⋅ft2⋅°F)). If the 

program being tested does not allow direct user input of convective surface coefficients or combined 

surface coefficients, input a value for IR emittance such that an equivalent value for combined surface 

coefficient of 100 W/(m2

⋅K) is obtained, or nearly obtained if possible (based on the convective surface 

coefficient that the program being tested automatically calculates). Discuss in your modeler report any 

deviation from the specified convective surface coefficient.

1.3.1.1.3.5 Mechanical System. The mechanical system provides sensible heating only (no cooling), and 

is ideal. The purpose of the heating system is to give results for energy consumption that are equal to the 

sensible heating load. Model the heating system as closely as the program being tested allows, as follows: 

• Set points 

o Heat = ON if temperature < 30°C (86°F); otherwise Heat = OFF 

o Cool = always OFF. 

• Set the heating system capacity as needed so there is at least enough capacity to maintain the zone 

air temperature set point; for example, 1000 kW (3412 kBtu/h). 

• Uniform zone air temperature (well mixed air). 

• 100% efficiency. 

• 100% convective air system. 

• Ideal controls (zone always at set point); for example, assume the heat addition rate equals the 

equipment capacity (non-proportional control) and there is continuous ON/OFF cycling within 

the hour as needed. 

• Thermostat sensing the zone air temperature only. 

1.3.1.1.3.6 Weather Data. Use constant temperature TMY2-format weather data provided with the file:

GCSS-W20.TM2 

TMY2 weather data format is described in Appendix A. Table 1-3 (see Section 1.1.1.1) provides a 

summary of site and weather data parameters. This weather data file is based on Miami.TM2, but includes 

many data elements set to: 0 or approximate lower limits, approximate higher limits, or neutral (nonextreme) constant values. A description follows: 

• Global horizontal, direct normal, and diffuse horizontal radiation and illuminance all set to 0. 

• Extraterrestrial horizontal and direct normal radiation were left unchanged from the original 

weather data file. 

• Total and opaque sky cover = 10 tenths, implying the entire sky dome is covered by clouds to 

reduce exterior IR radiation exchange. 

• Outdoor dry-bulb temperature (To,a) = 10°C (50°F). 

• Outdoor dew-point temperature = -56.6°C (-69.9°F) (corresponds with humidity ratio of 

0.000007 kg/kg and standard atmospheric pressure); calculation of dew-point temperature applies 

common psychrometric formulae (ASHRAE 2001 [Chapter 6]; Brandemuehl 1993). TMY2 

documentation indicates that -60°C is the lower limit for TMY2 data. 

• Relative humidity = 0.09% (corresponds with humidity ratio of 0.000007 kg/kg, standard 

atmospheric pressure, and given dry-bulb temperature); calculations apply common 

psychrometric formulae (ASHRAE 2001 [Chapter 6]; Brandemuehl 1993). This value rounds to 

0% in the weather data. 

• Atmospheric pressure = 1013 millibars (= standard atmosphere of 14.696 psia). 

12 
• Wind speed = 19.9 m/s (44.52 miles/h). Extrapolating (see ASHRAE 2005 Handbook of 

Fundamentals, p. 25.1) equations described by Walton (1983) and assuming a rough surface, this 

may correspond with combined radiative/convective h,ext = 104.47 W/(m2

⋅K). Subtracting out 

the equivalent radiative portion of the combined coefficient of 4.63 W/(m2

⋅K) based on IEA 

BESTEST (Judkoff and Neymark 1995), Appendix D, yields convective only h,ext = 99.84 

W/(m2

⋅K) (rounds to 100 W/(m2⋅K)). 

• Visibility = 20 km (rough annual average for Miami and Denver). 

• Ceiling height = 2000 m (rough annual average for Miami and Denver). 

• Present weather: no rain, hail, etc. 

• Precipitable water = 0 mm. 

• Aerosol optical depth = 0.1 broadband turbidity (rough annual average of Miami and Denver) 

• Snow depth = 0 cm, with ≥ 88 days since last snowfall. 

1.3.1.1.4 Output Requirements. If possible for the software being tested, the simulation should be run 

long enough that there is ≤ 0.1% variation between the floor slab conduction for the last hour of the last 

year of the simulation and the last hour of the preceding year of the simulation; i.e., ≤ 0.1% variation over 

an interval of 8760 hours. 

If a numerical model is being tested that allows variation of thermal node meshing, it is recommended to 

demonstrate for a subset of the steady-state and steady-periodic cases (e.g., GC30b, GC40b, and others if 

desired) that the tested mesh detail yields negligible (≤ 0.1%) change in results versus a less detailed 

mesh, or that the mesh is as detailed as possible for the available computing hardware. 

If the software being tested allows user specification of convergence tolerance, it is recommended to 

demonstrate for a subset of the steady-state and steady-periodic cases (e.g., GC30b, GC40b) that the 

current level of heat-flow or temperature convergence tolerance yields negligible (≤ 0.1%) change in 

results versus the next finer convergence tolerance. 

Provide the following outputs for the last hour of the simulation: 

• Conduction through the floor slab (qfloor) in W or Wh/h; this is specifically conduction through the 

interior surface of the slab defined by dimensions B × L in Figure 1-2. 

• Zone load (qzone) in W or Wh/h; this output should only vary from floor slab conduction if the 

program being tested does not allow fully adiabatic above-grade walls; if the program being 

tested (particularly for models run independently of whole-building simulations) does not have 

different outputs for zone load and floor conduction, report the output where it is most 

appropriate and leave the other output blank (e.g., report the results only as floor conduction, and 

do not report any zone load results). 

• Zone air temperature (Tzone) (°C); this output checks the temperature that results from the given 

thermostat set point. 

• “Steady state” near-surface temperatures (Tsurf,n) (°C) as described in Table 1-5 and Figure 1-4; 

for defining coordinates the center of the floor slab is designated as “(0,0)” as shown in Figure 1-

4; Figure 1-4 represents a single quadrant of the symmetric slab/perimeter-boundary/exterior 

surfaces. Provide temperatures (at consistent depth) for the uppermost-modeled layer of soil just 

below the ground. 

Provide the following other outputs: 

• Duration of simulation (tsim) in hours. This is the number of hours simulated; e.g., if 10 years are 

simulated, indicate 87600 hours. 

13 
Table 1-5. x and y Coordinates of Near-Surface Temperature Outputs 

Location,n y (cm) x (cm) Tsurf,n (°C)

1 0 0

2 0 433

3 0 554

4 0 587

5 0 596

6 0 600

7 0 602

8 0 605

9 0 612

10 0 619

11 0 622

12 0 624

13 0 628

14 0 640

15 0 687

16 0 876

17 0 1628

18 0 4624

Location,n y (cm) x (cm) Tsurf,n (°C)

1 0 0

19 433 433

20 554 554

21 587 587

22 596 596

23 600 600

24 602 602

25 605 605

26 612 612

27 619 619

28 622 622

29 624 624

30 628 628

31 640 640

32 687 687

33 876 876

34 1628 1628

35 4624 4624

14 
Not to 

Scale

x

y

Center (0,0)

Slab

Perimeter 

Boundary Exterior Ground 

Surface

Figure 1-4. Conceptual plan view of near-surface temperature outputs 

1.3.1.2 Case GC40b – Harmonic Variation of Ambient Temperature 

1.3.1.2.1 Objective. Compare heat flow results for approximate steady-periodic (harmonic) variation of 

ambient temperature (To,a) from whole-building simulation programs versus verified numerical-model 

results. Analyze the phase shift between variation of heat flow and ambient air temperature. 

1.3.1.2.2 Method. This case is similar to Case GC30b but uses harmonically varying To,a. Hourly TMY2 

format weather data are provided for approximating a sinusoidal annual cycle of varying daily average 

temperatures with a sinusoidal diurnal temperature cycle overlaid (a high frequency cycle overlaid on a 

low frequency cycle). Comparing GC40b with GC30b (GC40b–GC30b) annual hourly average floor 

conduction checks the sensitivity of average floor heat loss of the harmonic condition versus the steadystate condition. 

1.3.1.2.3 Input Specification. This case is exactly as Case GC30b except for the following changes: 

1. Use weather data provided with the file GCSP-W20.TM2. 

GCSP-W20.TM2 is the same as GCSS-W20.TM2 except harmonically varying outdoor air 

temperatures are approximated. In this file atmospheric pressure and dew-point temperature were 

set to constant values, and relative humidity was adjusted to be consistent with other listed values 

using common psychrometric formulae. (ASHRAE 2001 [Chapter 6]; Brandemuehl 1993). 

TMY2 weather data format is described in Appendix A. Table 1-3 (see Section 1.1.1.1) provides 

a summary of site and weather data parameters. 

15 
In these weather data To,a varies hourly according to the following formula: 

To,a = Tday – Tswingday*(cos((IHOUR-ILOWHOUR)/24*2*PI)) 

where 

Tday = Tmean – Tswingseason*(cos((IDAY-ILOWDAY)/365*2* PI)) 

where: 

• Tswingday is diurnal temperature swing (±), = 2°C, for 4°C diurnal range from minimum 

to maximum 

• IHOUR is the daily hour counter, from 1 to 24 with reset to 1 after end of day 

• ILOWHOUR is hour of lowest temperature, = 4, for 4th hour 

• PI = 3.1415927 (≈ π); cosine function uses radians 

• Tmean = annual mean temperature, = 10°C 

• Tswingseason is seasonal temperature variation (±), = 6°C, for 12°C range (minimum to 

maximum) of average daily temperature over the year 

• IDAY is the day counter, from 1 to 365 

• ILOWDAY is the day of lowest temperature, = 15, for January 15. 

From this, To,a varies over a range of 16°C: from a minimum of 2°C to maximum of 18°C over 

the year. 

2. Set the heating system capacity as needed so there is at least enough capacity to maintain the zone 

air temperature set point during the peak heating-load hour (and therefore all other hours). 

1.3.1.2.4 Output Requirements. If possible for the software being tested, the simulation should be run 

long enough that there is ≤ 0.1% variation between the annual floor slab conduction for the last year of 

the simulation and the preceding year of the simulation. 

If a numerical model is being tested that allows variation of thermal node meshing, it is recommended to 

demonstrate that the tested mesh detail yields negligible (≤ 0.1%) change in results versus a less detailed 

mesh, or that the mesh is as detailed as possible for the available computing hardware. 

If the software being tested allows user specification of convergence tolerance, it is recommended to 

demonstrate that the current level of heat-flow or temperature convergence tolerance yields negligible 

(≤ 0.1%) change in results versus the next finer convergence tolerance. 

Provide the following outputs for only the last full year of the simulation: 

• Annual total conduction through the floor slab (Qfloor) (kWh/y); this is specifically conduction 

through the interior surface of the slab defined by dimensions B × L in Figure 1-2. 

• Annual total zone load (Qzone) (kWh/y); this output should vary from floor slab conduction only if 

the program being tested does not allow fully adiabatic above-grade walls; if the program being 

tested (particularly for models run independently of whole-building simulations) does not have 

different outputs for zone load and floor conduction, report the output where it is most 

appropriate and leave the other output blank (e.g., report the results only as floor conduction, and 

do not report any zone load results). 

16 
• Annual average zone temperature (Tzone,mean) (°C); this output checks the temperature that results 

from the given thermostat set point. 

• Annual hourly integrated peak floor conduction (qfloor,max) (Wh/h or W) for the year including 

hour of occurrence; this is specifically the peak conduction through the interior surface of the slab 

defined by dimensions B × L in Figure 1-2. 

• Annual hourly integrated peak zone load (qzone,max) (Wh/h or W) for the year, including hour of 

occurrence; this output should only vary from floor slab conduction if the program being tested 

does not allow fully adiabatic above-grade walls. 

• Minimum hourly ambient temperature (TODB,min) (°C) and first hour of occurrence. 

• Number of hours with minimum hourly To,a. 

• Hourly floor conduction (Wh/h or W) for the entire year; this is specifically hourly conduction 

through the interior surface of the slab defined by dimensions B × L in Figure 1-2. 

• Hourly time convention; e.g., Hour 1 = 0:00–1:00, or Hour 1 = 0:30–1:30, etc. 

Provide the following other outputs: 

• Duration of simulation (tsim) in hours. This is the number of hours simulated, e.g., if 10 years are 

simulated, indicate 87600 hours. 

1.3.1.3 Case GC45b – Aspect Ratio 

1.3.1.3.1 Objective. Test the sensitivity to variation of aspect ratio (AR) in the context of steady-periodic 

(harmonic) variation of To,a. The AR for a given slab area directly affects the ratio of perimeter heat 

transfer to core heat transfer. In this context the use of the term perimeter is different from the perimeter 

boundary described in Case GC10a. Here, perimeter heat transfer is the heat transfer driven by the zone to 

ambient air temperature difference, through a relatively thin layer of soil; core heat transfer is driven by 

the zone to deep ground temperature difference, through a relatively thick layer of soil. 

1.3.1.3.2 Method. This case is similar to Case GC40b. It uses a slab with same surface area, but different 

AR. Comparison of results for GC45b versus GC40b (GC45b-GC40b) checks the sensitivity of AR. 

Compare heat-flow results from whole-building simulation programs to verified numerical-model results. 

Analyze phase shift between variation of heat flow and To,a. 

1.3.1.3.3 Input Specification. This case is exactly as Case GC40b except for the slab dimensions, as 

noted in Table 1-6. 

Table 1-6. Input parameters

Test parameters SI Units IP Units 

Slab length (L) 36 m 118.11 ft 

Slab width (B) 4 m 13.12 ft 

Set the heating system capacity as needed so there is at least enough capacity to maintain the zone air 

temperature set point during the peak heating-load hour (and therefore all other hours). 

1.3.1.3.4 Output Requirements. See Case GC40b. However, do not provide hourly floor conduction 

outputs for the entire year. 

17 
1.3.1.4 Case GC50b – Large Slab 

1.3.1.4.1 Objective. Test the sensitivity to variation of slab size in the context of steady-periodic 

(harmonic) variation of To,a. Increasing the slab size yields a larger fraction of core-driven ground heat 

transfer that is driven by the difference between the zone air temperature and the deep ground 

temperature. 

1.3.1.4.2 Method. This case is similar to Case GC40b but uses a large slab. Comparing results for heat 

flow per unit floor area (flux) for GC50b versus GC40b (GC50b–GC40b) checks the sensitivity to heat 

transfer caused by increasing the slab size. Compare heat-flow results from whole-building simulation 

programs to verified numerical-model results. Analyze phase shift between variation of heat flow and 

To,a. 

1.3.1.4.3 Input Specification. This case is exactly as Case GC40b except for the following. 

Adjust dimensions as noted in Figure 1-5 and Table 1-7. 

F = 15 m

Soil E= 15m

q = 0 Tdg q = 0

Floor Slab

80 m

Elevation Section

Figure 1-5. Case GC50b-1 dimensions and below-grade boundary donditions 

Table 1-7. Input parameters

Test parameters SI Units IP Units 

Slab length (L) 80 m 262.47 ft 

Slab width (B) 80 m 262.47 ft 

Deep ground boundary depth (E) 15 m 49.21 ft 

Far field boundary distance (F) 15 m 49.21 ft 

Set the heating system capacity as needed so there is at least enough capacity to maintain the zone air 

temperature set point during the peak heating-load hour (and therefore all other hours). 

1.3.1.4.4 Output Requirements. See Case GC40b. However, do not provide hourly floor conduction 

outputs for the entire year. 

18 
1.3.1.5 Case GC55b – Shallow Deep Ground Temperature 

1.3.1.5.1 Objective. Test the sensitivity to variation of deep ground temperature depth in the context of 

steady-periodic (harmonic) variation of To,a. This case is relevant for areas with a relatively shallow 

groundwater table, which increases the effect of core heat flow that is driven by the difference between 

the zone air temperature and the deep ground temperature. 

1.3.1.5.2 Method. This case is similar to Case GC40b but uses a shallower deep ground boundary (heat 

sink) location. Comparison of results for GC55b versus GC40b (GC55b–GC40b) checks the sensitivity of 

deep ground temperature depth. Compare heat-flow results from whole-building simulation programs to 

verified numerical-model results. Analyze phase shift between variation of heat flow and To,a. 

1.3.1.5.3 Input Specification. This case is exactly as Case GC40b except for the deep ground 

temperature boundary depth as noted in Table 1-8. 

Table 1-8. Input parameters

Test parameters SI Units IP Units 

Deep ground boundary depth (E) 2 m 6.562 ft 

Set the heating system capacity as needed so there is at least enough capacity to maintain the zone air 

temperature set point during the peak heating-load hour (and therefore all other hours). 

1.3.1.5.4 Output Requirements. See Case GC40b. However, do not provide hourly floor conduction 

outputs for the entire year. 

1.3.1.6 Case GC60b – Steady State with Typical Interior Convective Surface Coefficient 

1.3.1.6.1 Objective. Test sensitivity to the use of a more realistic interior convective surface heat transfer 

coefficient (h,int) in the steady-state context. With a more realistic coefficient, the zone floor surface 

temperature will be less uniform, and will exhibit greater decrease outward from the center toward the 

zone perimeter boundary. 

1.3.1.6.2 Method. This case is similar to Case GC30b but uses decreased h,int. Comparison of results for 

GC60b versus GC30b (GC60b–GC30b) checks the sensitivity of h,int. Compare heat-flow results from 

whole-building simulation programs to verified numerical-model results. 

1.3.1.6.3 Input Specification. This case is exactly as Case GC30b except for h,int (see Table 1-9). This 

value of h,int is applied to the interior side of the floor and other zone surfaces (walls and ceiling). 

Table 1-9. Input parameters

Test parameters SI Units IP Units 

h,int (interior convective surface coefficient) 7.95 W/(m2

⋅K) 1.3999 Btu/(h⋅ft2⋅°F) 

Recall the simplification that surface IR emittances have been specified as 0 (or as low as the program 

being tested allows). If the program being tested allows direct user input of interior convective surface 

coefficients and interior surface IR emittances, ignore the remainder of this paragraph. If the program 

being tested allows direct user input of combined interior surface coefficients only, set that value to 7.95 

19 
W/(m2

⋅K) (1.3999 Btu/(h⋅ft2⋅°F)). If the program being tested does not allow direct user input of 

convective surface coefficients or combined surface coefficients, input a value for IR emittance such that 

an equivalent value for combined surface coefficient of 7.95 W/(m2

⋅K) is obtained (based on the 

convective surface coefficient that the program being tested automatically calculates). Discuss in your 

modeler report any deviation from the convective surface coefficient.

1.3.1.6.4 Output Requirements. See Case GC30b. 

1.3.1.7 Case GC65b – Steady State with Typical Interior and Exterior Convective 

Surface Coefficients 

1.3.1.7.1 Objective. Test sensitivity to the use of a more realistic exterior convective surface coefficient 

(h,ext) in the steady-state context. With a more realistic coefficient the exterior ground surface 

temperature will be less uniform, and will exhibit greater increase near the exterior side of the adiabatic 

wall. 

1.3.1.7.2 Method. This case is similar to Case GC60b but uses decreased h,ext. Comparison of results for 

GC65b versus GC60b (GC65b–GC60b) checks the sensitivity of h,ext. Comparison of results for GC65b 

versus GC30b (GC65b–GC30b) checks the combined effect of sensitivity to h,int and h,ext. Compare 

heat-flow results from whole-building simulation programs to verified numerical-model results. 

1.3.1.7.3 Input Specification. This case is exactly as Case GC60b except: 

1. Use h,ext as listed in Table 1-10. This value of h,ext is applied to the exterior ground surface, and 

to other zone exterior surfaces (walls and ceiling). The value for h,int is repeated in Table 1-10 

for convenience. 

Table 1-10. Input parameters

Test parameters SI Units IP Units 

h,int (interior convective surface coefficient) 7.95 W/(m2

⋅K) 1.3999 Btu/(h⋅ft2⋅°F) 

h,ext (exterior [ground] convective surface 

coefficient) 11.95 W/(m2

⋅K) 2.1043 Btu/(h⋅ft2⋅°F) 

Recall the simplification that surface IR emittances have been specified as 0 (or as low as the 

program being tested allows). If the program being tested allows direct user input of h,ext and 

exterior surface IR emittances, ignore the remainder of this paragraph. If the program being tested 

allows direct user input of combined exterior surface coefficients only, set that value to 11.95 

W/(m2

⋅K) (2.1043 Btu/(h⋅ft2⋅°F)). If the program being tested does not allow direct user input of 

convective surface coefficients or combined surface coefficients, input a value for IR emittance 

such that an equivalent value for combined surface coefficient of 11.95 W/(m2

⋅K) is obtained 

(based on the convective surface coefficient that the program being tested automatically 

calculates). Discuss in your modeler report any deviation from the convective surface coefficient.

2. Use weather data provided with the file GCSS-W01.TM2. 

GCSS-W01.TM2 is the same as GCSS-W20.TM2 except that wind speed is set to 1.0 m/s (2.24 

miles/h). 1.0 m/s wind speed is consistent with convective h,ext = 11.95 W/(m2

⋅K). This value for 

h,ext comes from a resulting combined convective/radiative coefficient of 16.58 W/(m2

⋅K) for 1.0 

20 
m/s based on equations described by Walton (1983) and assuming ground surface roughness is 

equivalent to that for typical brick or rough plaster, and then subtracting out the equivalent 

radiative portion of the combined coefficient of 4.63 W/(m2

⋅K) based on IEA BESTEST (Judkoff 

and Neymark 1995), Appendix D. TMY2 weather data format is described in Appendix A. Table 

1-3 (see Section 1.1.1.1) provides a summary of site and weather data parameters. 

1.3.1.7.4 Output Requirements. See Case GC30b. 

1.3.1.8 Case GC70b – Harmonic Variation of Ambient Temperature with Typical Interior 

and Exterior Convective Surface Coefficients 

1.3.1.8.1 Objective. Test sensitivity to the use of more realistic h,int and h,ext in the context of steadyperiodic (harmonic) variation of To,a. 

1.3.1.8.2 Method. This case is similar to Case GC40b but uses decreased h,int and h,ext. Comparison of 

results for GC70b versus GC40b (GC70b–GC40b) checks the combined sensitivities of h,int and h,ext. 

Compare heat-flow results from whole-building simulation programs to verified numerical-model results. 

Analyze phase shift between variation of heat flow and To,a. Comparison of GC70b versus GC65b 

(GC70b–GC65b) annual hourly average floor conduction checks the sensitivity of average floor heat loss 

of the harmonic versus the steady-state condition in the context of using realistic convective surface 

coefficients. 

1.3.1.8.3 Input Specification. This case is exactly as Case GC40b except: 

 

1. Use h,int and h,ext of Table 1-10 (see Section 1.3.1.7.3). 

2. Use weather data provided with the file GCSP-W01.TM2. 

GCSP-W01.TM2 is the same as GCSP-W20.TM2 except that constant wind speed is set to 1.0 

m/s (2.24 miles/h). 1.0 m/s wind speed is consistent with convective h,ext = 11.95 W/(m2

⋅K). 

This value for h,ext comes from a resulting combined convective/radiative coefficient of 16.58 

W/(m2

⋅K) for 1.0 m/s based on equations described by Walton (1983) and assuming ground 

surface roughness is equivalent to that for typical brick or rough plaster, and then subtracting out 

the equivalent radiative portion of the combined coefficient of 4.63 W/(m2

⋅K) based on IEA 

BESTEST (Judkoff and Neymark 1995), Appendix D. TMY2 weather data format is described in 

Appendix A. Table 1-3 (see Section 1.1.1.1) provides a summary of site and weather data 

parameters. 

1.3.1.8.4 Output Requirements. See Case GC40b. However, do not provide hourly floor conduction 

outputs for the entire year. 

1.3.1.9 Case GC80b – Reduced Slab and Ground Conductivity 

1.3.1.9.1 Objective. Test sensitivity to reduced slab and ground conductivity in the context of steadyperiodic (harmonic) variation of To,a. 

1.3.1.9.2 Method. This case is similar to Case GC40b but uses decreased slab and ground conductivity. 

Comparison of results for GC80b versus GC40b (GC80b–GC40b) checks the sensitivity of slab and 

21 
ground conductivity. Compare heat-flow results from whole-building simulation programs to verified 

numerical-model results. Analyze phase shift between variation of heat flow and To,a. 

1.3.1.9.3 Input Specification. This case is exactly as Case GC40b except: 

Soil and slab thermal conductivity = 0.5 W/(m⋅K) (0.289 Btu/(h⋅ft⋅°F)) 

1.3.1.9.4 Output Requirements. See Case GC40b. However, do not provide hourly floor conduction 

outputs for the entire year. 

1.3.2 “a”-Series Cases 

1.3.2.1 Case GC10a – Steady-State Analytical Verification Base Case 

1.3.2.1.1 Objective. Compare steady-state heat flow results for detailed 3-D numerical models used 

independently from whole-building energy simulation programs, versus an analytical solution. Users of 

such detailed models are to determine appropriate inputs to match the boundary conditions and 

assumptions of the analytical solution, including appropriate meshing, the amount of ground that needs to 

be modeled, length of simulation, etc. Attention to such modeling details is needed to obtain consistent 

high-quality results throughout these test cases. In later cases where exact analytical solutions are not 

known – and if there is good agreement among detailed numerical models, and appropriate application of 

the models is well documented – the detailed numerical-model results can then be used to establish quasianalytical solutions. Such solutions provide a secondary mathematical truth standard, founded on the 

range of disagreement of the verified numerical-model results, for comparing results of other models 

typically used with whole-building energy simulation programs. 

1.3.2.1.2 Method. This case is based on Delsante et al. (1983; see also Spitler et al. 2001), which 

calculates steady-state heat flow using fundamental 3-D heat transfer analysis of a semi-infinite solid. 

Figure 1-6 shows the boundary conditions at the upper surface of the semi-infinite solid and describes a 

rectangular floor surface bounded by a concentrically rectangular perimeter surface of finite width that 

separates the rectangular floor surface from the exterior ground surface. The concentrically rectangular 

surface may also be thought of as the base of a wall that separates the interior floor surface from the 

exterior ground surface. 

Check sensitivity (if applicable) to mesh detail, length of simulation, amount of ground modeled, 

convergence tolerance, etc., and demonstrate that the modeling is at a level of detail where including 

further detail yields negligible sensitivity to results. 

1.3.2.1.3 Input Specification. Geometry is described in Figure 1-6. Parameters related to Figure 1-6 and 

other input parameters are described in Table 1-11. 

22 
W 

L 

B 

W 

Ti

W To

W

Figure 1-6. Plan view of the floor geometry

Table 1-11. Input parameters 

Test parameters SI Units IP Units 

Slab length (L) 12 m 39.37 ft 

Slab width (B) 12 m 39.37 ft 

Perimeter surface boundary width (W) 0.24 m 0.7874 ft 

Interior (slab) surface temperature (Ti) 30°C 86°F 

Exterior (ground) surface temperature (To) 10°C 50°F 

Thermal conductivity of the slab and soil 1.9 W/(m⋅K) 1.098 Btu/(h⋅ft⋅°F) 

The following boundary conditions and assumptions are applied: 

• Interior floor surface temperature (Ti) is constant and everywhere equal. 

• Exterior ground surface temperature (To) is constant and everywhere equal. 

• Linear variation between Ti and To over a perimeter surface boundary of finite width (W) is 

imposed only at the surface of the ground (this avoids a discontinuity at the interior/exterior 

boundary). 

• Semi-infinite solid: the ground surface extends outward infinitely in all horizontal directions from 

the perimeter surface boundary defined in Figure 1-6, and the ground extends infinitely 

downward from all points on the infinite horizontal surface (including from the surfaces of Figure 

1-6 and beyond). 

• Deep ground boundary condition at infinite soil depth = To. 

• Thermal conductivities of slab and soil are equal.

• There is no radiative exchange. 

23 
1.3.2.1.4 Output Requirements. Run the simulation long enough that there is ≤ 0.1% variation between 

the floor slab conduction for the last hour of the last year of the simulation and the last hour of the 

preceding year of the simulation, i.e., ≤ 0.1% variation over an interval of 8760 hours. 

Similarly, demonstrate that the current level of modeling detail yields negligible (≤ 0.1%) change in 

results versus a lesser level of detail; examine the effects of shallower deep ground boundary, shorter farfield boundary distance, and less detailed mesh (if applicable). For ground depth and far-field length 

variations, increase the number of mesh nodes proportionally to the increase in soil volume being 

modeled. (The IEA-34/43 numerical-methods modelers documented sensitivity tests for this in their 

modeler reports.) 

If the software being tested allows user specification of convergence tolerance, demonstrate that the 

current level of heat-flow or temperature convergence tolerance yields negligible (≤ 0.1%) change in 

results versus the next finer convergence tolerance.

Provide the following outputs for the last hour of the simulation: 

• Steady-state conduction through the floor slab (qfloor) in W or Wh/h; this is specifically hourly 

conduction through the interior surface of the slab defined by dimensions B × L in Figure 1-6. 

• Steady-state near-surface temperatures (Tsurf,n) (°C) as described in Figure 1-4 and Table 1-5 (see 

Section 1.3.1.1.4); to define coordinates the center of the floor slab is designated as (0,0) per 

Figure 1-4; Figure 1-4 represents a single quadrant of the symmetric slab/perimeterboundary/exterior surfaces. Provide temperatures (at consistent depth) for the uppermost modeled 

layer of soil just below the ground. These outputs are for comparison with models that do not 

provide results precisely at the surface. 

• Steady-state surface temperatures (T@surf,n) (°C) as described for Tsurf,n in Figure 1-4 and Table 1-5 

(see Section 1.3.1.1.4); to define coordinates the center of the floor slab is designated as “(0,0)” 

as shown in Figure 1-4; Figure 1-4 represents a single quadrant of the symmetric slab/perimeterboundary/exterior surfaces. These outputs are for checking proper application of surface 

temperature boundary conditions. 

Provide the following other outputs: 

• Duration of simulation (tsim) in hours 

• Deep ground temperature depth (E, see Figure 1-1 [Section 1.3.1.1.3]) 

• Far-field boundary distance (F, see Figure 1-1 [Section 1.3.1.1.3]). 

1.3.2.1.5 Analytical Solution for Steady-State Heat Flow through the Floor Slab. For the conditions 

of Figure 1-6, given the slab of area surrounded by a perimeter surface boundary of thickness W , 

assume the surface temperature of the floor is , and the temperature falls linearly across the perimeter 

boundary from to the exterior ground surface temperature , the exact solution for the problem under 

steady state 3-D conditions is given by Delsante et al. (1983). The total heat flow through the slab into the 

ground is: 

× BL

Ti

Ti To

( ) ( WBLF

π

TTkq oi ,, 1 −= ) (GC10a-1) 

Where: Ti = surface temperature of the floor, °C

To = temperature of the outside ground, °C

24 
 k = conductivity of floor slab and soil, W/(m⋅K) 

And ( ,, WBLF ) is a function of L, B, and W with the units of length (m): 

( ) [ ] ( )( ) [ ( ) ]

[ ] ( ) ( )

[ ] ( ) [ ] ( )

[ ] ( )

( )

( ) [ ] ( )( )

( ) [ ] ( )( )

( ) ( ) ( ) ( )

[ ] ( )

[ ] ( )

( ) [ ] ( )

( ) [ ] ( )

[ ] ( )

[ ] ( )

⎪⎭

⎪

⎬

⎫

⎪⎩

⎪

⎨

⎧ ++ ++

+

⎪⎭

⎪

⎬

⎫

⎪⎩

⎪

⎨

⎧ ++ ++

+

⎪⎭

⎪

⎬

⎫

⎪⎩

⎪

⎨

⎧ ++++

++

⎪⎭

⎪

⎬

⎫

⎪⎩

⎪

⎨

⎧ ++++

++

⎪⎭

⎪

⎬

⎫

⎪⎩

⎪

⎨

⎧

+

+++

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − −

⎪⎭

⎪

⎬

⎫

⎪⎩

⎪

⎨

⎧

+

+++

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − −

⎪⎭

⎪

⎬

⎫

⎪⎩

⎪

⎨

⎧ ++

⎥

⎦

⎤ ⎢

⎣

⎡ +

⎪⎭

⎪

⎬

⎫

⎪⎩

⎪

⎨

⎧ ++

⎥

⎦

⎤ ⎢

⎣

⎡ +

⎪⎭

⎪

⎬

⎫

⎪⎩

⎪

⎨

⎧

+

+++++ ⎥ ×

⎦

⎤ ⎢

⎣

⎡ +−

+

⎪⎭

⎪

⎬

⎫

⎪⎩

⎪

⎨

⎧

+

+++++ ⎥ ×

⎦

⎤ ⎢

⎣

⎡ +−

+

⎪⎭

⎪

⎬

⎫

⎪⎩

⎪

⎨

⎧

++

++ ++ −

+ −++− ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ +

+

⎟ + ⎠

⎞ ⎜

⎝

⎛ + ⎟ ++ − ⎠⎞ ⎜

⎝

⎛ +−

⎟ ++ ⎠

⎞ ⎜

⎝

⎛ ⎟ +−+++ ⎠

⎞ ⎜

⎝

⎛ +

+=

B

WBWBB

W

B

L

WLWLL

W

L

W

WBWBW

W

WLWLW

WB

WWBW

W

W

WL

WWLW

W

W

B

LBL

L W

BBL

W

WB

WLWBWL

W

WLG

WL

WBWBWL

W

WBG

DDG

WDWDG

W

G

W

BL

W

BL WBB

W

B

WLL

W

L WBWL

W

BL WBLF

2 2 ln 2 

2 2 ln 2 

lnW2B 

lnW2L 

ln B 

ln L 

ln B-2LB ln L-2BL 

 ln

 ln

2 2 ln 2 

12ln2212ln21

W

BL 

2

2

12 

2

2 2,, 12

21 2 2 2

21 2 2 2

21 2 2

21 2 2

21 22 2 2

21 22 2 2

21 22 21 22

21 2 2 2 2

21 2 2 2 2

21 22

21 2 2 2

22

21 22 21 2 2

21 2 2 21 2 2

(GC10a-2) 

Where −= BLG , and D += BL

25 
1.3.2.2 Case GC30a – Steady-State Comparative Test Base Case with Direct Input of 

Surface Temperatures 

1.3.2.2.1 Objective. Compare steady-state heat flow results from detailed numerical models to each other. 

Compare whole-building simulation programs (if possible) versus verified numerical-model results. 

Constant temperature surface boundary conditions may limit the number of models that can run this case. 

1.3.2.2.2 Method. This case drives floor conduction based on the direct-input temperature difference 

between the interior surface of the floor slab and the exterior surface of the ground (and deep ground 

boundary condition). This case is similar to Case GC10a but uses an adiabatic wall/ground interface 

boundary (see Figure 1-1 [Section 1.3.1.1.3]). The adiabatic wall/ground interface boundary replaces the 

linearly varying temperature perimeter surface boundary of Case GC10a. Soil and far-field boundary 

conditions are also described. Hourly TMY2-format weather data with constant ambient temperature are 

provided. Comparison of GC30a versus GC10a (GC30a–GC10a) checks the sensitivity to perimeter 

surface boundary conditions for an adiabatic versus a linearly varying temperature condition. 

For programs that cannot directly input surface temperatures, but can input very high surface coefficients 

(h >> 100 W/(m2

⋅K)), a constant/uniform surface temperature can be mimicked with h ≥ 5000 W/(m2⋅K). 

Check sensitivity (if applicable) to mesh detail, length of simulation, amount of ground modeled, 

convergence tolerance, etc., and demonstrate that the modeling is at a level of detail where including 

further detail yields negligible sensitivity to results.

1.3.2.2.3 Input Specification. This case is exactly as Case GC30b except for the following changes. 

1.3.2.2.3.1 Soil and Slab Thermal Properties and Boundary Conditions. Changes to surface 

temperatures and soil geometry are given in Table 1-12. 

Table 1-12. Input parameters 

Test parameters SI Units IP Units 

Interior slab surface temperature (Ti) 30°C 86°F 

Exterior ground surface temperature (To) 10°C 50°F 

Deep ground boundary depth (E) 30 m 98.43 ft 

Far field boundary distance (F) 20 m 65.62 ft 

Ti and To are applied directly to the surfaces and are constant and everywhere equal. 

Although this case provides a zone description (per Case GC30b), for programs that can input surface 

temperatures directly and output resulting floor conductance, only the floor slab needs to be modeled; the 

other above-grade (adiabatic) surfaces of the zone do not need to be modeled. 

For programs that cannot directly input surface temperatures, but can input very high surface coefficients 

(h), sensitivity tests indicate that a constant/uniform surface temperature can be mimicked by setting zone 

and ambient air temperatures to Ti and To and applying h ≥ 5000 W/(m2

⋅K). If the program being tested 

allows input of such very high surface coefficients, use the greatest value allowed and document the 

values in your modeler report. Be aware that very high surface coefficients may cause some programs to 

become unstable. For programs that do not allow direct input of surface temperatures and do not allow 

convective surface coefficients much greater than 100 W/(m2

⋅K), run Case GC30b instead of Case 

GC30a. 

26 
1.3.2.2.3.2 Weather Data. Use constant temperature TMY2-format weather data provided with the file: 

GCSS-W40.TM2. 

TMY2 weather data format is described in Appendix A. Table 1-3 (see Section 1.1.1.1) provides a 

summary of site and weather data parameters. This weather data file is based on the weather data file used 

for Case GC30b (GCSS-W20.TM2), except that wind speed = 40 m/s (89.48 miles/h). The wind speed 

given in the weather data file is the maximum of the value range indicated by TMY2 weather data 

documentation (Marion and Urban, 1995). Extrapolating (see ASHRAE 2005 Handbook of 

Fundamentals, p. 25.1) equations described by Walton (1983) and assuming a rough surface, this may 

correspond with combined radiative/convective h,ext = 219.89 W/(m2

⋅K). Subtracting out the equivalent 

radiative portion of the combined coefficient of 4.63 W/(m2

⋅K) based on IEA BESTEST (Judkoff and 

Neymark 1995), Appendix D, yields convective only h,ext = 215.26 W/(m2

⋅K). Because some wholebuilding energy simulation software may flag weather data values outside of TMY2 documented limits 

(e.g. DOE-2.1E), a value greater than 40 m/s (99.9 m/s is format limit) was not used. 

1.3.2.2.4 Output Requirements. See Case GC30b. If the model being tested uses direct input of interior 

slab surface temperature such that modeling of a building zone is not necessary, then do not include 

results for: 

• Zone load (qzone) in W or Wh/h 

• Zone air temperature (Tzone) (°C). 

1.3.2.3 Case GC40a – Harmonic Variation of Direct-Input Exterior Surface Temperature 

1.3.2.3.1 Objective. Compare heat flow results for approximate steady-periodic (harmonic) variation of 

exterior ground surface temperature (To) from detailed numerical models to each other. Compare wholebuilding simulation programs (if possible) to verified numerical-model results. Analyze the phase shift 

between variation of heat flow and To. Direct-input surface temperature boundary conditions may limit 

the number of models that can run this case. 

1.3.2.3.2 Method. This case is similar to Case GC30a but uses harmonically varying To,a for input as To. 

Hourly TMY2-format weather data are provided for approximating a sinusoidal annual cycle of varying 

daily average temperature with sinusoidal diurnal temperature cycle overlaid (a high-frequency cycle 

overlaid on a low-frequency cycle). Comparison of GC40a versus GC30a (GC40a–GC30a) annual hourly 

average floor conduction checks the sensitivity of average floor heat loss of the harmonic condition 

versus the steady-state condition. 

For programs that cannot directly input surface temperatures, but can input very high surface coefficients 

(h >> 100 W/(m2

⋅K)), a constant/uniform surface temperature can be mimicked with h ≥ 5000 W/(m2⋅K). 

Check sensitivity (if applicable) to mesh detail, length of simulation, amount of ground modeled, 

convergence tolerance, etc., and demonstrate that the modeling is at a level of detail where including 

further detail yields negligible sensitivity to results. 

1.3.2.3.3 Input Specification. This case is exactly as Case GC30a except for the following changes: 

1. Use weather data provided with the file GCSP-W40.TM2. 

27 
GCSP-W40.TM2 is the same as GCSS-W40.TM2 except harmonically varying To,a is 

approximated by using the same method as for GCSP-W20.TM2 (see Case GC40b, Section 

1.3.1.2.3, for a detailed description). In this file atmospheric pressure and dew-point temperature 

were set to constant values, and relative humidity was adjusted to be consistent with other listed 

values using common psychrometric formulae. (ASHRAE 2001 [Chapter 6]; Brandemuehl 1993). 

TMY2 weather data format is described in Appendix A. Table 1-3 (see Section 1.1.1.1) provides 

a summary of site and weather data parameters. 

2. Set the heating system capacity as needed so there is at least enough capacity to maintain the zone 

air temperature set point during the peak heating-load hour (and therefore all other hours). 

1.3.2.3.4 Output Requirements. Output for GC40a is the same as for Case GC40b except: 

If the model being tested uses direct input of interior slab surface temperature such that modeling of a 

building zone is not necessary, do not include results for: 

• Annual total zone load (Qzone) (kWh/y) 

• Annual average zone temperature (Tzone,mean) (°C) 

• Annual hourly integrated peak zone load (qzone,max) (Wh/h or W) for the year including hour of 

occurrence. 

1.3.3 “c”-Series Cases 

1.3.3.1 Case GC30c – Steady-State Comparative Test Base Case with BASESIMP 

Boundary Conditions 

1.3.3.1.1 Objective. Compare whole-building simulation programs versus verified numerical-model 

results. The constant temperature exterior surface boundary condition may limit the number of models 

that can run this case. 

1.3.3.1.2 Method. This case drives floor conduction based on the difference between the zone air 

temperature and To (and deep ground boundary temperature). This case is similar to GC30a and GC30b 

but uses boundary conditions compatible with assumptions of BASESIMP. Comparison of GC30c versus 

GC30a (GC30c–GC30a) checks the sensitivity to reduced interior surface coefficient; sensitivity may also 

be affected (secondarily) by reduced ground depth and reduced far-field ground distance. 

For programs that cannot directly input exterior surface temperatures, but can input very high exterior 

surface coefficients (h >> 100 W/(m2

⋅K)), a constant/uniform exterior surface temperature can be 

mimicked with h ≥ 5000 W/(m2

⋅K). 

1.3.3.1.3 Input Specification. This case is exactly as Case GC30b except for the following changes. 

1.3.3.1.3.1 Soil and Slab Thermal Properties and Boundary Conditions. Table 1-13 documents changes 

to interior and exterior surface boundary conditions and the amount of soil modeled (versus Case GC30b). 

If the program being tested allows direct user input of combined interior surface coefficients, ignore the 

remainder of this paragraph. If the program being tested allows direct user input of convective surface 

coefficients, but allows only automatically calculated surface IR radiative exchange, set the convective 

surface coefficient to 7.95 W/(m2

⋅K) (1.3999 Btu/(h⋅ft2⋅°F)) and set the surface IR emittance to 0 (or as 

28 
low as the program being tested allows). If the program being tested does not allow direct user input of 

convective surface coefficients or combined surface coefficients, input a value for IR emittance such that 

an equivalent value for combined surface coefficient of 7.95 W/(m2

⋅K) is obtained (based on the 

convective surface coefficient that the program being tested automatically calculates). Discuss in your 

modeler report any deviation from the combined surface coefficients. 

Table 1-13. Input parameters 

Test parameters SI Units IP Units 

Interior combined surface coefficient (h,int) 7.95 W/(m2

⋅K) 1.3999 Btu/(h⋅ft2⋅°F)

Exterior ground surface temperature (To) 10°C 50°F 

Far field boundary distance (F) 8 m 26.24 ft 

Exterior ground surface temperature (To) is applied directly to the surface and is constant and everywhere 

equal. For programs that cannot directly input To, but can input very high h,ext, sensitivity tests indicate 

that a constant/uniform surface temperature can be mimicked by setting To,a to To and applying h,ext ≥

5000 W/(m2

⋅K). If the program being tested does not allow input of such very high h,ext, use the greatest 

value allowed and document the values in your modeler report. Be aware that very high surface 

coefficients may cause some programs to become unstable. 

1.3.3.1.3.2 Weather Data. Use constant temperature TMY2-format weather data provided with the file: 

GCSS-W40.TM2. 

TMY2 weather data format is described in Appendix A. Table 1-3 (see Section 1.1.1.1) provides a 

summary of site and weather data parameters. This weather data file is based on the weather data file used 

for Case GC30b (GCSS-W20.TM2), except that wind speed = 40 m/s (89.48 miles/h). The wind speed 

given in the weather data file is the maximum of the value range indicated by TMY2 weather data 

documentation (Marion and Urban 1995). Extrapolating (see ASHRAE 2005 Handbook of Fundamentals, 

p. 25.1) equations described by Walton (1983) and assuming a rough surface, this may correspond with 

combined radiative/convective h,ext = 219.89 W/(m2

⋅K). Subtracting out the equivalent radiative portion 

of the combined coefficient of 4.63 W/(m2

⋅K) based on IEA BESTEST (Judkoff and Neymark 1995), 

Appendix D, yields convective only h,ext = 215.26 W/(m2

⋅K). Because some whole-building energy 

simulation software may flag weather data values outside of TMY2 documented limits (e.g. DOE-2.1E), a 

value greater than 40 m/s (99.9 m/s is format limit) was not used. 

1.3.3.1.4 Output Requirements. See Case GC30b. However, do not provide steady-state near-surface 

temperature (Tsurf,n) results. 

1.3.3.2 Case GC40c – Harmonic Variation of Direct-Input Exterior Surface Temperature 

with BASESIMP Boundary Conditions 

1.3.3.2.1 Objective. Compare heat flow results for approximate steady-periodic (harmonic) variation of 

exterior ground surface temperature (To) from whole-building simulation programs versus verified 

numerical-model results. Analyze the phase shift between variation of heat flow and To. The direct-input 

To boundary condition may limit the number of models that can run this case. 

1.3.3.2.2 Method. This case is similar to Case GC30c but uses harmonically varying To,a for input as To. 

Hourly TMY2-format weather data are provided for approximating a sinusoidal annual cycle of varying 

29 
daily average temperature with sinusoidal diurnal temperature cycle overlaid (a high-frequency cycle 

overlaid on a low-frequency cycle). Comparison of GC40c versus GC30c (GC40c–GC30c) annual hourly 

average floor conduction checks the sensitivity of average floor heat loss of the harmonic condition 

versus the steady-state condition. 

For programs that cannot directly input To, but can input very high exterior surface coefficients (h >> 100 

W/(m2

⋅K)), a constant/uniform exterior surface temperature can be mimicked with h ≥ 5000 W/(m2⋅K). 

1.3.3.2.3 Input Specification. This case is exactly as Case GC30c except for the following changes: 

1. Use weather data provided with the file GCSP-W40.TM2. 

GCSP-W40.TM2 is the same as GCSS-W40.TM2 except harmonically varying To,a is 

approximated using the same method as for GCSP-W20.TM2 (see Case GC40b, Section 

1.3.1.2.3, for a detailed description). In this file atmospheric pressure and dew-point temperature 

were set to constant values, and relative humidity was adjusted to be consistent with other listed 

values using common psychrometric formulae. (ASHRAE 2001 [Chapter 6]; Brandemuehl 1993). 

TMY2 weather data format is described in Appendix A. Table 1-3 (see Section 1.1.1.1) provides 

a summary of site and weather data parameters. 

2. Set the heating system capacity as needed so there is at least enough capacity to maintain the zone 

air temperature set point during the peak heating-load hour (and therefore all other hours). 

1.3.3.2.4 Output Requirements. Output for GC40c is the same as for Case GC40b. 

1.3.3.3 Case GC45c – Aspect Ratio with BASESIMP Boundary Conditions 

1.3.3.3.1 Objective. Test the sensitivity to variation of AR in the context of steady-periodic (harmonic) 

variation of To. The AR for a given slab area directly affects the ratio of perimeter heat transfer to core 

heat transfer. In this context the term perimeter is different from the perimeter boundary described in 

Case GC10a. Here, perimeter heat transfer is the heat transfer driven by the zone to ambient air 

temperature difference, through a relatively thin layer of soil; core heat transfer is driven by the zone to 

deep ground temperature difference, through a relatively thick layer of soil. 

1.3.3.3.2 Method. This case is similar to Case GC40c. It uses a slab with same surface area, but a 

different AR. Comparison of results for GC45c versus GC40c (GC45c–GC40c) checks the sensitivity of 

AR. Compare heat-flow results from whole-building simulation programs to verified numerical-model 

results. Analyze phase shift between variation of heat flow and To. 

1.3.3.3.3 Input Specification. This case is exactly as Case GC40c except for the slab dimensions as noted 

in Table 1-14. 

Table 1-14. Input parameters

Test parameters SI Units IP Units 

Slab length (L) 36 m 118.11 ft 

Slab width (B) 4 m 13.12 ft 

Set the heating system capacity as needed so there is at least enough capacity to maintain the zone air 

temperature set point during the peak heating-load hour (and therefore all other hours). 

30 
1.3.3.3.4 Output Requirements. See Case GC40b. However, do not provide hourly floor conduction 

outputs for the entire year. 

1.3.3.4 Case GC55c – Shallow Deep Ground Temperature with BASESIMP Boundary 

Conditions 

1.3.3.4.1 Objective. Test the sensitivity to variation of deep ground temperature depth in the context of 

steady-periodic (harmonic) variation of To. This case is relevant for areas with a relatively shallow 

groundwater table, which increases the effect of core heat flow that is driven by the difference between 

the zone air temperature and the deep ground temperature. 

1.3.3.4.2 Method. This case is similar to Case GC40c but uses a shallower deep ground boundary (heat 

sink) location. Comparison of results for GC55c versus GC40c (GC55c–GC40c) checks the sensitivity of 

deep ground temperature depth. Compare heat-flow results from whole-building simulation programs to 

verified numerical-model results. Analyze phase shift between variation of heat flow and To. 

1.3.3.4.3 Input Specification. This case is exactly as Case GC40c except for the deep-ground 

temperature boundary depth as noted in Table 1-15. 

Table 1-15. Input parameters

Test parameters SI Units IP Units 

Deep ground boundary depth (E) 5 m 16.40 ft 

Set the heating system capacity as needed so there is at least enough capacity to maintain the zone air 

temperature set point during the peak heating-load hour (and therefore all other hours). 

1.3.3.4.4 Output Requirements. See Case GC40b. However, do not provide hourly floor conduction 

outputs for the entire year. 

1.3.3.5 Case GC80c – Reduced Slab and Ground Conductivity with BASESIMP 

Boundary Conditions 

1.3.3.5.1 Objective. Test sensitivity to reduced slab and ground conductivity in the context of steadyperiodic (harmonic) variation of To. 

1.3.3.5.2 Method. This case is similar to Case GC40c but uses decreased slab and ground conductivity. 

Comparison of results for GC80c versus GC40c (GC80c–GC40c) checks the sensitivity of slab and 

ground conductivity. Compare heat-flow results from whole-building simulation programs to verified 

numerical-model results. Analyze phase shift between variation of heat flow and To. 

1.3.3.5.3 Input Specification. This case is exactly as Case GC40c except: 

Soil and slab thermal conductivity = 0.85 W/(m⋅K) (0.491 Btu/(h⋅ft⋅°F)). 

1.3.3.5.4 Output Requirements. See Case GC40b. However, do not provide hourly floor conduction 

outputs for the entire year. 

31 
Appendix A. TMY2 File Format 

This format information was taken from the TMY2 User’s Manual (Marion and Urban 1995), and can be 

found at www.nrel.gov. 

Data and Format 

For each station, a TMY2 file contains 1 year of hourly solar radiation, illuminance, and meteorological 

data. The files consist of data for the typical calendar months during 1961-1990 that are concatenated to 

form the typical meteorological year for each station. 

Each hourly record in the file contains values for solar radiation, illuminance, and meteorological 

elements. A two-character source and uncertainty flag is attached to each data value to indicate whether 

the data value was measured, modeled, or missing, and to provide an estimate of the uncertainty of the 

data value. 

File Header 

The first record of each file is the file header that describes the station. The file header contains the 

WBAN number, city, state, time zone, latitude, longitude, and elevation. The field positions and 

definitions of these header elements are given in Table A-1, along with sample FORTRAN and C formats 

for reading the header. 

Table A-1. TMY2 weather file header format (for first record of each file) 

Field Position Element Definition

 002 - 006 WBAN Number 

Station's Weather Bureau Army Navy 

number (see Table 2-1 of Marion and Urban 

[1995]) 

 008 - 029 City City where the station is located (maximum of 22 

characters) 

 031 - 032 State State where the station is located (abbreviated to 

two letters) 

 034 - 036 Time Zone 

Time zone is the number of hours by which the 

local standard time is ahead of or behind 

Universal Time. For example, Mountain Standard 

Time is designated -7 because it is 7 hours 

behind Universal Time. 

 038 - 044

 038 

 040 - 041 

 043 - 044 

 Latitude Latitude of the station 

N = North of equator 

Degrees 

Minutes 

 046 - 053

 046 

 048 - 050 

 052 - 053

 Longitude Longitude of the station 

W = West, E = East 

Degrees 

Minutes 

 056 - 059 Elevation Elevation of station in meters above sea level 

FORTRAN Sample Format: 

 ( 1X,A5,1X,A22,1X,A2,1X,I3,1X,Al,lX,I2,1X,I2,1X,Al,lX,I3,1X,I2,2X,I4 )

C Sample Format: 

 ( %s %s %s %d %s %d %d %s %d %d %d )

32 
Hourly Records 

Following the file header, 8760 hourly data records provide 1 year of solar radiation, illuminance, and 

meteorological data, along with their source and uncertainty flags. Table A-2 provides field positions, 

element definitions, and sample FORTRAN and C formats for reading the hourly records. 

Each hourly record begins with the year (field positions 2-3) from which the typical month was chosen, 

followed by the month, day, and hour information in field positions 4-9. The times are in local standard 

time (previous TMYs based on SOLMET/ERSATZ data are in solar time). 

For solar radiation and illuminance elements, the data values represent the energy received during the 60 

minutes preceding the hour indicated. For meteorological elements (with a few exceptions), observations 

or measurements were made at the hour indicated. A few of the meteorological elements had 

observations, measurements, or estimates made at daily, instead of hourly, intervals. Consequently, the 

data values for broadband aerosol optical depth, snow depth, and days since last snowfall represent the 

values available for the day indicated. 

Source and Uncertainty Flags 

With the exception of extraterrestrial horizontal and extraterrestrial direct radiation, the two field 

positions immediately following the data value provide source and uncertainty flags both to indicate 

whether the data were measured, modeled, or missing, and to provide an estimate of the uncertainty of the 

data. Source and uncertainty flags for extraterrestrial horizontal and extraterrestrial direct radiation are not 

provided because these elements were calculated using equations considered to give exact values. 

For the most part, the source and uncertainty flags in the TMY2 data files are the same as the ones in 

NSRDB, from which the TMY2 files were derived. However, differences do exist for data that were 

missing in the NSRDB, but then filled while developing the TMY2 data sets. Uncertainty values apply to 

the data with respect to when the data were measured, and not as to how "typical" a particular hour is for 

a future month and day. More information on data filling and the assignment of source and uncertainty 

flags is found in the TMY2 User’s Manual (Marion and Urban 1995). 

33 
Table A-2. TMY2 data records 

Field 

Position Element Values Definition 

 002 - 009 

 002 - 003 

 004 - 005 

 006 - 007 

 008 - 009 

 Local Standard Time 

 Year 

 Month 

 Day 

 Hour 

 61 - 90 

 1 - 12 

 1 - 31 

 1 - 24 

 Year, 1961-1990 

 Month 

 Day of month 

 Hour of day in local standard time 

 010 - 013 Extraterrestrial Horizontal 

 Radiation 

 0 - 1415 Amount of solar radiation in Wh/m2

 

 received on a horizontal surface at the 

 top of the atmosphere during the 60 

 minutes preceding the hour indicated 

 014 - 017 Extraterrestrial Direct 

 Normal Radiation 

 0 - 1415 Amount of solar radiation in Wh/m2

 

 received on a surface normal to the 

 sun at the top of the atmosphere 

 during the 60 minutes preceding the 

 hour indicated 

 018 - 023 

 018 - 021 

 022 

 023 

 Global Horizontal Radiation 

 Data Value 

 Flag for Data Source 

 Flag for Data Uncertainty 

 0 - 1200 

 A - H, ? 

 0 - 9 

 Total amount of direct and diffuse 

 solar radiation in Wh/m2

 received on 

 a horizontal surface during the 60 

 minutes preceding the hour indicated 

 024 - 029 

 024 - 027 

 028 

 029 

 Direct Normal Radiation 

 Data Value 

 Flag for Data Source 

 Flag for Data Uncertainty 

 0 - 1100 

 A - H, ? 

 0 - 9 

 Amount of solar radiation in Wh/m2 

 received within a 5.7° field of view 

 centered on the sun during the 60 

 minutes preceding the hour indicated 

 030 - 035 

 030 - 033 

 034 

 035 

 Diffuse Horizontal Radiation 

 Data Value 

 Flag for Data Source 

 Flag for Data Uncertainty 

 0 - 700 

 A - H, ? 

 0 - 9 

 Amount of solar radiation in Wh/m2 

 received from the sky (excluding the 

 solar disk) on a horizontal surface 

 during the 60 minutes preceding the 

 hour indicated 

 036 - 041 

 036 - 039 

 040 

 041 

 Global Horiz. Illuminance 

 Data Value 

 Flag for Data Source 

 Flag for Data Uncertainty 

 0 - 1300 

 I, ? 

 0 - 9 

 Average total amount of direct and 

 diffuse illuminance in hundreds of lux 

 received on a horizontal surface 

 during the 60 minutes preceding the 

 hour indicated 

 0 to 1300 = 0 to 130,000 lux 

 042 - 047 

 042 - 045 

 046 

 047 

 Direct Normal Illuminance 

 Data Value 

 Flag for Data Source 

 Flag for Data Uncertainty 

 0 - 1100 

 I, ? 

 0 - 9 

 Average amount of direct normal 

 illuminance in hundreds of lux 

 received within a 5.7° field of view 

 centered on the sun during the 60 

 minutes preceding the hour indicated. 

 0 to 1100 = 0 to 110,000 lux 

 048 - 053 

 048 - 051 

 052 

 053 

 Diffuse Horiz. Illuminance 

 Data Value 

 Flag for Data Source 

 Flag for Data Uncertainty 

 0 - 800 

 I, ? 

 0 - 9 

 Average amount of illuminance in 

 hundreds of lux received from the sky 

 (excluding the solar disk) on a 

 horizontal surface during the 60 

 minutes preceding the hour indicated. 

 0 to 800 = 0 to 80,000 lux 

34 
Field 

Position Element Values Definition 

 054 - 059 

 054 - 057 

 058 

 059 

 Zenith Luminance 

 Data Value 

 Flag for Data Source 

 Flag for Data Uncertainty 

 

 0 - 7000 

 I, ? 

 0 - 9 

 

 Average amount of luminance at the 

 sky's zenith in tens of Cd/m2

 during 

 the 60 minutes preceding the hour 

 indicated. 

 0 to 7000 = 0 to 70,000 Cd/m2

 060 - 063 

 060 - 061 

 062 

 063 

 Total Sky Cover 

 Data Value 

 Flag for Data Source 

 Flag for Data Uncertainty 

 0 - 10 

 A - F 

 0 - 9 

 Amount of sky dome in tenths 

 covered by clouds or obscuring 

 phenomena at the hour indicated 

 064 - 067 

 064 - 065 

 066 

 067 

 Opaque Sky Cover 

 Data Value 

 Flag for Data Source 

 Flag for Data Uncertainty 

 0 - 10 

 A - F 

 0 - 9 

 Amount of sky dome in tenths 

 covered by clouds or obscuring 

 phenomena that prevent observing the 

 sky or higher cloud layers at the hour 

 indicated 

 068 - 073 

 068 - 071 

 072 

 073 

 Dry Bulb Temperature 

 Data Value 

 Flag for Data Source 

 Flag for Data Uncertainty 

 -500 to 500 

 A - F 

 0 - 9 

 Dry bulb temperature in tenths of °C 

 at the hour indicated 

 -500 to 500 = -50.0 to 50.0°C 

 074 - 079 

 074 - 077 

 078 

 079 

 Dew Point Temperature 

 Data Value 

 Flag for Data Source 

 Flag for Data Uncertainty 

 -600 to 300 

 A - F 

 0 - 9 

 Dew point temperature in tenths of 

 °C at the hour indicated 

 -600 to 300 = -60.0 to 30.0°C 

 080 - 084 

 080 - 082 

 083 

 084 

 Relative Humidity 

 Data Value 

 Flag for Data Source 

 Flag for Data Uncertainty 

 0 - 100 

 A - F 

 0 - 9 

 Relative humidity in percent at the 

 hour indicated 

 085 - 090 

 085 - 088 

 089 

 090 

 Atmospheric Pressure 

 Data Value 

 Flag for Data Source 

 Flag for Data Uncertainty 

 700 - 1100 

 A - F 

 0 - 9 

 Atmospheric pressure at station in 

 millibars at the hour indicated 

 091 - 095 

 091 - 093 

 094 

 095 

 Wind Direction 

 Data Value 

 Flag for Data Source 

 Flag for Data Uncertainty 

 0 - 360 

 A - F 

 0 - 9 

 Wind direction in degrees at the hour 

 indicated. ( N = 0 or 360, E = 90, 

 S = 180,W = 270 ). For calm winds, 

 wind direction equals zero. 

 096 - 100 

 096 - 098 

 099 

 100 

 Wind Speed 

 Data Value 

 Flag for Data Source 

 Flag for Data Uncertainty 

 0 - 400 

 A - F 

 0 - 9 

 Wind speed in tenths of meters per 

 second at the hour indicated. 

 0 to 400 = 0 to 40.0 m/s 

 101 - 106 

 101 - 104 

 105 

 106 

 Visibility 

 Data Value 

 Flag for Data Source 

 Flag for Data Uncertainty 

 0 - 1609 

 A - F, ? 

 0 - 9 

 Horizontal visibility in tenths of 

 kilometers at the hour indicated. 

 7777 = unlimited visibility 

 0 to 1609 = 0.0 to 160.9 km 

 9999 = missing data 

 107 - 113 

 107 - 111 

 112 

 113 

 Ceiling Height 

 Data Value 

 Flag for Data Source 

 Flag for Data Uncertainty 

 0 - 30450 

 A - F, ? 

 0 - 9 

Ceiling height in meters at the hour 

indicated. 

 77777 = unlimited ceiling height 

 88888 = cirroform 

 99999 = missing data 

35 
Field 

Position Element Values Definition 

 114 - 123 Present Weather 

 See 

Appendix B 

of Marion and 

Urban (1995) 

Present weather conditions denoted by 

a 10-digit number. See Appendix B in 

the Marion and Urban (1995) for key to 

present weather elements. 

 124 - 128 

 124 - 126 

 127 

 128 

 Precipitable Water 

 Data Value 

 Flag for Data Source 

 Flag for Data Uncertainty 

 0 - 100 

 A - F 

 0 - 9 

 Precipitable water in millimeters at 

 the hour indicated 

 129 - 133 

 129 - 131 

 132 

 133 

 Aerosol Optical Depth 

 Data Value 

 Flag for Data Source 

 Flag for Data Uncertainty 

 0 - 240 

 A - F 

 0 - 9 

 Broadband aerosol optical depth 

 (broad-band turbidity) in thousandths 

 on the day indicated. 

 0 to 240 = 0.0 to 0.240 

 134 - 138 

 134 - 136 

 137 

 138 

 Snow Depth 

 Data Value 

 Flag for Data Source 

 Flag for Data Uncertainty 

 0- 150 

 A - F, ? 

 0 - 9 

 Snow depth in centimeters on the day 

 indicated. 

 999 = missing data 

 139 - 142 

 139 - 140 

 141 

 142 

 Days Since Last Snowfall 

 Data Value 

 Flag for Data Source 

 Flag for Data Uncertainty 

 0 - 88 

 A - F, ? 

 0 - 9 

 Number of days since last snowfall. 

 88 = 88 or greater days 

 99 = missing data 

FORTRAN Sample Format: 

 (lX,4I2,2I4,7(I4,Al,I1),2(I2,Al,Il),2(I4,Al,Il),l(I3,Al,Il), 

 l(I4,Al,Il),2(I3,Al,I1),l(I4,Al,Il),l(I5,Al,Il),l0Il,3(I3,Al,Il), 

 l(I2,Al,Il)) 

 C Sample Format: 

 (%2d%2d%2d%2d%4d%4d%4d%1s%1d%4d%1s%1d%4d%1s%1d%4d%1s%1d%4d%1s%1d%4d%1s 

 %1d%4d%1s%1d%2d%1s%1d%2d%1s%1d%4d%1s%1d%4d%1s%1d%3d%1s%1d%4d%1s%1d%3d 

 %1s%1d%3d%1s%1d%4d%1s%ld%51d%1s%1d%1d%1d%1d%1d%1d%1d%1d%1d%1d%1d%3d%1s 

 %1d%3d%1s%1d%3d%1s%1d%2d%1s%1d) 

 Note: For ceiling height data, integer variable should accept data values as large as 99999. 

36 
Appendix B. Output Spreadsheet Instructions 

GC-InDepth-Out.XLS 

Output spreadsheet for Ground Coupling In-Depth Cases: GC10a-GC80c 

 

INSTRUCTIONS 

1. Use specified units 

2. Data entry is restricted to the following ranges: 

 E53, I53, L53: Software Name, Version, and Date of Results 

 E58..H63; J58, K58: Steady-State Case Outputs 

 E70..R70: Harmonic Case “a"-Series Outputs 

 E71..R76: Harmonic Case "b"-Series Outputs 

E77..R80: Harmonic Case "c"-Series Outputs 

 G86..K103; G105..K122: Steady-State Near-Surface Temperature Outputs 

 M86..M103; M105..M122: GC10a At-Surface Temperature Outputs 

 G126: Hourly Time Convention 

 E131..G8890: Hourly Floor Conduction Outputs 

 

3. Annual sums and means are values for the entire final year of the multiyear simulation. Similarly, 

annual means, maxima, and minima are values that occur for the final year of the entire multiyear 

simulation. 

 

4. Output terminology is defined in the output section of the specification for each case, where applicable. 

 

5. Format dates using the appropriate two-digit date followed by a three-letter month code and two-digit 

hour code (24-hour clock) as shown below. 

 MONTH CODES: 

 MONTH CODE 

 JANUARY Jan 

 FEBRUARY Feb 

 MARCH Mar 

 APRIL Apr 

 MAY May 

 JUNE Jun 

 JULY Jul 

 AUGUST Aug 

 SEPTEMBER Sep 

 OCTOBER Oct 

 NOVEMBER Nov 

 DECEMBER Dec 

 

For example, a maximum value occurring on August 16 during the 15th hour interval (2:00 p.m. to 3:00 

p.m.), should be input as: 

 Date Hour 

 16-Aug 15 

37 
Appendix C. Abbreviations and Acronyms

AR aspect ratio 

ASHRAE American Society of Heating, Refrigerating and Air-Conditioning Engineers 

B floor slab length in north/south direction 

BESTEST Building Energy Simulation Test and Diagnostic Method 

Coeff. coefficient 

E deep ground boundary depth (m) 

ECBCS Energy Conservation in Building and Community Systems Programme of IEA 

F far field boundary distance (m) 

h convective surface coefficient 

h,int interior convective surface coefficient 

h,ext exterior convective surface coefficient 

h.t. heat transfer 

IEA International Energy Agency 

IEA 34/43 IEA SHC Task 34/ECBCS Annex 43 

ISO International Organization for Standardization 

ksoil soil/slab thermal conductivity (W/(m⋅K)) 

L floor slab length in east/west direction 

N,E,S,W north, east, south, west 

NSRDB National Solar Radiation Data Base 

q heat flow (W or Wh/h) 

qfloor floor conduction (W or Wh/h) 

qfloor,max annual hourly integrated peak floor conduction (Wh/h or W) 

qzone zone load (W or Wh/h) 

qzone,max annual hourly integrated peak zone load (Wh/h or W) 

Qfloor annual total floor conduction (kWh/y) 

Qzone annual total zone load (kWh/y) 

SHC Solar Heating and Cooling Programme of IEA 

Tdg deep ground temperature (°C) 

Temp. temperature 

Ti interior slab surface temperature (°C) 

Ti,a zone air temperature (°C) 

To exterior ground surface temperature (°C) 

To,a ambient air temperature (°C) 

TODB,min minimum hourly ambient temperature (°C) 

tsim number of hours simulated (hours) 

Tsurf,n near-surface temperature (°C) 

T@surf,n at-surface temperature, Case GC10a only (°C) 

Tzone zone air temperature (°C) 

Tzone,mean annual average zone air temperature (°C) 

TMY2 typical meteorological year 2 

UA conductance (W/°C) 

W slab/soil perimeter boundary width or wall thickness 

WBAN Weather Bureau Army Navy 

38 
Appendix D. Glossary 

Note: This glossary highlights terms that are either already defined in ANSI/ASHRAE Standard 140-2007 

(ANSI/ASHRAE 2007), or may be included or revised in a later version of Standard 140. Italicized terms 

are defined elsewhere in the glossary. 

Adiabatic is without loss or gain of heat; an adiabatic boundary does not allow heat to flow through it. 

Analytical solution is the mathematical solution of a model that has an exact result for a given set of 

parameters and simplifying assumptions. 

Analytical verification is where outputs from a program, subroutine, algorithm, or software object are 

compared to results from a known analytical solution, or to results from a set of closely agreeing quasianalytical solutions or verified numerical models.

Annual hourly integrated peak floor conduction is the hourly floor conduction that represents the 

maximum for the final year of the simulation period. 

Annual hourly integrated peak zone load is the hourly zone load that represents the maximum for the 

final year of the simulation period. 

Aspect ratio is the ratio of the floor slab length to the floor slab width. 

Convective surface coefficient is a constant of proportionality relating the rate of convective heat 

transfer at a surface to the temperature difference across the air film on that surface. 

Convergence tolerance is, for an iterative solution process, the maximum acceptable magnitude of a 

selected error estimate; when the error criterion is satisfied, the process is considered to have converged 

on a sufficiently accurate approximate solution. 

Deep ground temperature is the ground temperature at the deep ground boundary depth. 

Detailed ground heat transfer model employs transient 3-D numerical-methods (finite-element or 

finite-difference) heat transfer modeling throughout the modeled domain. 

Mathematical truth standard is the standard of accuracy for predicting system behavior based on an 

analytical solution. 

Mid-level detailed ground heat transfer model is based on a transient 2-D or 3-D numerical-methods 

heat transfer model, applying some simplification(s) for adaptation to a whole-building energy simulation 

program; such models include correlation methods based on extensive 2-D or 3-D numerical analysis. 

Quasi-analytical solution is the mathematical solution of a model for a given set of parameters and 

simplifying assumptions, which may include minor interpretation differences that cause minor results 

variations; such a solution may be computed by generally accepted numerical methods or other means, 

provided that such calculations occur outside the environment of a whole-building energy simulation 

program and can be scrutinized.

Secondary mathematical truth standard is the standard of accuracy for predicting system behavior 

based on the range of disagreement of a set of closely agreeing verified numerical models or other quasianalytical solutions, to which other simulations may be compared. 

39 
Simplified ground heat transfer model is based on a 1-D dynamic or steady-state heat transfer model; 

implementation of such a model usually requires no modification to a whole-building energy simulation 

program. 

Verified numerical model is a numerical model with solution accuracy verified by close agreement with 

an analytical solution and/or other quasi-analytical or numerical solutions, according to a process that 

demonstrates solution convergence in the space and time domains. Such numerical models may be 

verified by applying an initial comparison with an analytical solution(s), followed by comparisons with 

other numerical models for incrementally more realistic cases where analytical solutions are not available. 

40 
Appendix E. Remarks about the Test Cases 

The following remarks relate to development of the test cases. 

GC30b 

k = 1.9 W/(m⋅K) matches upper limit of BASESIMP. 

Per M. Deru of NREL, an adiabatic far-field boundary condition is typically what ground heat transfer 

specialists have assumed for years, and a reasonable physical basis would be a similar neighboring 

building that generates similar isotherms. For a relatively large far-field dimension (F), the floor 

conduction heat will either have surfaced via the exterior ground surface or gone to the deep ground sink, 

which is also compatible with an adiabatic far-field assumption.

GC40b 

This is used as the base case for sensitivity tests of aspect ratio (GC45b), deep ground temperature 

(GC55b), etc. because: 

• Harmonic variation of outside air temperature variation provides a more realistic dynamic. 

• High convective surface coefficients provide a more uniform floor surface temperature, which 

may match assumptions of some simulations. 

• High convective surface coefficients allow more heat transfer overall (a more robust signal to 

work with). 

GC45b 

Per M. Deru of NREL, for much less than 4 m width there is little reduction in core surface area (where 

heat transfer is to deep ground boundary condition). 

GC50b 

Fifteen meter ground depth (same as GC30b) gives a good comparison of core and perimeter flux effects 

versus GC30b. Far-field dimension (F) = 15 m is consistent with GC30b; F much greater than 15 m is 

probably a waste of computer time (an issue when we model a lot of ground). 

GC60b 

h,int = 7.95 W/(m2

⋅K) was chosen because it is equal to the combined convective/radiative surface 

coefficient that is the hardwired assumption of BASESIMP. Note: the Standard-140 default combined 

surface coefficient for downward heat transfer on a horizontal surface is 6.13 W/(m2

⋅K), which is based 

on values of the 2005 ASHRAE Handbook of Fundamentals (p. 25.2).

To document the disagreement effect of BASESIMP’s geometry assumption differences, direct-input 

exterior surface temperature boundary conditions, and other assumptions, BASESIMP results for GC30c 

may be compared with other programs’ results for GC60b and GC65b (GC60b is better according to the 

verified numerical-model results), and BASESIMP results for GC40c may be compared with other 

programs’ results for GC70b. 

41 
GC80b 

A lower limit of k = 0.5 W/(m⋅K) was recommended by M. Deru of NREL as representative of dry clay. 

GC10a 

An additional aspect ratio test (Case GC15a?) in this context seems unnecessary unless the numericalmodel results disagree for Case GC45b. The current geometry incorporates elements of core driven and 

perimeter driven heat transfer in the results; a 36 m × 4m slab puts greater emphasis on perimeter heat 

transfer. If an AR test is included here, put surface temperature outputs along the narrower axis for that 

case to examine a more extreme temperature gradient than would occur over the longer axis; outputs 

remain symmetric along the diagonal. 

GC30c 

EnergyPlus can match the constraints of GC30c (and therefore GC40c, GC45c, and GC80c) except for 

the direct-input exterior surface temperature boundary condition. Use of h,ext = 120 W/(m2

⋅K) 

(approximate E+ limit) versus direct-input exterior surface temperature is expected to cause about 2% 

results variation.

GC80c 

k = 0.85 W/(m⋅K) is the lower limit for BASESIMP. 

Harmonic Weather Data 

Harmonic weather data have more than one occurrence of the minimum hourly ambient temperature 

because of limited precision allowed by TMY2 format. 

42 

SI to I-P Unit Conversions 

I-P units given in Part I were calculated during an early version of the test specification using conversion 

factors of ASHRAE (2001). Updated conversion factors published by ASHRAE (2005) yield slightly 

different values for I-P units. The effect of the difference is < 0.1% for the listed I-P values. 
Appendix F. Diagnosing the Results Using the Flow Diagrams

F.1 General Description 

Figures F-1, F-2, and F-3 contain a set of flow diagrams that serve as a guide for diagnosing the cause of 

disagreeing results that may arise from using this test. These flow diagrams list the features being tested 

and indicate potential sources of algorithmic differences. Flow diagrams are included here for the “a”-

series cases (Figure F-1), the “b”-series cases (Figure F-2), and the “c”-series cases (Figure F-3). For 

detailed numerical models the “a”-series cases are to be run first. For most other models the “b”-series 

cases should be run first. The “c”-series cases are for models that can match the constraints of NRCan’s 

BASESIMP model. 

For slab-on-grade models integrated with whole-building energy simulation programs, the flow diagrams 

may be used in two ways. The most powerful but time-consuming way is to perform all “b”-series and 

“c”-series cases (and the “a”-series cases if the model being tested is a detailed numerical model), and 

then use the diagnostic logic in the flow diagrams to analyze the results. The least time-consuming way is 

to perform the tests in sequence according to the flow diagrams, beginning with Figure F-1 for detailed 

numerical models, and Figure F-2 for other less detailed models. 

F.2 Comparing Tested Software Results to Verified Numerical-Model Results and 

Example Simulation Results 

Verified numerical-model and example simulation results are presented in Part III. At a minimum, the 

user should compare output with the verified numerical-model results. The user may also choose to 

compare output with the example simulation results, or with other results that were generated with this 

test procedure. Information about how the analytical solutions and example simulation results were 

produced is included in the modeler reports of Part II (Section 2.9). For convenience to users who wish to 

plot or tabulate their results along with the analytical solution or example simulation results, or both, an 

electronic version of the example results has been included with the file GC-InDepth-Results.XLS with 

the accompanying electronic files. 

There are no formal for when results agree or disagree; determination of the agreement or disagreement of 

results is left to the user. In making this determination, the user should consider that the verified 

numerical-model results represent a “secondary mathematical truth standard” based on acceptance of the 

underlying physical assumptions represented by the case specifications. The authors recognize that the 

underlying physical assumptions of the case definitions are a simplification of reality and may not fully 

represent empirical behavior. As discussed in Part I, Section 1.2.2.1, in making a determination about the 

agreement of results, the user should also consider: 

• Magnitude of results for individual cases 

• Magnitude of difference in results between certain cases (e.g., “Case GC45b–Case GC40b”) 

• Same direction of sensitivity (positive or negative) for difference in results between certain cases 

(e.g., “Case GC45b–Case GC40b”) 

• If results are logically counterintuitive with respect to known or expected physical behavior 

• Availability of analytical solution or verified numerical-model results (i.e., a mathematical truth 

standard or secondary mathematical truth standard) 

• Where a mathematical or secondary-mathematical truth standard is provided, the degree of 

disagreement that occurred for other simulation results versus such an analytical-verification truth 

standard 

• Example simulation results – other than the verified numerical-model results – do not represent a 

secondary mathematical truth standard. 

43 
Check the program being tested for agreement with verified numerical-model results for the absolute 

outputs and the sensitivity (or “delta”) outputs. For example, when comparing to the analytical solution 

results for Case “GC45b–GC40b” in Figure F-2, the program results are compared with the Case GC45b 

results and the Case GC45b–GC40b sensitivity results. 

Compare all available output types specified for each case that can be produced by the program being 

tested. This includes appropriate floor conduction, zone heating load, peak-hour results, and supporting 

results presented in Part III, for all the listed output that the software being tested can produce. A 

disagreement with any output type may be cause for concern. 

Performing/analyzing results of the tests in logical blocks as shown in the flow diagrams, or all at once 

for each series of cases, is recommended. The diagnostic logic indicates that for some cases (e.g., GC45b) 

if a disagreement is uncovered other cases (e.g. GC50b) may be run without fixing the previous 

disagreement. However, the found disagreement should be fixed if possible, and all the cases rerun. 

The flow diagram of Figure F-2 begins with a basic performance test (Case GC30b). It is very important 

to have confidence in your Case GC30b results before proceeding to the other cases. If output from the 

tested program agrees satisfactorily with the verified numerical-model results for Case GC30b, continue 

to check output for the remaining cases according to the flow diagram. If output from the tested program 

disagrees with verified numerical-model results for Case GC30b, check for input errors. If no input error 

is found, run all other test cases and follow the diagnostic logic accordingly, as this may help to isolate 

the source of the difference to one of the specifically tested parameters. 

In some cases it is possible to proceed even if disagreements were uncovered in the previous case. For 

example, in Case GC55b, the inability to model a shallow deep ground boundary (water table) depth does 

not necessarily affect the usefulness or testability of the program for modeling scenarios with more 

typical deep ground boundary depth. Thus, the flow diagram has an extra arrow connecting Case GC55b 

and Case GC70b, which denotes that you may proceed regardless of the results for Case GC55b. Where 

cases are connected by a single arrow, a satisfactory result is required to proceed to the next case. For 

example, in Case GC60b, the inability to model the effect of the realistic interior surface coefficient 

makes it difficult to proceed with Case GC65b until the disagreement is reconciled. 

When testing detailed numerical models with the “a”-series cases, experience from field trials of the test 

procedure indicates to initially begin by checking the results of each case individually before moving on 

to additional cases. Specifically, first run only Case GC10a and check the results versus the analytical 

solution. If the result is satisfactory, move on to only Case GC30a, and similarly for GC40a, then GC30b, 

then GC40b, as each addresses a fundamental change in boundary conditions for steady-state and 

dynamic modeling. After each case is checked, it is reasonable to proceed with batch-running the 

remaining cases: recommend to run GC60b, GC65b and GC30c as one batch followed by the remaining 

“b”- and “c”-series dynamic cases. Because of geometry variations for GC45b, GC45c, and GC50c it may 

be preferable to run those cases last.

F.2.1 If Tested Software Results Disagree with Example Results 

If the tested program shows disagreement with the verified numerical-model results, recheck the inputs 

against the specified values. Use the diagnostic logic flow diagrams to help isolate the source of the 

difference. If no input error can be found, look for an error in the software. If an error is found, fix it and 

rerun the tests. If in the engineering judgment of the user the disagreement is caused by a reasonable 

difference in algorithms between the tested software and the example results, continue with the next test 

case. 

44 
F.2.2 Example 

A program shows disagreement with GC80b. Figure F-2 suggests the potential source of algorithmic 

differences includes modeling of interior and exterior surface heat transfer coefficients. The user is 

directed to check diagnostics B1 and B2. If the disagreement persists for B1, the cause is likely related to 

modeling of the slab interior surface heat transfer coefficient. If there is no disagreement for B1, go on to 

B2. If the disagreement appears for B2, its cause is likely related to modeling the exterior surface heat 

transfer coefficient. If there is no disagreement for B1 or B2, the difference could be related to dynamic 

modeling versus steady-state modeling or some other problem. 

Section 2.4 (Part II) gives examples of how the tests were used to trace and correct specific algorithmic 

and input errors in the programs used in the field trials. 

START "a"-Series

(Detailed Numerical-Methods Models Only) PROBABLE CAUSE OF DISAGREEMENT

Analytical Solution Base Case

GC10a D Linearly Varying Perimeter Surface Temperature;

Constant/Uniform Slab and Soil Surface Temps.;

A Basic Modeling (e.g., Node Meshing)

GC30a & (GC30a-GC10a) D Adiabatic Perimeter Surface Boundary

GC30b & (GC30a-GC30b) D h,int = h,ext = 100 W/m2

K (Steady-State Model)

A

GC40a & (GC40a-GC30a) D Dynamic versus Steady-State Modeling

GC40b & (GC40a-GC40b) D h,int = h,ext = 100 W/m2

K (Dynamic Model)

& (GC40b-GC30b) D Dynamic versus Steady-State with h,int and h,ext

A

GOTO Continue A, and Remaining "b"-Series Dynamic Cases

AND

GOTO Continue SSb (remaining Steady-State Cases)

ABBREVIATIONS

 A = Agree; D = Disagree. For these test cases, agreement/disagreement is determined relative to quasi-analytical

 solution results, including listed sensitivity cases.

Figure F-1. Diagnostic logic flow diagram “a”- series cases 

45 
START PROBABLE CAUSE OF DISAGREEMENT DIAGNOSE (GOTO)

Steady-State Base Case

GC30b D Constant ODB; h,int = h,ext = 100 W/m2

K;

ksoil = 1.9 W/mK; adiabatic above-grade wall

A

("b"-Series Dynamic Cases)

Steady-Periodic Base Case

GC40b & (GC40b-GC30b) D Harmonic ODB; h,int = h,ext = 100 W/m2

K; CONTINUE SSb

ksoil = 1.9 W/mK; adiabatic above-grade wall

A

A GC45b & (GC45b-GC40b) D Aspect Ratio, high perimeter h.t. fraction

A

GC50b & (GC50b-GC40b) D Slab Area, high core heat transfer fraction

A

GC55b & (GC55b-GC40b) D Shallow Deep Ground Temperature Depth,

high core heat transfer fraction

A

GC70b & (GC70b-GC40b) D Interior and Exterior Surface Coefficients CONTINUE B1 & B2

h,int = 7.95 W/m2

K; h,ext = 11.95 W/m2K (SSb)

A

GC80b & (GC80b-GC40b) D Slab/Soil Conductivity, ksoil = 0.5 W/mK

A

END

CONTINUE SSb (Steady-State Cases)

B1 GC60b & (GC60b-GC30b) D Interior Surface Coeff., h,int = 7.95 W/m2

K

(Steady-State Model)

A

B2 GC65b & (GC65b-GC60b) D Exterior Surface Coeff., h,ext = 11.95 W/m2

K

(Steady-State Model)

A

STOP

ABBREVIATIONS

 A = Agree; D = Disagree. For these test cases, agreement/disagreement is determined relative to quasi-analytical

 solution results, including listed sensitivity cases.

Figure F-2. Diagnostic logic flow diagram for “b”- series cases 

46 
START ("c"-Series Diagnostic Logic) PROBABLE CAUSE OF DISAGREEMENT

"c"-Series Steady-State Base Case

GC30c D Constant ODB; h,int = h,ext = 100 W/m2

K;

ksoil = 1.9 W/mK; adiabatic above-grade wall

A

"c"-Series Steady-Periodic Base Case

GC40c & (GC40c-GC30c) D Harmonic ODB; h,int = h,ext = 100 W/m2

K;

ksoil = 1.9 W/mK; adiabatic above-grade wall

A

GC45c & (GC45c-GC40c) D Aspect Ratio, high perimeter h.t. fraction

A

GC55c & (GC55c-GC40c) D Shallow Deep Ground Temperature Depth,

high core heat transfer fraction

A

GC80c & (GC80c-GC40c) D Slab/Soil Conductivity, ksoil = 0.85 W/mK

A

END

ABBREVIATIONS

 A = Agree; D = Disagree. For these test cases, agreement/disagreement is determined relative to quasi-analytical

 solution results, including listed sensitivity cases.

Figure F-3. Diagnostic logic flow diagram for “c”- series cases 

47 
References for Part I 

ANSI/ASHRAE Standard 140-2007. Standard Method of Test for the Evaluation of Building Energy 

Analysis Computer Programs. (2007). Atlanta, GA: American Society of Heating, Refrigerating, and AirConditioning Engineers. 

ASHRAE. (2005). Handbook of Fundamentals. Atlanta, Georgia, US: American Society of Heating, 

Refrigerating and Air-Conditioning Engineers. 

ASHRAE. (2001). Handbook of Fundamentals. Atlanta, Georgia, US: American Society of Heating, 

Refrigerating and Air-Conditioning Engineers. 

Brandemuehl M. (1993). HVAC 2 Toolkit. Atlanta, Georgia, US: American Society of Heating, 

Refrigerating and Air-Conditioning Engineers. (See p. 7-15.) 

Delsante A.E.; Stokes, A.N.; Walsh, P.J. (1983). Application of Fourier Transforms to Periodic Heat 

Flow into the Ground under a Building. International Journal of Heat Mass Transfer, 26(1): 121-132. 

Judkoff, R.; Neymark, J. (1995). International Energy Agency Building Energy Simulation Test 

(BESTEST) and Diagnostic Method. NREL/TP-472-6231, Golden, Colorado, US: National Renewable 

Energy Laboratory. www.nrel.gov/docs/legosti/old/6231.pdf. 

Marion, W.; Urban, K. (1995). User’s Manual for TMY2s. Golden, Colorado, US: National Renewable 

Energy Laboratory. 

Spitler, J.D.; Rees, S.J.; Xiao, D. (2001). Development of an Analytical Verification Test Suite for Whole 

Building Energy Simulation Programs – Building Fabric. Final Report for ASHRAE 1052-RP. Atlanta, 

Georgia, US: American Society of Heating, Refrigerating and Air-Conditioning Engineers. 

Walton, G. (1983). Thermal Analysis Research Program Reference Manual (TARP). NBSIR 83-2655. 

Washington, D.C.: National Bureau of Standards (now called National Institute of Standards and 

Technology).

48 
Part II: Production of Simulation Results 

2.1 Introduction 

In this section we describe what the working group members did to produce quasi-analytical solutions 

with verified state-of-the-art numerical models, along with other example results for several mid-level 

detailed models typically used with state-of-the-art whole-building energy simulation programs in Europe 

and North America. The objectives of developing the simulation results were to: 

• Demonstrate the applicability and usefulness of the Building Energy Simulation Test In-Depth 

Diagnostic Cases for Ground-Coupled Heat Transfer Related to Slab-on-Grade Construction test 

suite. 

• Improve the test procedure through field trials. 

• Identify the range of disagreement that may be expected for simulation programs relative to each 

other (see Part III). 

• Establish a methodology for developing a secondary mathematical truth standard based on the range 

of disagreement of verified numerical models. 

The field trial effort took about 3 years and involved revisions to the test specifications and subsequent reexecution of the computer simulations. The process was iterative in that executing the simulations led to 

the refinement of the test suite, and the results of the tests led to improving and debugging the groundcoupled heat transfer models in the programs. This process underscores the importance of International 

Energy Agency (IEA) participation in this project; such extensive field trials, and resulting enhancements 

to the tests, were much more cost-effective with the participation of the IEA Solar Heating and Cooling 

(SHC) Programme Task 34/Energy Conservation in Buildings and Community Systems (ECBCS) Annex 

43 experts. 

Table 2-1 describes the models used to generate the simulation results. Appendix II (Section 2.9) presents 

reports written by the modelers for each simulation program. 

The tables and graphs in Part III present the final results from all the models used in this study. 

Abbreviations and acronyms used in Sections 2.2 through 2.6 are given in Section 2.7. References cited in 

Section 2.2 through 2.6 are given in Section 2.8. 

49 
Table 2-1. Participating Organizations and Models 

Analytical Solution, 

Case GC10a Authoring Organization Implemented by

Delsante, Stokes, and 

Walsh (1983) 

Commonwealth Scientific and Industrial 

Research Organisation, Australia NREL/JNA, a,b United States 

Verified Numerical 

Model Authoring Organization Implemented by

FLUENT 6.0.20 Fluent, Incorporated, United States PAAET,c Kuwait 

MATLAB 7.0.4.365 (R14) The MathWorks, Inc., United States Dublin Institute of Technology, Ireland 

TRNSYS 16.1 University of Wisconsin/TESS,d United States TESS,d United States 

Simulation Program Authoring Organization Implemented by

BASECALC V1.0e CETC,e

 Canada CETC,e Canada 

EnergyPlus 2.0.0.025 LBNL/UIUC/DOE-BT,f,g,h United States GARD Analytics, Inc., United States 

ESP-r/BASESIMP CETC/ESRU,e,i Canada/United Kingdom CETC,e

 Canada 

GHT NREL,a

 United States NREL,a United States 

SUNREL-GC 1.14.01 NREL,a

 United States NREL,a United States 

VA114 2.20/ISO-13370 VABI Software BV, The Netherlands; 

CEN/ISOj,k VABI Software BV, The Netherlands 

a

NREL: National Renewable Energy Laboratory, United States 

b

JNA: J. Neymark & Associates, United States 

c

PAAET: Public Authority for Applied Education and Training, Kuwait 

d

TESS: Thermal Energy Systems Specialists, United States 

e

CETC: CANMET Energy Technology Centre, Natural Resources Canada, Canada 

f

LBNL: Lawrence Berkeley National Laboratory, United States 

g

UIUC: University of Illinois Urbana/Champaign, United States h

DOE-BT: U.S. Department of Energy, Office of Building Technologies, Energy Efficiency and Renewable Energy, United States 

i

ESRU: Energy Systems Research Unit, University of Strathclyde, United Kingdom 

j

CEN: European Committee for Standardization, Belgium 

k

ISO: International Organization for Standardization, Switzerland

2.2 Selection of Simulation Programs and Modeling Rules for Simulations 

The countries participating in this IEA task made the initial selections of the simulation programs used in 

this study. For the numerical models used to develop quasi-analytical solutions, the selection criteria 

required: 

• 3-D modeling 

• Ability to model all boundary conditions of Case GC10a, for true analytical verification 

• Adjustable node meshing 

• Adjustable duration of simulation (e.g., more than 5 years) 

• Adjustable convergence tolerance, where applicable 

• Adjustable ground depth and far-field dimensions 

• Calculative time increments of 1 hour or less 

50 
• Meeting quasi-analytical solution definitional requirements 

o Calculations occur outside the environment of a whole-building energy simulation program 

(i.e., a means to run the slab/ground model by itself without interacting with additional 

calculation routines of a larger whole-building simulation) 

o Ability to scrutinize calculations (supporting input files and detailed modeler reports provided). 

For the mid-level detailed models, the selection criteria required: 

• The whole-building simulation program platform be a true simulation based on hourly weather data 

and calculative time increments of 1 hour or less, and be representative of the state-of-the-art in 

whole-building energy simulation as defined by the country making the selection. 

• The mid-level detailed ground heat transfer model used by the whole-building simulation platform 

be representative of the state-of-the-art as defined by the country making the selection. 

The modeling rules were somewhat more stringent for the simulation programs used for Part III example 

results than for a given program to be normally tested with this BESTEST suite (see Section 1.2.1, 

Modeling Rules). For the Part III simulation results, we allowed a variety of modeling approaches. 

However, we required that these cases be modeled in the most detailed way possible for each simulation 

program. Whenever possible with all ground-coupled heat transfer models (required for verified 

numerical models) demonstrate that modeling is at a level of detail where including further detail yields 

negligible sensitivity (0.1% or lower) to results versus the previous level of detail. Sensitivity tests, when 

possible (required for verified numerical models), should cover at least the following aspects of the 

models: node mesh detail, simulation duration (for non-steady-state cases or when dynamic models are 

applied to steady-state cases), convergence tolerance (when applicable), and amount of ground modeled 

(for Case GC10a only). Such sensitivity tests may be performed for a subset of the test cases if the 

modeler can logically demonstrate that the appropriate level of detail identified for a given case (e.g. 

GC40a or GC40b) will also be appropriate for other cases (GC70b, etc.). 

To minimize the potential for user error, we encouraged more than one modeler to develop input files for 

each program. Where only a single modeler was involved, we strongly recommended that another modeler 

familiar with the program check the inputs carefully. 

Where improvements to simulation programs or simulation inputs were made as a result of running the 

tests, such improvements must have a mathematical and physical basis, and must be applied consistently 

across tests. In addition, all improvements were required to be documented in modeler reports. Arbitrary 

modification of a simulation program’s input or internal code just for the purpose of more closely 

matching a given set of results is not allowed. The diagnostic process of trapping bugs discussed in Section 

2.4 also isolated input errors that were corrected, as noted there and in the modeler reports (Section 2.9). 

2.3 Improvements to the Test Specification as a Result of the Field Trials 

Based on comments by the IEA SHC Task 34/ECBCS Annex 43 participants during the field trials, we 

made a number of improvements and revisions to the test specification. Although researching the 

comments and communicating specification revisions to the field trial participants was very time 

consuming, the importance of the accuracy and clarity of the test specification for this type of work 

cannot be overstated. 

The contribution of the IEA SHC Task 34/ECBCS Annex 43 participating countries was particularly 

valuable because the project experts supplied continuous feedback throughout the 3-year field trial effort. 

Their feedback resulted in several revisions to the test specifications and subsequent re-execution of the 

computer simulations. This iterative process led to refinement of the test cases, and the results of the tests 

51 
led to the improvement and debugging of the programs. The process underscores the leveraging of 

resources for the IEA countries participating in this project. Such extensive field trials, and resulting 

enhancements to the tests, would not have occurred without the participation of the IEA SHC Task 34/ 

ECBCS Annex 43 experts. 

2.3.1 Revisions to the Initial Draft Test Specification 

The initial draft of these in-depth diagnostic test cases was issued in June 2004. The parametric sensitivity 

tests in that version formed the basis of the current test cases; details were revised for the final version as 

documented below. 

Observations of the initial results based on simulations of the June 2004 version of the test specification 

indicated the following issues. 

• Convective surface coefficients > 100 W/(m2⋅K) are too high for some models. 

• The base case ground depth (60 m) is too deep for some models. 

• Case GC50’s 200 m × 200 m slab is too large for the models. 

• NRCan identified a number of hardwired assumptions and limitations in BASECALC and 

BASESIMP that caused modeling difficulties for the GC30 base case, along with inability to 

model (or fully model) several of the sensitivity test cases. NRCan requested specification of at 

least one test case for directly comparing BASECALC/BASESIMP/ESP-r to the detailed 

numerical models. 

Based on these issues, other participant comments, and further consideration by the lead authors, the 

following revisions were made for the June 2005 version of the test specification: 

• To accommodate the wide variety of capabilities and constraints of participating software, the 

number of test cases was expanded from 9 to 17, and subdivided into 3 categories: 

o “a”-series cases to demonstrate proper application of detailed numerical models (3 cases) 

o “b”-series cases to test mid-level detailed models used with whole-building energy 

simulation programs (9 cases) 

o “c”-series cases conforming to specific BASESIMP model constraints (5 cases). 

• Test case revisions included a number of parameter adjustments for better compatibility with the 

simulation models, and more robust sensitivity tests, including: 

o Ground conductivity change from 2.0 W/(m⋅K) to 1.9 W/(m⋅K) for all test cases, to be 

compatible with BASESIMP’s allowable maximum value. 

o Ground depth (E) and far-field (F) dimensions were reduced from 60 m and 40 m, 

respectively, as follows: 

- For “a”-series cases (except GC10a), E = 30 m and F = 20 m; per TRNSYS 

sensitivity tests greater values do not affect results (but cause longer run times). 

- For “b”-series cases (except GC50b and GC55b), E = 15 m and F = 15 m; 15 m 

ground depth allowed EnergyPlus to use its automated grid feature (EnergyPlus 

has since been revised to facilitate use of this feature), and E = 15 m matches 

BASESIMP’s maximum depth; per TRNSYS sensitivity tests for E = 15 m, F > 

15 m does not affect results (but causes longer run times). 

- For “c”-series cases (except GC55c), E = 15 m and F = 8 m, to match 

BASESIMP maxima. 

o Convective surface coefficients (h,int and h,ext) were changed from 5000 W/(m2⋅K) for 

various cases as follows: 

52 
- For GC30a and GC40a, h,int = h,ext = infinity, which is equivalent to directly 

applying a uniformly constant or uniformly varying surface temperature 

boundary condition to an entire given surface. 

- For “b”-series cases (except where h is varied in GC60b, GC65b, and GC70b), 

h,int = h,ext = 100 W/(m2

⋅K), which results in roughly 4% reduced floor 

conduction versus a constant temperature boundary condition. 

- For GC60b, GC65b, and GC70b, h,int = 7.95 W/(m2

⋅K), to match BASESIMP’s 

assumption for combined convective and radiative heat transfer; this value falls 

between ASHRAE’s (2005, p. 25.2) listing of 6.13 W/(m2

⋅K) for downward heat 

transfer on a horizontal surface and BESTEST’s (Judkoff and Neymark 1995a) 

default of 8.29 W/(m2

⋅K) for programs that do not allow scheduling of horizontal 

surface coefficients. For simplification of the test specification h,int = 7.95 

W/(m2

⋅K) is specified as a convection-only coefficient, along with surface 

emittance = 0 (or as low as possible) so that radiative exchange is suppressed. 

- For GC65b and GC70b, h,ext = 11.95 W/(m2

⋅K), which is consistent with wind 

speed of 1.0 m/s (Walton 1983; Judkoff and Neymark 1995a). 

- For “c”-series cases, h,int = 7.95 W/(m2

⋅K) and h,ext = infinity (directly applied 

surface temperature boundary condition); this matches the BASESIMP 

assumptions. 

o For Case GC10a appropriate mesh detail demonstration, added specification “For ground 

depth and far-field length variations, increase the number of mesh nodes proportionally to 

the increase in soil volume.” 

o Aspect ratio of 24 m × 6 m of Case GC45 was changed to 36 m × 4 m for cases GC45b 

and GC45c, which gives a more robust sensitivity test versus GC40b and GC40c; further 

increasing this ratio would cause negligible further decrease in the “core” surface area 

(area over which heat flow is generally considered to go to deep ground rather than to the 

exterior perimeter surface). 

o Ground depth (E) of Case GC55 was changed from E = 3 m as follows 

- For GC55b, E = 2 m, for more robust sensitivity test 

- For GC55c, E = 5 m, to match BASESIMP minimum. 

• Ground conductivity test cases were added with soil/slab conductivities (k) as: 

o For GC80b, k = 0.5 W/(m⋅K) (realistic minimum for dry clay) 

o For GC80c, k = 0.85 W/(m⋅K) (to match BASESIMP minimum soil conductivity). 

• Added specification to demonstrate that next level of detail for convergence tolerance changes 

heat flow results by 0.1% or lower. 

• Added specification that for models requiring input of slab thickness, use the least slab thickness 

allowed by the model. 

• For cases GC40a, GC40b, and GC40c, added specification for hourly outputs for the last full year 

of the simulation for ODB and floor conduction, and to describe the simulation’s time convention 

(e.g., hour 1 = 0:00–1:00 or 0:30–1:30). 

• New weather data files were provided as follows: 

o GCSS-W20.TM2 and GCSP-W20.TM2 were provided for the “b”-series test cases; these 

have wind speed set to 19.9 m/s to match h,ext = 100 W/(m2

⋅K) (Walton 1983; Judkoff 

and Neymark 1995a). 

o GCSS-W01.TM2 and GCSP-W01.TM2 were provided for GC65b and GC70b; these 

have wind speed set to 1.0 m/s to match h,ext = 11.95 W/(m2

⋅K) (Walton 1983; Judkoff 

and Neymark 1995a). 

o GCSS-W40.TM2 and GCSP-W40.TM2 were provided for GC30a, GC40a, and the “c”-

series cases; these have wind speed set to 40.0 m/s, which is the maximum value 

documented in the TMY2 data manual (Marion and Urban 1995). 

53 
• The test specification was reorganized to present GC30b as the primary base case, presuming that 

most programs being tested would primarily apply the “b”-series cases. 

• Added specification of modeling rules to match HVAC BESTEST Volume 2 (Neymark and 

Judkoff 2004), Section 1.2.2. 

• Added section “Comparing Your Output to the Analytical Solution and Example Simulation 

Results” based on HVAC BESTEST Volume 2 (Neymark and Judkoff 2004), Section 1.2.3. 

• Editorial revisions. 

As the 200 m × 200 m slab initially proposed for Case GC50 was too large for the programs (that tried) to 

model, modifications were proposed (for discussion) to reduce the slab area to 80 m × 80 m, which would 

be the maximum allowed by EnergyPlus and would have a more reasonable run time. Deep ground 

boundary depth of 20 m (new EnergyPlus maximum for automated grid) versus 15 m (as in GC40b) was 

also discussed among the participants. Far-field dimension of 60 m was also proposed. 

2.3.2 Second Round of Revisions 

The primary observation regarding the second iteration of results, based on simulations of the June 2005 

version of the test specification, was the importance of understanding the geometry assumptions of the 

various models as well as possible. To address this issue, a proforma model description template (table) 

was developed by NREL and distributed to the project participants in November 2005. The proforma 

template surveyed modeling capabilities and assumptions with respect to geometry and material 

properties, with the intent to revise the test cases, if appropriate, based on the results of the survey. 

Conclusions of the proforma survey were that for the “b”-series test cases, the current test case geometry is 

appropriate for the variety of models being tested, and that use of uniform material properties (floor slab = 

foundation wall = footer = soil) is appropriate for the models. 

For the “c”-series cases, which apply the same geometry as the “b”-series cases, NRCan noted that the 

BASECALC/BASESIMP slab-on-grade model (which is derived from their basement model) assumes that 

the floor slab upper surface is 5 cm below grade, and that assumptions about above-grade wall material 

properties are also included in this model. Because locating a slab floor surface 5 cm below grade is not 

typical for slab-on-grade construction, and because BASECALC’s most insulating above-grade wall (k = 

0.1 W/(m⋅K)) is not adiabatic (which could compensate for the additional soil resistance for the 5 cm belowgrade slab), the specified “c”-series case geometry was not changed. 

Based on the observations and recommendations from field trials of the June 2005 version of the test 

specification, the following revisions were made for the test specification version dated March 2006: 

 

• Deleted hourly ODB from output requirements for GC40a, GC40b, and GC40c; reporting 8760 

hours of ODB is unnecessary as minimum ODB and time of occurrence are already reported, and 

hourly ODB is given in the raw weather data. 

• Defined ground/adiabatic wall interface temperatures (for cases GC30a, GC30b, GC60b, GC65b) 

as for uppermost-modeled layer of soil just below the interface; surface temperatures at 

soil/adiabatic wall interface are not definable. 

• Rearranged steady-state surface temperatures in the output spreadsheet template to facilitate chart 

development. 

• Added GC50b large slab case using 80 m × 80 m floor slab with ground depth (E) of 15 m and farfield dimension (F) of 15 m. 

• Added clarifications including: 

o Schematic diagram of slab edge detail 

54 
o Uniform scaling in figure for Case GC30b, which defines floor slab and conditioned zone 

dimensions 

o Foundation wall dimensions (if needed) are as small as the software being tested allows; 

foundation wall material properties same as soil 

o Floor conduction output is specifically through area of B × L at interior of slab surface 

o If software doesn’t have different outputs for floor load and zone conduction, report only 

one of them. 

• Added clauses from ANSI/ASHRAE Standard 140-2004, Addendum b (ANSI/ASHRAE 2004b) 

regarding: 

o Equivalent modeling methods (ANSI/ASHRAE 2007, Section 5.1.5) 

o To include input files with final results (ANSI/ASHRAE 2007, Section 4.3.2) 

o Explaining test case results omissions (ANSI/ASHRAE 2007, Section 4.3.1) 

o Changes to software must have a logical basis (revisions to previous language) 

(ANSI/ASHRAE 2007, Section 4.4.3). 

• Added proforma survey materials to modeler report template. 

• Editorial revisions. 

2.3.3 Third Round of Revisions 

Field trials of the March 2006 test specification engendered further revisions as listed below: 

• Previously required output of cumulative first 3-year floor conduction was deleted, because 

o Many mid-level detailed programs give only 1 year of output 

o Detailed numerical models that run a true steady-state simulation cannot give this result 

o Detailed numerical dynamic models can have results differences caused by differences in 

initial conditions 

o Cases with harmonically varying temperature boundary conditions address dynamic 

mass-storage behavior of the models. 

• Redefined all surface temperature outputs for GC10a, GC30a, GC30b, GC60b, and GC65b as for 

uppermost-modeled layer of soil (“near-surface”) just below the interface (consistent depth); this 

matches the actual final results submitted by the IEA-34/43 project participants. Previously, we 

requested at-surface temperatures except for at the soil/adiabatic wall interface, which caused an 

inconsistency in the temperature profiles. For GC10a, at-surface temperature results are also 

specified in addition to “near-surface” temperatures, to check proper application of boundary 

conditions. 

• Clarified that peak hour results are annual hourly integrated peak results; this matches the actual 

final results submitted by the IEA-34/43 project participants. 

Additional minor clarifications were made for the final version of the user’s manual, including: 

• Introductory discussion of the development of quasi-analytical solutions based on verified 3-D 

numerical models to be used as a secondary mathematical truth standard for comparing other 

simulation results. Other relevant language was revised throughout to be consistent with this 

discussion. 

• Typical users to apply consistent modeling methods; IEA-34/43 field trial participants applied most 

detailed methods their program allowed. 

o For “b”- and “c”-series cases, for typical users we relaxed (to a recommendation) the IEA34/43 participant requirement to demonstrate (where possible) that the modeling is at a 

level of detail where including further detail (node meshing, simulation duration, etc.) 

yields negligible sensitivity to results. 

55 
o For the “a”-series cases the requirement remains to demonstrate that modeling is at a level 

of detail where including further detail yields negligible sensitivity to results. 

• For Case GC10a, clarified the definition of semi-infinite solid; this matches the assumption of the 

IEA-34/43 numerical-methods modelers (where they had demonstrated that their finite ground 

depth and far-field dimensions were large enough to well-approximate a semi-infinite domain). 

• For convenience to future users we added the following appendices: 

o Appendix C, “Abbreviations and Acronyms” 

o Appendix D, “Glossary” 

o Appendix E, “Remarks about the Test Cases”; this consolidates informational remarks 

previously included with each case into one section (for background) 

o Appendix F, Diagnosing the Results Using the Flow Diagrams. 

• Editorial revisions 

o Section, table, and figure numbering 

o Other miscellaneous. 

2.4 Examples of Error Trapping with BESTEST Diagnostics 

This section summarizes examples that demonstrate how the IEA BESTEST in-depth diagnostic cases for 

ground-coupled heat transfer related to slab-on-grade construction were used to isolate and correct bugs in 

the simulation programs used for the field trials of the test specification. Further descriptions may be found 

in the individual modeler reports presented in Appendix II (see Section 2.9). 

Simulations were performed for each test case with the participating computer programs. At each stage of 

the exercise, output data from the simulations were compared to each other, to numerical-models being 

developed as quasi-analytical solutions, and to the Case GC10a analytical solution, according to the 

diagnostic logic of the test cases. The test diagnostics revealed (and led to the correction of) bugs, faulty 

algorithms, input errors, or some combination of those in all of the models. In the following examples 

improvements to the numerical models that were used for developing quasi-analytical solutions (i.e. 

TRNSYS, PAAET’s FLUENT model, and DIT’s MATLAB model) are presented first in sections 2.4.1 to 

2.4.3. Improvements and issues identified for other models (e.g., EnergyPlus, VA114/ISO-13370, 

BASESIMP/ESP-r, BASECALC, and SUNREL-GC) follow in sections 2.4.4 to 2.4.7. 

2.4.1 TRNSYS Version 16.1 

TRNSYS (Klein et al. 2007) is a modular system simulation tool that has been widely used in the study of 

buildings, renewable energy technologies, and HVAC systems. The program was originally written by the 

Solar Energy Laboratory at the University of Wisconsin; but recently has been maintained, supported, and 

distributed by a consortium of international companies and government agencies. TRNSYS Version 16.1 

was used for the most recent analysis as well as an extended library of TRNSYS components written by 

Thermal Energy System Specialists (TESS) LLC of Madison, WI. The 3-D numerical finite difference 

ground conduction model used for this analysis is part of the commercially available TESS ground-coupling 

library for TRNSYS. This model was established as a quasi-analytical solution method based on rigorous 

comparison with the Case GC10a analytical solution and comparison with the FLUENT and MATLAB 

detailed 3-D numerical-model results for other cases. 

2.4.1.1 First noding algorithm improvement, 10% floor conduction increase for Case 

GC10 

The original preliminary model – applied before the January 2005 initial TRNSYS results were submitted – 

employed a user-specified number of nodes along the slab and in the near field (X and Y directions) as well 

56 
as a user-specified number of nodes in the depth direction. In this case a 22 × 22 × 22 mesh of uniformly 

spaced nodes for a model of one-fourth of the slab (maximum amount of rectangular slab/soil volume 

needed for application of symmetry principles) was employed. As shown in Table 2-2, this model had a 

nearly 12% disagreement versus the analytical solution. (Thornton 2007a). For the January 2005 field trial 

results submittal, the assumption of uniformly sized nodes under the slab was changed to a user-specified 

number of nodes under the slab with the nodes growing in size by a factor of 2 as they progressed inward, 

outward and downward from the edges of the slab. As shown in Table 2-2 (see results labeled “1/14/05”), 

this improvement caused a 10% increase in floor conduction versus the original node mesh, but still had 

about a 3% disagreement with the analytical solution. 

Table 2-2. Initial Results for the TRNSYS Ground Heat Transfer Model 

 Steady-State Analytical Verification, Case GC10

qfloor % Difference versus

(W) Analytical Solution

Analytical Solution 2561 --

TRNSYS (Initial Results) 2261 -11.71%

TRNSYS (Results of 1/14/05) 2486 -2.93%

2.4.1.2 Second noding algorithm improvement, 2% floor conduction increase for Case 

GC10a 

For the next improvement an automatic noding scheme was applied using 

1 * − = i

i Nom XSizeSize

where SizeNom is the user input size of the smallest node (typically 1 inch); X is a user-input scalar 

(typically 1.2 to 2); and i is a nodal indicator (1 = next to the slab/surface). The algorithm also limits the size 

of i, keeping identical size nodes beyond a fixed point. This algorithm groups small nodes close to the edges 

and soil surface and increases the sizes of the nodes as they progress away from these edges. The results for 

this new algorithm (submitted in June 2005) applied the following specifications: 

• SizeNom = 1 inch 

• X = 1.5 to 2, depending on the test 

• Maximum i = 10. 

These results are shown in Table 2-3 (labeled “6/21/2005”) along with the results submitted in January 2005 

(labeled “1/14/2005”). Note when comparing “1/14/05” versus “6/21/05” results in this table that there are 

specification differences for cases GC30 versus GC30a and GC40 versus GC40a, where the “a”-series cases 

specify ksoil = 1.9 and constant temperature surface boundaries, and the prior preliminary series cases 

specified ksoil = 2.0 along with interior and exterior surface coefficients of h = 5000 W/(m2

⋅K). The 

difference in ground conductivity should reduce floor conduction in the “a”-series cases versus the 

preliminary cases; the effect of varying the surface boundary condition should be negligible, as h = 5000 

W/(m2

⋅K) approximates a constant temperature surface boundary condition. 

57 
 

Table 2-3. TRNSYS Results Summary for Three Iterations of Simulations

Submittal Date 1/14/2005 6/21/2005 5/23/2006

Noding Scheme "x (2)" Full slab "x (1.5)" 1/4 slab "x (1.2 to 1.3)" 1/4 slab

 Steady-State Analytical Verification

 GC10 GC10a

qfloor del % v. qfloor del % v. qfloor del % v.

(W) AnnSoln (W) AnnSoln (W) AnnSoln

Analytical Soln. 2561 n/a 2433 n/a 2433 n/a

TRNSYS 2486 -2.93% 2417 -0.64% 2427 -0.24%

 Steady-State Cases GC30

qfloor del % v. qfloor del % v. qfloor del % v.

(W) previous (W) previous (W) previous

GC30 & GC30a 2620 n/a 2606 -0.52% 2642 1.34%

GC30b 2494 n/a 2533 1.53%

GC30c 2104 n/a 2137 1.56%

GC60b 2085 n/a 2113 1.36%

GC65b 1965 n/a 1994 1.43%

 Harmonic Cases GC40

Qfloor del % v. Qfloor del % v. Qfloor del % v.

(kWh/y) previous (kWh/y) previous (kWh/y) previous

GC40 & GC40a 22994 n/a 22831 -0.71% 23033 0.88%

GC40b 21852 n/a 22099 1.12%

GC45b 32405 n/a 32758 1.08%

GC55b 34952 n/a 35075 0.35%

GC70b 17214 n/a 17396 1.05%

GC80b 5970 n/a 6029 0.97%

GC40c 18425 n/a 18649 1.20%

GC45c 26735 n/a 27004 1.00%

GC55c 20760 n/a

GC80c 9086 n/a 9192 1.16%

2.4.1.3 Third noding algorithm improvement, 0.4% floor conduction increase for Case 

GC10a, 1%–2% floor conduction increase for cases GC30a-GC80c 

Based on the results of June 2005, the TRNSYS model node meshing was further revised so that the mesh 

size increases by a factor of 1.2 to 1.3 moving away from the slab edge, and the size of node i is allowed to 

increase without limit. Figure 2-1 shows the difference in mesh sizing between the meshing schemes. 

The May 2006 results set applied the following specifications: 

• SizeNom = 1 inch 

• X = 1.2 to 1.3, depending on the test 

• Maximum i = infinity. 

Final results using this noding scheme are also included in Table 2-3 (see results labeled “5/23/2006”). 

58 
-

0.5000

1.0000

1.5000

2.0000

2.5000

0 5 10 15 20 25 30

Node Number

Size (m)

Old Scheme at 1.5,10

New scheme at 1.2

Figure 2-1. Comparison of TRNSYS model noding schemes 

2.4.2 DIT 3-D Numerical Model using MATLAB Version 7.0 

Dublin Institute of Technology (DIT) developed a 3-D numerical ground-coupled heat transfer model run 

independently of a whole-building energy simulation tool prepared within MATLAB 7.0 (The MathWorks, 

Inc., 2007). MATLAB’s functions for interpolation and the solution of linear algebraic equations and 

ordinary differential equations were applied; a large part of the work of these functions is matrix processing, 

an area where MATLAB is considered state-of-the-art. This model was established as a quasi-analytical 

solution method based on rigorous comparison with the Case GC10a analytical solution and comparison 

with the FLUENT and TRNSYS detailed 3-D numerical-model results for other cases. 

2.4.2.1 Surface convection modeling improvement, 1%-4% floor conduction decrease 

for cases GC30b, GC30c, GC60b, and GC65b 

A programming error in DIT’s model became apparent when convective boundary conditions were first 

introduced. Floor heat loss predictions for cases GC30b, GC30c, GC60b, and GC65b were initially 3%–5% 

higher than those of TRNSYS and FLUENT. An error in the modeling of convection within the edge loss 

routine was quickly located and corrected; the edge loss subprogram models floor heat loss just inside the 

perimeter boundary. Figure 2-2 shows MATLAB results versus TRNSYS and FLUENT results before and 

after DIT’s model improvements. 

59 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-State Floor Conduction

1700

1900

2100

2300

2500

2700

GC30b h,int = 100; 

h,ext = 100 

GC30c h,int = 7.95; 

h,ext = ideal

GC60b h,int = 7.95; 

h,ext = 100

GC65b h,int = 7.95; 

h,ext = 11.95

Floor Heat Flow (W or Wh/h)

TRNSYS/TESS FLUENT/PAAET MATLAB/DIT-before MATLAB/DIT-after

Figure 2-2. DIT’s MATLAB results versus TRNSYS and FLUENT results, before and after DIT’s slab 

edge model improvement (Increased minimum y-axis value magnifies differences.)

2.4.2.2 Slab edge loss modeling improvement, 0.3% change for GC30a 

A further minor interpolation improvement was included in the edge loss routine, which models floor heat 

loss just inside the perimeter boundary. This resulted in a 0.3% change in the result for GC30a and a 0.002% 

(negligible) change in the result for GC10a (see Table 2-4; in this table dx0, dz0, fxL0, fxF0, and fz0 are 

node meshing input parameters, as described in DIT’s modeler report in Section 2.9). 

Table 2-4. Effects of Interpolation Improvement in Edge Loss Routine 

Case F 

(m) 

E 

(m) 

dx0 

(m) 

dz0 

(m) fxL0 fxF0 fz0 Number of nodes 

Floor slab 

heat loss Comments 

GC10a* 150 300 0.020 0.012 1.150 1.495 1.150 892,552 2431.87 W Before improvement 

GC10a* 150 300 0.020 0.012 1.150 1.495 1.150 892,552 2431.82 W After improvement 

GC30a 20 30 0.015 0.009 1.135 1.4755 1.135 840,840 2686.33 W Before improvement 

GC30a 20 30 0.015 0.009 1.135 1.4755 1.135 840,840 2694.99 W After improvement 

*Analytical solution is 2432.60 W. 

2.4.2.3 Near-surface temperature reporting improvement, no effect on floor conduction 

A 3-D interpolation function was initially used to produce two lines of subsurface temperatures emanating 

from the origin at exact locations specified for the steady-state tests (see Part I, Figure 1-4 and Table 1-5). 

60 
The results disagreed with FLUENT and TRNSYS (see the DIT modeler report, Section 2.9, Figure 2C-2). 

Use of a 1-D interpolation function, where the required interpolation points are collinear with the subsurface 

nodes, produced better agreement (see final results in Part III). The nature of the problem with the 3-D 

interpolation method was not established with certainty. However, MATLAB’s 3-D interpolation function 

applied for determining these temperatures uses 64 neighboring points, and may have used nonrepresentative nodal temperatures considering the small scale of the perimeter boundary and the large 

temperature gradients in its vicinity. The method used for reporting temperatures at specific locations called 

out by the test specification has no effect on the floor conduction calculated by the model. 

2.4.3 PAAET 3-D Numerical Model Using FLUENT 6.0 

Public Authority for Applied Education and Training (PAAET) developed a 3-D numerical groundcoupled heat transfer model run independently of a whole-building energy simulation tool, prepared with 

FLUENT 6.0 (FLUENT Inc. 2001). FLUENT is a state-of-the-art computer program for modeling fluid 

flow and heat transfer in complex geometries. PAAET ran the test cases using an earlier version of 

FLUENT (6.0) than was available at the time of testing (version 6.2). PAAET’s model was established as 

a quasi-analytical solution method based on rigorous comparison with the Case GC10a analytical solution 

and comparison with the TRNSYS and MATLAB detailed 3-D numerical-model results for other cases. 

2.4.3.1 Two output-reporting issues, no effect on overall floor conduction; fixed in later version 

of FLUENT before this testing 

Two output reporting issues occurred in FLUENT 6.0: 

• The monitored values of hourly heat flux through the floor slab differed from those obtained for 

the same variable via FLUENT’s postprocessing utilities. The total heat flux through the inside 

slab can be obtained in two ways from the postprocessing utilities: (1) via report “fluxes”, (2) via 

report “surface integrals”. These two postprocessing methods for calculating total heat flux 

through the inside slab produced the same value that is different from that provided by the 

monitoring utility (a built-in utility for automatic reporting of the value of a predefined variable at 

the end of each solver iteration or time step). This issue occurred only for monitoring of coplanar 

surfaces; for example, the slab, perimeter, and outside surfaces, which are all within a single 

plane at the same level (top surface) and have similar slope (in this case horizontal). PAAET 

hypothesized that this may be an interpolation related issue because nodes at adjacent surfaces 

have different boundary conditions. For example, when FLUENT performs integration over the 

floor slab, it uses values of nodes adjacent to the slab (the perimeter surface, which has a different 

boundary condition). PAAET bypassed this issue by defining a postprocessing surface (dummy 

surface used for data presentation purposes) that exactly overlaps the inside slab. The monitored 

heat flux through the created dummy surface matched the heat flux values provided by both postprocessing utilities. PAAET hypothesized that this may occur because FLUENT works with 

dummy surfaces in isolation as defined by the user, without investigating what is adjacent to the 

dummy surface. 

• A bug in FLUENT produced diagonal surface temperature profile results twice (each node value 

is reported twice within a single file). FLUENT facilitates two types of lines for postprocessing 

purposes: “line” and “rake”. “Line” was used to report the temperature profile across the diagonal 

of the upper surface of the domain. The values reported across the “line” are at actual nodes of 

the domain mesh. PAAET bypassed the double reporting issue by using the “rake” option, which 

allows the number of reporting points to be specified at equal spacing, although “rake” produces 

interpolated values at the specified points instead of exact node values. 

61 
Fluent Inc. later investigated the above reporting errors and confirmed that both were present in FLUENT 

.4.3.2 Modeling error, 0.7% increase for Case GC30b

uring early results development and comparison, PAAET reported a modeling error for Case GC30b. 

.4.4 EnergyPlus 

nergyPlus (2007) is developed and maintained by DOE, and is the department’s next-generation building 

 for 

Table 2-5. Summary of EnergyPlus Changes that Were Implemented 

ersion 

6.0; both errors were already fixed before this testing for FLUENT 6.2 (Watve 2006). 

2

D

(Ben-Nakhi 2006) The initially submitted result had floor conduction of 2487 W; the fixed result has 

floor conduction of 2504 W. 

2

E

energy simulation program. The EnergyPlus Slab program, which is used for ground heat transfer analysis, 

is run independently of EnergyPlus; output from the Slab program is manually input to the main EnergyPlus

program. Table 2-5 describes field trial iterations by GARD Analytics (GARD) for this project and for 

selected preliminary work that occurred during IEA SHC Task 22. Input file and software modifications

each iteration are also shown. A single results set was submitted corresponding to changes described in each 

row of the table. 

V Code Changes Input File Changes

1.0.3.019

r 2002) sion for IEA SHC Task 22 (Decembe Initially tested ver Initial Task 22 input files

1.1.0.003 

(April 2003) 

• Allow user to define interior convective urface) 

surface coefficients adjacent to floor slab

• User input h,int (slab s

applied 

1.2.1.012 

(December 2004) 

Initially tested version for IEA SHC Task 34/ Initial Task 34/Annex 43 input 

Annex 43 in-depth cases files 

1.2.2.031 

(June 2005) ound surface) 

• 

eter and 

• boundary depth 

er input h,ext (ground 

• ground 

•

40 

•

• Allow user input for Tdg

• Allow user input for h,ext (gr

• Documentation clarified input description 

for far-field boundary distance 

Gridding scheme improvements

• Allow separate simulation of perim

core portions of floor 

Allow user input deep

• Us

surface) applied 

Far-field and deep

boundary inputs corrected 

Slab perimeter and core

temperatures input for GC

(corrected previous input) 

User input of deep ground 

boundary depth applied to 

GC55b, GC55c 

1.3.0.007 

6) 

• Slab program output added to facilitate 

d 

• b (large slab) 

(March 200 separate simulation of slab perimeter an

core areas in a building 

Run Case GC50

.4.4.1 Allow user-defined interior convective surface coefficient, increased floor 

0 

itial annual heating load results disagreements for EnergyPlus versus BASESIMP-HOT3000 and 

e user 

es 

2

conduction by a factor of 2.7 (270%) for IEA SHC Task 22 preliminary Case GC18

In

SUNREL-GC are shown in Figure 2-3 for preliminary in-depth cases of IEA SHC Task 22 (Deru, 

Judkoff, and Neymark 2003). The cause of the disagreements was that EnergyPlus did not allow th

to input constant interior surface coefficients adjacent to the floor slab. The interior surface convective 

coefficient value initially calculated and used by EnergyPlus was 0.948 W/(m2

⋅K), which is greatly 

different from the value of 3.16 W/(m2

⋅K) that IEA BESTEST (Judkoff and Neymark 1995a) indicat

62 
could accompany a specified combined convective/radiative coefficient of 8.29 W/(m2

⋅K). Based on this

problem, the code authors added new capability to the software that allows the user the option to set a 

constant value for interior and exterior convective heat transfer coefficients for a surface. The modelers

then reran the simulations to model the specified combined interior surface coefficient by inputting 8.29 

W/(m2

⋅K) as an interior surface convective coefficient and setting the interior surface emittances to 0.001

This resulted in improved agreement. 

 

. 

 cases 

.4.4.2 Allow user-defined lower deep ground boundary temperature, no effect on floor 

ser definition of a specific lower deep boundary temperature was added to match requirements of the 

s 

s 

.4.4.3 Allow user-defi d ground surface heat transfer coefficient, probably minor 

ost test cases required that this parameter be set to 100 W/(m2

⋅K), a high value that is useful for robust 

IEA BESTEST Ground Coupling

Annual Heating Load

0

2

4

6

8

10

12

14

16

18

GC100: Pure Slab GC180: Pure Slab, 12x16 GC180-100: Slab Area

MWh

BASESIMP-HOT3000/Nrcan SUNREL-GC/NREL

EnergyPlus/GARD, Before Fix EnergyPlus/GARD, Af

Figure 2-3. EnergyPlus annual heating load disagreements: IEA SHC Task 22 preliminary

GC100, GC180, and GC180–GC100 

2

conduction 

U

test specification. Before this enhancement was made, this temperature was calculated by the EnergyPlu

Slab program and set to the annual mean outdoor dry-bulb temperature as determined from the weather 

file. The lower deep boundary temperature required by the specification was 10°C for all test cases and 

each weather file used as part of the test suite already had annual mean ambient dry-bulb air temperature

of 10°C, so use of this new capability did not change the test results. 

2 ne

effect on floor conduction 

M

diagnosis. However, cases GC65b and GC70b required that this parameter be set at 11.95 W/(m2

⋅K). In 

the original version of the EnergyPlus Slab program, the user could not define this parameter; instead, it 

ter Fix

63 
was calculated internally by the program as a function of the ambient temperature and wind speed from 

the weather file. A later version of EnergyPlus allowed direct user input of the exterior surface coefficien

for the soil. We could not isolate the effect of this improvement because of other accompanying changes 

during the field trial iteration. However, the wind speeds of the weather data were set to match the 

specified exterior surface coefficient (using ASHRAE 2005, ch. 25), so the impact of this improvem

on the test results is probably minor. 

t 

ent 

.4.4.4 Documentation clarified regarding the input parameter “Distance from edge of 

aused 

arlier versions of the Slab program documentation caused confusion about the input parameter 

r the 

r 

Table 2-6. Effect of Juxtaposed Deep-Ground Boundary Depth and Far-Field Dimensions 

ase 

Juxtaposed Parameters, Correct Parameters, 

y) % Effect 

2

slab to domain edge”; misinterpretation can cause approximately 4%-7% error 

depending on ratio of far-field dimension to deep ground boundary depth, and c

the program to crash for the shallow deep ground boundary depth of GC55b

E

“Distance from edge of slab to domain edge.” Whether this was the horizontal far-field distance o

deep boundary depth was unclear. Later documentation changes clarified the definition of parameters fo

these inputs. Table 2-6 shows EnergyPlus sensitivity test results for three of the “b”-series and “c”-series 

cases that have far-field dimension not equal to deep-ground depth, which identifies the effect of the 

documentation improvement.

on EnergyPlus Floor Conduction 

C Floor Conduction (kWh/y) Floor Conduction, (kWh/

GC40c 20978 20255 3.6% 

GC55b C rashed 39932 Allows run 

GC55c 20951 22570 7.2% 

2.4.4.5 Input error related to manual interface between floor slab model and main 

C40

One issue that came up in the early stages of the work was a disagreement about the results of Case GC40 

 of 

nt 

at 

t 

EnergyPlus program, approximate 35%–40% decrease in floor conduction, Case G

(Neymark, Judkoff, and Deru 2004); see Figure 2-4. This disagreement was traced to an input error where 

the monthly slab perimeter temperatures output by the slab model were input to the main EnergyPlus 

program, rather than the monthly overall average (of perimeter and core) slab temperatures. Figure 2-5

indicates corrected results, which show a roughly 45% decrease in floor conduction versus Figure 2-4. A

simultaneous secondary effect on these results is variation of soil conductivity from 2.0 W/(m⋅K) for Case

GC40 to 1.9 W/(m⋅K) for Case GC40b, which should have about a 5% effect on all model results. 

Another secondary effect is the difference between the specified ideal (infinite) surface coefficients

Case GC40 and surface coefficients of 100 W/(m2

⋅K) for Case GC40b. This secondary effect can accou

for at most a 4–5% variation based on FLUENT, SUNREL-GC, and TRNSYS results for cases GC40a 

and GC40b, and is probably less because for Case GC40 EnergyPlus did not run for interior surface 

coefficient greater than 180 W/(m2

⋅K). Therefore, the effect of correcting the input error is estimated 

about a 35–40% decrease for floor conduction, i.e., 45% – (5% for reduced conductivity) – (a few percen

for reduced surface coefficient). To assist users with the current manual interface between the Slab model 

and the main EnergyPlus program, the Slab model output was revised to include example floor model 

inputs to the main EnergyPlus program. Better automation of the interface between the Slab model and

EnergyPlus is recommended. 

64 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Floor Conduction

0

5000

10000

15000

20000

25000

30000

35000

40000

GC40, base case 

ideal films

GC45, aspect ratio GC50, large slab GC55, shallow

ground depth

GC70, hint=1

hext=17

Floor Heat Flow (kWh)

EnergyPlus/GARD GHT/NREL SUNREL-GC/NREL TRNSYS/TESS

Figure 2-4. EnergyPlus GC40 and GC55 disagreements, shown with Feb 2005 results 

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Floor Conduction

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

GC40a, ideal films GC40b, h=100 GC45b, AR=36x4 GC50b, large slab GC55b, 2m

depth

GC70b, hint=7.95,

hext=11.95

GC80b, k=0.5

Floor Heat Flow (kWh)

TRNSYS/TESS

EnergyPlus 

with input error 

for Case GC40 

EnergyPlus with 

default soil depth 

(15 m), Case GC55 

EnergyPlus input 

error corrected, 

Case GC40b 

EnergyPlus 

with correct soil 

depth (2 m), 

Case GC55b 

GHT/NREL SUNREL-GC/NREL EnergyPlus/GARD

Figure 2-5. EnergyPlus with input error correction, and improvement to allow deep ground 

boundary depth as user input, shown with June 2005 results

65 
2.4.4.6 Allow user-defined deep-ground boundary depth, estimated 35% increase in 

floor conduction for Case GC55b (versus preliminary Case GC55)

This capability was required because the test specification requested the simulation of shallow and deep 

boundary depths for the “b”-series and “c”-series cases ranging from 2 m to 15 m. Before this 

enhancement was made deep boundary depth was automatically set to 15 m or 20 m depending on floor 

area/perimeter (A/P) ratio. This new capability was applied only for cases GC50b, GC55b, and GC55c 

because GC55b and GC55c specify deep ground boundary depth of 2 m and 5 m, respectively, and 

because for all cases except GC50b the A/P ratio is such that EnergyPlus applies a deep ground boundary 

depth of 15 m. Initial field-trial results submitted in December 2004 for preliminary Case GC55 without 

the ability to set ground depth shallower than 15 m were about 20% below the initial TRNSYS and 

SUNREL-GC numerical results (see Figure 2-4). The second iteration of results submitted in June 2005, 

which allows direct user input for shallow ground depth, are about 15% above the numerical-model 

results (see Figure 2-5). This indicates a roughly 35% effect in EnergyPlus for including this change, and 

indicates that EnergyPlus has a greater sensitivity to soil depth than the numerical models. This issue is 

further discussed in Section 2.4.4.8. 

2.4.4.7 Sensitivity disagreement for variation of ground surface heat transfer coefficient, 

GC65b has 18% lower floor conduction than average of all other results 

From the current results set (see Figure 2-6) the EnergyPlus results are more sensitive to ground surface 

heat transfer coefficient than the verified numerical models and other programs. This disagreement may 

be caused by the EnergyPlus Slab program’s shorter heat flow path underneath the adiabatic exterior wall 

(EnergyPlus assumes perimeter boundary width = 0), which would overestimate the slab perimeter heat 

flow for the test cases. Also shown in Figure 2-6 (gray arrow) is the difference in the annual average floor 

conduction for Case GC70b versus the steady-state floor conduction of Case GC65b (see data for 

GC70b–GC65b). This difference occurs for the lower (more realistic) exterior ground surface heat 

transfer coefficient of GC70b–GC65b but not for the higher exterior ground surface heat transfer 

coefficient of GC40b–GC30. This smaller difference may be related to ground surface heat transfer 

modeling, or some other aspect of the model. The EnergyPlus development team is examining these 

issues. 

2.4.4.8 Sensitivity disagreement for variation of soil depth, 15% higher floor conduction 

than verified numerical model results for shallow soil depth (Case GC55b)

Also, from the current results set (see Figure 2-7), EnergyPlus has good agreement with verified 

numerical model results for 15 m soil depth, but has 15% greater floor conduction for shallow soil depth 

(GC55b) and comparable oversensitivity to reduction of ground depth (GC55b-GC40b). The ISO-13370 

model implemented in VA114 also indicates good agreement at 15 m soil depth, but has 9% lower floor 

conduction versus the verified numerical-model results at shallow soil depth (see gray arrows in Figure 2-

7). The similar magnitude of the EnergyPlus and ISO-13370 differences versus the verified numericalmodel results indicates that such differences may be reasonable for less detailed models. However, the 

EnergyPlus development team is examining this issue.

66 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-State Floor Conduction

-100

400

900

1400

1900

2400

GC60b 

h,ext = 100

GC65b 

h,ext = 11.95

GC60b-GC65b 

h,ext sensitivity

GC70b*-GC65b,

sp v. ss, 

h,ext = 11.95

GC40b*-GC30b,

sp v. ss, 

h,ext = 100

Floor Heat Flow (W or Wh/h)

TRNSYS/TESS

EnergyPlus has high sensitivity to h,ext. 

GC60b: h,ext = 100 W/m2

K 

GC65b: h,ext = 11.95 W/m2K

FLUENT/PAAET MATLAB/DIT

SUNREL-GC/NREL EnergyPlus/GARD VA114-ISO13370/VABI

Figure 2-6. EnergyPlus exterior ground surface heat transfer coefficient sensitivity disagreement 

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Floor Conduction

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

GC40b 15m Soil Depth GC55b 2m Soil Depth GC55b-GC40b Depth

Sensitivity

Floor Heat Flow (kWh)

TRNSYS/TESS FLUENT/PAAET MATLAB/DIT

SUNREL-GC/NREL EnergyPlus/GARD VA114-ISO13370/VABI

Figure 2-7. EnergyPlus soil depth sensitivity disagreement 

67 
2.4.5 VA114 Version 2.20 with ISO 13370 Ground Heat Transfer Model 

VA114 (VABI 2007), initial development by TNO, current development and distribution, maintenance, and 

support by VABI Software BV, The Netherlands, is widely used in The Netherlands. VABI is adapting the 

ISO-13370 European standard ground heat transfer calculation method (ISO 13370:1998) for VA114. 

2.4.5.1 Adapt ISO-13370 ground heat transfer calculation method for VA114, 100% and 

70% increases in annual heating load for preliminary IEA SHC Task 22 cases GC100 

and GC180, respectively 

In preliminary work during IEA SHC Task 22 (Deru, Judkoff, and Neymark 2003), results for the Task 22 

cases using VA114’s 1-D conduction model indicated low heating loads compared with other programs. 

Based on these results, VABI decided to explore implementing the ISO-13370 (ISO 11370:1998) ground 

heat transfer model into VA114. Figure 2-8 shows VA114 results versus results of other models before and 

after initial implementation of ISO 13370 (Neymark 2003; Wijsman 2005). 

IEA BESTEST: Task 22 Preliminary Ground Coupling 

Annual Heating Loads

0

2

4

6

8

10

12

14

16

18

GC100: Pure Slab GC180: Pure Slab, 12x16 GC180-100: Slab Area

Sensitivity

Annual Load (MWh)

HOT3000-BASESIMP/NRCan (2002) SUNREL-GC/NREL (2002)

EnergyPlus/GARD (2003) VA114/VABI (2002)

VA114-ISO13370/VABI (2005)

Figure 2-8. IEA SHC Task-22 test results for VA114 versus other models, before (“VA114/VABI 

(2002)”) and after (“VA114-ISO13370/VABI (2005)”) preliminary adaptation of the ISO-13370 

European standard ground heat transfer calculation method with VA114. 

2.4.5.2 Implementation of ISO-13370 soil depth modeling for VA114, 29% and 49% 

increase in annual floor conduction for cases GC50b and GC55b, respectively 

The initial implementation of ISO-13370 with VA114 was then tested using the IEA-34/43 test cases (see 

Figure 2-9). Except for cases GC50b and GC55b, good agreement is indicated for VA114/ISO 13370 versus 

the TRNSYS and SUNREL-GC detailed 3-D numerical models. The largest disagreement is for Case 

GC55b, which has shallow water table depth; Case GC50b is for large slab with no change in modeled soil 

depth versus GC40b, so in GC50b water table depth also becomes somewhat shallow relative to the slab 

68 
surface area. The initial implementation of ISO 13370 in VA114 did not include ISO 13370’s model for 

water table depth sensitivity. Based on these results, the ISO-13370 shallow water table depth model was 

implemented; improved agreement resulting from this implementation is shown in Figure 2-10. 

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Floor Conduction

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

GC40a,

ideal films

GC40b,

h=100

GC45b,

AR=36x4

GC50b,

large

slab/10

GC55b, 

2m depth

GC70b,

hint=7.95,

hext=11.95

GC80b,

k=0.5

GC40c,

hint=7.95,

hext=ideal

GC45c,

AR=36x4

GC55c, 

5m depth

GC80c,

k=0.85

Floor Heat Flow (kWh)

VA114/ISO13370 disagreeing 

for GC50b and GC55b 

TRNSYS/TESS GHT/NREL SUNREL-GC/NREL

FLUENT/PAAET EnergyPlus/GARD VA114-ISO13370/VABI

ESP-r-BASESIMP/NRCan BASECALC/NRCan

Figure 2-9. Steady-periodic annual floor conduction, from April 2006 results 

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Floor Conduction

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

GC40a,

ideal films

GC40b,

h=100

GC45b,

AR=36x4

GC50b,

large

slab/10

GC55b, 

2m depth

GC70b,

hint=7.95,

hext=11.95

GC80b,

k=0.5

GC40c,

hint=7.95,

hext=ideal

GC45c,

AR=36x4

GC55c, 

5m depth

GC80c,

k=0.85

Floor Heat Flow (kWh)

VA114/ISO13370, water table 

depth sensitivity model included 

TRNSYS/TESS GHT/NREL SUNREL-GC/NREL

FLUENT/PAAET EnergyPlus/GARD VA114-ISO13370/VABI

ESP-r-BASESIMP/NRCan BASECALC/NRCan

Figure 2-10. Steady-periodic annual floor conduction, from October 24, 2006 results 

69 
2.4.5.3 Time of occurrence for peak heat flow is later than for other models, peak 

delayed 700 hours for GC55b and 300-500 hours for other cases 

Final results for annual and peak-hour floor conduction (see Part III) show generally good agreement versus 

verified numerical models and other models. However, Figure 2-11 shows that time of peak occurrence is 

delayed by about 400 hours in Case GC40b. Figure 2-12 shows that peak occurrence is delayed about 700 

hours for Case GC55b and about 600 hours for Case GC80b, and delayed 300-500 hours for other cases. 

The VA114 authors consider this disagreement about delayed occurrence of peak heat flow to be 

acceptable, especially compared with more fundamental disagreements before the ISO-13370 model was 

adapted, and have no plans to address this issue. 

 

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Hourly Floor Conduction, GC40b

1500

1700

1900

2100

2300

2500

2700

2900

3100

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Hour

Floor Conduction (W or 

Wh/h)

0

2

4

6

8

10

12

14

16

18

20

Temperature (°C)

TRNSYS FLUENT MATLAB GHT VA114 EnergyPlus ODB Temperature

VA114 

Figure 2-11. Hourly floor conduction, Case GC40b 

70 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Phase Shift, Coldest ODB to Peak Floor Conduction

0

200

400

600

800

1000

1200

1400

GC40a

ideal films

GC40b

h=100

GC45b

AR=36x4

GC50b

large slab

GC55b 

2m depth

GC70b

hint=7.95,

hext=11.95

GC80b

k=0.5

GC40c

hint=7.95,

hext=ideal

GC45c

AR=36x4

GC55c 

5m depth

GC80c

k=0.85

Hours

TRNSYS/TESS

VA114 has biggest difference 

for GC55b, GC80b 

FLUENT/PAAET MATLAB/DIT

GHT/NREL SUNREL-GC/NREL VA114-ISO13370/VABI

ESP-r-BASESIMP/NRCan

Figure 2-12. Steady-periodic phase shift, coldest ODB to peak floor conduction 

2.4.6 BASESIMP/ESP-r and BASECALC 

BASESIMP (Beausoleil-Morrison and Mitalas 1997) is developed by NRCan. It is a regression-based 

algorithm based on more than 100,000 BASECALC runs. Solutions by BASECALC, which was also 

developed by NRCan (Beausoleil-Morrison 1996), are obtained by performing three, 2-D finite element 

simulations and using corner correction factors to obtain quasi-3-D solutions. In this project, NRCan 

evaluated its implantation of BASESIMP within ESP-r (ESRU 2007; Beausoleil-Morrison 1999). 

developed by NRCan (Beausoleil-Morrison 1996), are obtained by performing three, 2-D finite element 

simulations and using corner correction factors to obtain quasi-3-D solutions. In this project, NRCan 

evaluated its implantation of BASESIMP within ESP-r (ESRU 2007; Beausoleil-Morrison 1999). 

2.4.6.1 BASECALC input error, 1%–5% for “c”-series cases 

As BASESIMP is a correlation method based on BASECALC, some disagreement (up to 5%) may be 

expected. However, the 22% disagreement for GC80c and 6% disagreement for GC45c (see Figure 2-13) 

were more than expected. Review by NRCan revealed an error in the BASECALC input files. Corrected 

BASECALC input yielded results shown in Figure 2-14. 

As BASESIMP is a correlation method based on BASECALC, some disagreement (up to 5%) may be 

expected. However, the 22% disagreement for GC80c and 6% disagreement for GC45c (see Figure 2-13) 

were more than expected. Review by NRCan revealed an error in the BASECALC input files. Corrected 

BASECALC input yielded results shown in Figure 2-14. 

71 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Floor Conduction

0

5000

10000

15000

20000

25000

30000

35000

GC40c, hint=7.95,

hext=ideal

GC45c, AR=36x4 GC55c, 5m depth GC80c, k=0.85

Floor Heat Flow (kWh)

TRNSYS/TESS EnergyPlus/GARD

ESP-r-BASESIMP/NRCan BASECALC/NRCan

Figure 2-13. Results differences for BASESIMP versus BASECALC, 

 for results submitted March 2006 

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Floor Conduction

0

5000

10000

15000

20000

25000

30000

35000

GC40c, hint=7.95,

hext=ideal

GC45c, AR=36x4 GC55c, 5m depth GC80c, k=0.85

Floor Heat Flow (kWh)

TRNSYS/TESS EnergyPlus/GARD

VA114-ISO13370/VABI ESP-r-BASESIMP/NRCan

BASECALC/NRCan

Figure 2-14. Results differences for BASESIMP versus BASECALC, 

for results submitted June 2006 

72 
2.4.6.2 Allow direct input of BASECALC heat loss coefficients for configurations that fall 

outside the range of parameter variations allowed by current heat loss correlations, 21% 

for GC80c, 1%–4% for other “c”-series cases

After the BASECALC input error was corrected the difference between results of BASESIMP and 

BASECALC for Case GC45c was reduced; however, Figure 2-14 shows that BASESIMP results for Case 

GC80c are still 21% greater than the BASECALC results. NRCan’s further review of BASESIMP 

revealed that this difference is caused because BASESIMP correlation range constraints do not allow 

modeling of all specified features of Case GC80c. Specifically, as a simplification for the numericalmethods modelers, Case GC80c applies the same low-range conductivity value for soil as to the slab and 

foundation walls (0.85 W/(m⋅K)). Case GC80c can be modeled by BASECALC; however, BASESIMP 

fixes conductivity of concrete for the slab and foundation wall conductivities at 1.73 W/(m⋅K) (a typical 

value for concrete). As this issue was discovered too late in the project to revise the test specification and 

rerun the other participants’ numerical models, to test BASESIMP’s ability to model low conductivity 

Case GC80c NRCan developed a new configuration type for BASESIMP that allows the user to input the 

specific heat loss coefficients calculated by BASECALC for configurations that would normally fall 

outside the range of parameter variations covered by the current BASESIMP heat loss correlations. As 

shown in Figure 2-15, the BASESIMP heat loss results for the new configuration type are identical to 

those of the BASECALC runs used to supply the heat loss coefficients. 

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Floor Conduction

0

5000

10000

15000

20000

25000

30000

35000

GC40c, hint=7.95,

hext=ideal

GC45c, AR=36x4 GC55c, 5m depth GC80c, k=0.85

Floor Heat Flow (kWh)

TRNSYS/TESS FLUENT/PAAET MATLAB/DIT

EnergyPlus/GARD VA114-ISO13370/VABI ESP-r-BASESIMP/NRCan

BASECALC/NRCan

Figure 2-15. Final Results for BASESIMP versus BASECALC 

73 
2.4.6.3 BASECALC and BASESIMP results are 9% low versus verified numerical-model 

results for GC45c

Figure 2-15 indicates that results for BASECALC and BASESIMP disagree with the verified numericalmodel results substantially more than the VA114-ISO13370 and EnergyPlus results. This indicates a 

disagreement with calculation of perimeter heat flow, and should be checked. The BASECALC authors 

consider this disagreement at this relatively extreme aspect ratio to be acceptable, and have no plans to 

address this issue. 

2.4.7 GHT/SUNREL-GC 

SUNREL was developed by NREL. SUNREL-GC is a special version of SUNREL coupled with a groundcoupled heat transfer program called GHT. GHT uses finite element analysis to model 2-D or 3-D heat 

conduction problems (Deru 2003), and can be run independently or integrated with SUNREL. This model 

has sufficient detail and flexibility to potentially qualify as a quasi-analytical solution method if the 

software developer can address the disagreements noted below. 

2.4.7.1 Better integration of GHT model with SUNREL-GC, 5% and 8% relative 

decrease in SUNREL-GC floor conduction for cases GC30 (versus GC30b) and GC40 

(versus GC40b), respectively 

After the first field trial iteration, NREL revised integration of GHT with SUNREL-GC to improve the 

year-to-year data exchange between the programs and to make the specialized version of SUNREL easier 

to use. As shown in Figure 2-16, these revisions resulted in 5% and 8% decreases in floor conduction 

modeled by SUNREL-GC relative to GHT for cases GC30 (versus GC30b) and GC40 (versus GC40b), 

respectively. Also, for the initial results of preliminary cases GC30 and GC40, SUNREL-GC appears to 

have had better agreement with TRNSYS before these changes were made, although this could be 

evidence of initially compensating errors if a further error remains. 

2.4.7.2 Disagreements versus TRNSYS, MATLAB, and FLUENT results, 7% and 10% 

below average of verified numerical-model results for cases GC30a and GC40a 

respectively; 5%–8% below average of verified numerical-model results for the “b”-

series cases 

Figure 2-17 shows that current GHT results are within 1% of the analytical solution, but that GHT and 

SUNREL-GC results disagree with the verified numerical-model results by 5%–8% for the other steadystate cases. Similarly, Figure 2-18 shows that current SUNREL-GC results for cases with steady-periodic 

variation of outdoor temperature disagree with the verified numerical-model results by 5%–10%, where 

the greatest percentage disagreement occurs for Case GC40a. 

74 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-State Floor Conduction

0

500

1000

1500

2000

2500

3000

GC30, steady-state, 

ideal films, k=2.0

GC30b, steadystate, h=100,

k=1.9

GC40, harmonic, 

ideal films, k=2.0,

(kWh/8.760)

GC40b, harmonic, 

h=100, k=1.9, 

(kWh/8.760)

Floor Heat Flow (W or Wh/h)

TRNSYS/TESS GHT/NREL SUNREL-GC/NREL

FLUENT/PAAET MATLAB/DIT

Figure 2-16. Selected floor conduction results for early versus later iterations of GHT and 

SUNREL-GC compared with other detailed numerical models 

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-State Floor Conduction

0

500

1000

1500

2000

2500

3000

GC10a, 

linear dT

GC30a, 

adiab. wall,

ideal films

GC30b, 

adiab. wall, 

h = 100 

GC60b, 

h,int = 7.95;

h,ext = 100

GC65b, 

h,int = 7.95;

h,ext = 11.95

Floor Heat Flow (W or Wh/h)

Analytical TRNSYS/TESS FLUENT/PAAET

MATLAB/DIT GHT/NREL SUNREL-GC/NREL

EnergyPlus/GARD VA114-ISO13370/VABI

Figure 2-17. Floor conduction results for GHT/SUNREL-GC versus Other Models, 

Cases with Steady-State ODB

75 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Floor Conduction

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

GC40a, 

ideal films

GC40b, h=100 GC55b, 

2m depth

GC70b,

hint=7.95,

hext=11.95

GC80b, k=0.5

Floor Heat Flow (kWh)

TRNSYS/TESS FLUENT/PAAET MATLAB/DIT

GHT/NREL SUNREL-GC/NREL EnergyPlus/GARD

VA114-ISO13370/VABI

 

Figure 2-18. Floor conduction results for GHT/SUNREL-GC versus other models, 

cases with steady-periodic ODB

For diagnostic purposes GHT floor conduction differences versus the verified numerical-model results are 

further highlighted for the “a”-series cases in Figure 2-19. This figure shows that GHT has lower 

sensitivity (1.5%) than the other models (7%–10%) to varying the boundary condition from the linearly 

varying surface temperature of GC10a to the adiabatic surface of GC30a (see data labeled “GC30aGC10a”). Based on sensitivity tests by DIT using its MATLAB model (see Section 2.9 [DIT modeler 

report]), some of this difference may be attributable to node mesh density. However for the participant 

models, the finest node spacings are MATLAB = 0.9 cm (vertical), 1.5 cm (horizontal); TRNSYS = 2.5 

cm; GHT = 3.5 cm; and FLUENT = 6 cm. As the node spacing for FLUENT is greater than that for GHT, 

coarse node spacing may not be the cause of the GHT “GC30a-GC10a” sensitivity difference, but is 

worth rechecking in the GHT model. Also in Figure 2-19, the difference for GHT between the annual 

average floor conduction of Case GC40a versus the steady-state conduction of Case GC30a (see data 

labeled “GC40a-GC30a”) is greater than for the other models, where in this case a sensitivity equal to or 

near zero is expected. For the results shown the difference between the GC40a average value and the 

GC30a steady-state value is less than 0.6% for the verified numerical-model results (MATLAB’s high 

mesh density models produced less than 0.01% variation), but is 3.3% for GHT. 

76 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-State Floor Conduction Sensitivity

-100

-50

0

50

100

150

200

250

300

GC30a-GC10a, adiab v lin dT GC40a*-GC30a, sp v. ss

Floor Heat Flow (W or Wh/h)

TRNSYS/TESS

Recall for GC10a, 

qfloor = 2433 W 

FLUENT/PAAET MATLAB/DIT GHT/NREL

Figure 2-19. “a”-series floor conduction sensitivity results for GHT/SUNREL-GC 

versus verified numerical models 

GHT also exhibits less sensitivity to variation of surface coefficients and soil conductivity than the 

verified numerical models, as shown in Figure 2-20 (see data labeled “GC40a-GC40b” and “GC40bGC70b” for heat transfer coefficient sensitivity, and “GC40b-GC80b” for soil conductivity sensitivity). 

Figure 2-21 shows results for phase shift between the hour with the coldest ambient temperature and the 

hour with the highest heating load, for the cases with steady-periodic temperature boundary conditions. 

Here disagreement for GHT versus the verified numerical models seems apparent in Case GC40a; 

GHT/SUNREL-GC results are within or near the range of disagreement among the verified numerical 

models for the “b”-series cases. 

Given the agreement among the results for the TRNSYS, FLUENT, and MATLAB numerical models, 

and the rigorous effort to document improvements to those models when earlier disagreements were 

addressed, there are too many unaddressed disagreements for GHT/SUNREL-GC for this model to 

qualify as a quasi-analytical solution (verified numerical model). However, based on its model 

description, GHT/SUNREL-GC may have sufficient detail and flexibility to qualify as a quasi-analytical 

solution method if the software developer can address the disagreements. 

The GHT/SUNREL-GC author has been notified of these issues. When diagnosing the source of these 

disagreements, the GHT/SUNREL-GC author should also consider early discussion about GHT’s 

inability to model high convection coefficients greater than 100 W/(m2

⋅K) (Deru, Neymark, and Thornton 

2005), which may be caused by GHT’s explicit solution approach (where the temperature at any node at 

the current time step is a function of the temperature of the surrounding nodes at previous time steps). 

Also worth further considering is that SUNREL-GC had better agreement with TRNSYS-GC before 

changes described in Section 2.4.7.1 were made. 

77 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Floor Conduction Sensitivity

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

GC40a-GC40b,

h=inf. v h=100

GC55b-GC40b,

Depth = 2m

GC40b-GC70b,

hint=7.95

hext=11.95 

GC40b-GC80b,

k=0.5

Floor Heat Flow (kWh)

TRNSYS/TESS FLUENT/PAAET MATLAB/DIT

GHT/NREL SUNREL-GC/NREL EnergyPlus/GARD

VA114-ISO13370/VABI

 

Figure 2-20. Results for “b”-series floor conduction sensitivity, GHT/SUNREL-GC 

versus other models 

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Phase Shift, Coldest ODB to Peak Floor Conduction

0

100

200

300

400

500

600

700

GC40a, 

ideal films

GC40b, 

h=100

GC55b, 

2m depth

GC70b,

hint=7.95,

hext=11.95

GC80b, k=0.5

Hours

TRNSYS/TESS FLUENT/PAAET MATLAB/DIT

GHT/NREL SUNREL-GC/NREL

Figure 2-21. Steady-periodic phase shift for GHT/SUNREL-GC versus verified numerical models 

78 
2.5 Interpretation of Results 

2.5.1 Developing a Secondary Mathematical Truth Standard Based on an 

Analytical Solution and Verified Numerical Models 

A major accomplishment of this work is the development of a set of quasi-analytical solutions using 

verified numerical-model results for all the test cases; this represents a secondary mathematical truth 

standard founded on the range of disagreement of the numerical-model results. Another major 

accomplishment is the development of a methodology for establishing such a secondary mathematical 

truth standard. 

2.5.1.1 Analytical Verification and Mathematical Truth Standards 

Analytical verification is where outputs from a program, subroutine, algorithm, or software object are 

compared to results from a known analytical solution, or to results from a set of closely agreeing quasianalytical solutions or verified numerical models. Here the term analytical solution is the mathematical 

solution of a model that has an exact result for a given set of parameters and simplifying assumptions. The 

term quasi-analytical solution is the mathematical solution of a model for a given set of parameters and 

simplifying assumptions, which may include minor interpretation differences that cause minor results 

variations; such a solution may be computed by generally accepted numerical methods or other means, 

provided that such calculations occur outside the environment of a whole-building energy simulation 

program and can be scrutinized. The term verified numerical model is a numerical model with solution 

accuracy verified by close agreement with an analytical solution and/or other quasi-analytical or numerical 

solutions, according to a process that demonstrates solution convergence in the space and time domains. 

Such numerical models may be verified by applying an initial comparison with an analytical solution, then 

compared with other numerical models for incrementally more realistic cases where analytical solutions are 

not available. (Also see the glossary of Part I, Appendix D, for definition of terms used here.) 

In general, it is difficult to develop worthwhile test cases that can be solved analytically or quasianalytically, but such solutions are extremely useful when possible. An analytical solution provides an 

exact mathematical truth standard, limited to highly constrained cases for which exact analytical 

solutions can be derived. A secondary mathematical truth standard can be established based on the range 

of disagreement of a set of closely agreeing verified numerical models or other quasi-analytical solutions. 

Once verified against all available classical analytical solutions, and compared with each other for a 

number of other diagnostic test cases that do not have exact analytical solutions, the secondary 

mathematical truth standard can be used to test other models as implemented in whole-building 

simulation programs. Although an analytical solution provides the best possible mathematical truth 

standard, a secondary mathematical truth standard greatly enhances diagnostic capability for identifying 

software bugs and modeling errors relative to comparing simulation results to each other without a truth 

standard. This is because the range of disagreement among the results that comprise a secondary 

mathematical truth standard is typically much narrower than that among whole-building energy 

simulation results that may apply less rigorous modeling methods. The secondary mathematical truth 

standard also allows somewhat more realistic (less constrained) boundary conditions to be used in the test 

cases, extending the analytical verification method beyond the constraints inherent for classical analytical 

solutions.

In this work appropriate use of the numerical models is verified by comparing them with the Case GC10a 

analytical solution. Then the secondary mathematical truth standard is developed by carefully comparing 

the numerical-model results with each other as the cases progress toward more realistic conditions. For 

Case GC10a the underlying physical assumptions regarding the slab/ground geometry, thermal properties, 

79 
and boundary conditions are specific to an idealized case for a rectangular floor geometry that has an 

exact steady-state analytical solution for 3-D heat flow (Delsante, Stokes, and Walsh 1983). The linearly 

varying perimeter floor surface temperature boundary condition for this case is not reproducible in 

simplified and mid-level detailed ground heat transfer models that are typically used with whole-building 

energy simulation software. However, Case GC10a serves as a mathematical truth standard for checking 

the proper implementation of numerical models that were used to develop a secondary mathematical truth 

standard for more realistic cases that are compatible with a greater variety of models. 

The analytical solution used for Case GC10a was the only 3-D analytical solution with rectangular 

surface geometry we found. We investigated the possibility of finding or developing a comparable 3-D 

solution for a harmonic boundary condition. However, we did not find a ready-made solution, and several 

applied mathematicians advised that such a solution would be difficult, if not impossible, to derive. 

2.5.1.2 Methodology for Establishing a Secondary Mathematical Truth Standard 

The following methodology for verifying numerical models to develop a secondary mathematical truth 

standard facilitates extension of analytical verification techniques. The methodology applies to 

development of test cases and implementation of the numerical models. The logic for developing test 

cases may be summarized as follows: 

• Identify or develop exact analytical solutions that may be used as a mathematical truth standard 

for testing detailed numerical models with parameters and simplifying assumptions of the 

analytical solution. 

• Apply a numerical solution process that demonstrates convergence in the space and time domains 

for the analytical solution test cases and the additional test cases where numerical models are 

applied. 

• Once validated against the analytical solutions, use the numerical models to develop reference 

results for test cases that progress toward more realistic (less idealized) conditions, and that do 

not have exact analytical solutions. 

• Check the numerical models by carefully comparing their results to each other while developing 

the more realistic cases, and make corrections as needed. 

• Good agreement for the set of numerical models versus the analytical solution – and versus each 

other for subsequent test cases – verifies them as a secondary mathematical truth standard based 

on the range of disagreement among their results. 

• Use the verified numerical-model results as reference results for testing other models that have 

been incorporated into whole-building simulation computer programs. 

Additional rules for developing and implementing analytical verification test cases – some of which 

generally apply for all test techniques – are: 

• Make test cases as simple as possible, to minimize input errors. 

• Make test cases as robust as possible, to maximize signal to noise ratio for a tested feature. 

• Vary test cases incrementally – varying just a single parameter when possible – so disagreements 

among results can be quickly diagnosed. 

• For numerical models, check sensitivity to spatial and temporal discretization, length of 

simulation, convergence tolerance, etc., and demonstrate that modeling is at a level of detail 

where including further detail yields negligible sensitivity to results; this work by the modelers is 

documented in the modeler reports included with Section 2.9. 

• Use independently developed and implemented models, and revise the test specification as 

needed to accommodate various modeling approaches (including for less detailed models); this 

80 
reduces bias by ensuring that the test specification clearly addresses different modeling 

approaches. 

• For resolving disagreements among results that comprise a secondary truth standard, use an 

additional independent expert who is not directly involved in developing the results being 

compared. 

• Corrections to models must have a mathematical and a physical basis and be consistently applied 

across all cases. Changing a model arbitrarily to better match the results from other models is not 

allowed. 

This methodology was applied to extend the analytical solution based mathematical truth standard 

developed in Case GC10a for other cases that do not have exact analytical solutions. It allowed the 

participants to pinpoint relatively small errors in their models. This resulted in excellent agreement for 

annual and peak hour floor conduction (within 0.3%–4.2% for all cases) for three of the numerical models 

used in the study: FLUENT, MATLAB, and TRNSYS. This agreement is the basis of the secondary 

mathematical truth standard developed here. Such agreement also demonstrates that consistent and 

agreeing results are achievable by different modelers using different modeling tools, and that the test 

specification is clearly and consistently understandable to a variety of users. Furthermore, the use of more 

than two numerical models is better for diagnosing disagreements among the numerical models. If only 

two models are used, it may be difficult to identify which is causing the disagreement. For more than two 

models, if one disagrees with the others, an error likely lies with that model. 

During the iterative process of developing the test specification and simulation results, we documented 

the following improvements to numerical models as part of the process of verifying them (Section 2.4 

includes further details): 

• TRNSYS: Initial improvement to automated node meshing algorithm resulted in a 10% increase 

in floor conduction for Case GC10a. 

• TRNSYS: Second improvement to automated node meshing algorithm resulted in a 2% increase 

in floor conduction for Case GC10a. 

• TRNSYS: Third improvement to automated node meshing algorithm resulted in a 0.4% increase 

in floor conduction for Case GC10a, and a 1–2% increase in floor conduction for all other test 

cases. 

• DIT/MATLAB: Improvement to slab edge modeling when convective boundary conditions are 

applied resulted in a 1%–4% decrease in floor conduction for steady-state cases GC30b, GC30c, 

GC60b, and GC65b. 

• DIT/MATLAB: Improvement to slab edge loss routine resulted in 0.3% increase in GC30a floor 

conduction. 

• DIT/MATLAB: Node temperature output interpolation issue was addressed to give more 

meaningful temperature results for layers near the slab and soil surfaces; this had no effect on 

floor conduction results. 

• PAAET/FLUENT: Fixed modeling error resulting in a 0.7% increase in GC30b floor conduction. 

These revisions – along with demonstration that modeling is at a level of detail where including further 

detail yields negligible sensitivity to results (provided in the modeler reports) – improved the quality of 

the numerical-model results and the related secondary mathematical truth standard that is based on the 

range of disagreement of the verified numerical-model (quasi-analytical solution) results.

81 
2.5.1.3 Mathematical Truth Standard versus Absolute Truth Standard 

It is important to understand the difference between a mathematical truth standard and an absolute truth 

standard. In the former, we test the solution process for a model only, not for the appropriateness of the 

solution; that is, we accept the given underlying physical assumptions and recognize that these 

assumptions represent a simplification of physical reality. An approximate truth standard from an 

experiment tests the solution process and the appropriateness of the model within experimental 

uncertainty. The ultimate or absolute validation truth standard would be comparing simulation results 

with a perfectly performed empirical experiment, with all simulation inputs perfectly defined. In reality, 

an experiment is performed and the experimental object is specified within some acceptable range of 

uncertainty. Such experiments are possible, but expensive. We recommend developing a set of empirical 

validation experiments in the future. 

For the results presented in Part III, the Case GC10a analytical solution represents a mathematical truth 

standard; for all other cases the verified numerical models represent a secondary mathematical truth 

standard. 

2.5.2 Comparing Typical Simulation Model Results to Verified Numerical-Model 

Results 

The tables and graphs of Part III present the final results from all the whole-building energy simulation 

programs, analytical solution, and verified numerical models applied in this study. Because the verified 

numerical-model results constitute a reliable set of theoretical results (a secondary mathematical truth 

standard) based on the underlying physical assumptions in the test case definitions, the primary purpose 

of including other simulation results for the “b”- and “c”- series cases in Part III is to allow simulationists 

to compare their relative agreement (or disagreement) versus the verified numerical-model results to that 

for other simulation results. Perfect agreement among simulations using simplified and mid-level detailed 

models versus verified numerical-model results is not necessarily expected. The Part III results indicate 

the sort of agreement that is possible between typical simulation results and the verified numerical-model 

results. 

For simulation programs that can precisely model all the input assumptions of the test cases, a disagreement 

with the analytical solution results or verified numerical-model results indicates a coding error, questionable 

algorithm, documentation problem, input error, or a combination of such errors. Investigating the source of 

the error is strongly recommended. 

Where simulation programs applying simplified and mid-level detailed models have results that disagree 

substantially with the analytical solution results or verified numerical-model results, investigating the 

sources of the differences is also recommended. In this case a difference does not necessarily mean that such 

a program or model is faulty, because differences among modeling techniques, boundary condition 

approximations, and other input assumptions may cause unavoidable differences among results. However, 

our collective experience in this task has indicated that when such programs show substantial disagreement 

with analytical solution results or verified numerical-model results, we often find a coding error, a 

questionable algorithm, a documentation problem, or an input error. 

2.5.3 Improvements to Simulations during the Field Trials 

Because of iterative correction of input errors, software bugs, and clarifications of the test specifications, the 

agreement among simulation results improved with each iteration of the field trials. Improvements to the 

simulation programs are evident when the initial results set – in Figure 2-22 for the steady-state cases and 

82 
Figure 2-24 for the steady-periodic cases – is compared to the final results set in Figure 2-23 for the 

steady-state cases and Figure 2-25 for the steady-periodic cases. (In these figures verified numericalmodel results are shown with blue shaded background and the analytical solution result [Case GC10a] is 

shown with magenta background; abbreviations along the x-axis are shorthand for the case descriptions 

given in Part I.) Improvements to simulation programs or simulation inputs made by participants were 

required to have a mathematical and a physical basis, and to be applied consistently across tests. Arbitrary 

modification of a simulation program’s input or internal code to more closely match a given set of results 

was not allowed. All improvements were required to be documented in modeler reports. 

Because a number of parameters for the final set of test cases varied substantially from the first round of 

test cases distributed in June 2004 (preliminary test cases without “a”-, “b”-, or “c”-series designations) – 

see Section 2.3 – it was difficult to develop a direct comparison between cases for initial results that were 

submitted before the current test cases were developed in June 2005. Therefore, Figures 2-22 and 2-24 

include some results that were determined based on estimates of what they would have been, had 

corrections not occurred during earlier test cases. We also included estimates for what selected initial 

results would have been before fixes were documented in preliminary IEA SHC Task 22 work (Deru, 

Judkoff, and Neymark 2003) that directly preceded this project. Estimates are based on examples of error 

trapping documented in Section 2.4. For Figures 2-22 and 2-24 initial results are included for each model 

as follows. 

• TRNSYS: Initial results for Case GC10a were reduced based on Section 2.4.1.1, related to their 

earliest work with Case GC10. Results for remaining “a”- and “b”-series cases (except Case 

GC50b) were submitted after Case GC10 results, but still for the June 2004 cases; those results 

are reduced based on Section 2.4.1.2. Remaining results for “c”-series cases and Case GC50b 

were initially submitted for the June 2005 test cases; unadjusted initial results are included for 

those cases as they were submitted. 

• PAAET/FLUENT: Results were initially submitted for cases GC10a and GC30a; results for 

GC40a and GC30b were submitted soon afterward. PAAET found an error in its modeling for 

Case GC30b, which affected that case only (see Section 2.4.3.2). PAAET/FLUENT results 

submitted for the remaining cases, after fixing the Case GC30b error, were also the final results. 

• DIT/MATLAB: Results were initially submitted for test cases GC10a, GC30a, and GC40a. 

Remaining steady-state case results were submitted in a later batch. Model improvements 

documented in Section 2.4.2 and node-meshing refinements documented in DIT’s modeler report 

were then applied. MATLAB results submitted afterward for the remaining cases (and previously 

run cases) were also final results. 

• GHT: Results were initially submitted for the preliminary (June 2004) cases, then submitted in 

June 2005 for the June 2005 test cases. As no model revisions were reported for GHT between 

these submittals, initial results for the current cases are included as submitted. 

• SUNREL-GC: Results were initially submitted for the June 2004 test cases, and then submitted 

in June 2005 for the current test cases. For Figures 2-22 and 2-24, results for GC30a and GC40a 

were added and adjusted based on the model revision documented in Section 2.4.7.1 to show the 

earlier results disagreement versus GHT for preliminary cases GC30 and GC40. We showed this 

in the “a”-series context because preliminary cases GC30 and GC40 had slab and ground surface 

coefficients of 5000 W/(m2

⋅K), which is similar to the specified constant surface temperature 

boundary conditions in current cases GC30a and GC40a. All other results are shown for the June 

2005 cases as initially provided. 

83 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-State Floor Conduction

0

500

1000

1500

2000

2500

3000

GC10a 

linear dT

GC30a 

adiab. wall, 

ideal films

GC30b 

adiab. wall, 

h = 100 

GC30c 

h,int = 7.95; 

h,ext = ideal

GC60b 

h,int = 7.95; 

h,ext = 100

GC65b 

h,int = 7.95; 

h,ext = 11.95

Floor Heat Flow (W or Wh/h)

Analytical Solution/CSIRO TRNSYS/TESS FLUENT/PAAET

MATLAB/DIT GHT/NREL SUNREL-GC/NREL

EnergyPlus/GARD VA114-ISO13370/VABI ESP-r-BASESIMP/NRCan

BASECALC/NRCan

Figure 2-22. BESTEST slab/ground heat transfer steady-state cases – floor conduction, 

before BESTESTing 

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-State Floor Conduction

0

500

1000

1500

2000

2500

3000

GC10a 

linear dT

GC30a 

adiab. wall, 

ideal films

GC30b 

adiab. wall, 

h = 100 

GC30c 

h,int = 7.95; 

h,ext = ideal

GC60b 

h,int = 7.95; 

h,ext = 100

GC65b 

h,int = 7.95; 

h,ext = 11.95

Floor Heat Flow (W or Wh/h)

Analytical Solution/CSIRO TRNSYS/TESS FLUENT/PAAET

MATLAB/DIT GHT/NREL SUNREL-GC/NREL

EnergyPlus/GARD VA114-ISO13370/VABI ESP-r-BASESIMP/NRCan

BASECALC/NRCan

Figure 2-23. BESTEST slab/ground heat transfer steady-state cases – floor conduction, 

after BESTESTing

84 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Floor Conduction

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

GC40a

ideal films

GC40b

h=100

GC45b

AR=36x4

GC50b

large

slab/10

GC55b 

2m depth

GC70b

hint=7.95,

hext=11.95

GC80b 

k=0.5

GC40c

hint=7.95,

hext=ideal

GC45c

AR=36x4

GC55c 

5m depth

GC80c

k=0.85

Floor Heat Flow (kWh)

TRNSYS/TESS FLUENT/PAAET MATLAB/DIT

GHT/NREL SUNREL-GC/NREL EnergyPlus/GARD

VA114-ISO13370/VABI ESP-r-BASESIMP/NRCan BASECALC/NRCan

Figure 2-24. BESTEST slab/ground heat transfer steady-periodic cases – floor conduction, 

before BESTESTing 

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Floor Conduction

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

GC40a

ideal films

GC40b

h=100

GC45b

AR=36x4

GC50b

large

slab/10

GC55b 

2m depth

GC70b

hint=7.95,

hext=11.95

GC80b 

k=0.5

GC40c

hint=7.95,

hext=ideal

GC45c

AR=36x4

GC55c 

5m depth

GC80c

k=0.85

Floor Heat Flow (kWh)

TRNSYS/TESS FLUENT/PAAET MATLAB/DIT

GHT/NREL SUNREL-GC/NREL EnergyPlus/GARD

VA114-ISO13370/VABI ESP-r-BASESIMP/NRCan BASECALC/NRCan

Figure 2-25. BESTEST slab/ground heat transfer steady-periodic cases – floor conduction, 

after BESTESTing

85 
• EnergyPlus: As documented in Section 2.4.4.1, EnergyPlus was modified during the preliminary 

IEA SHC Task 22 test cases to allow user input of interior surface coefficient adjacent to the floor 

slab. To estimate the EnergyPlus results before this fix, we reduced the initially submitted results 

for the June 2005 test cases by 63% per Section 2.4.4.1 for a steady-state and a steady-periodic 

case with realistic interior surface coefficients (GC60b and GC70b, respectively). For this IEA34/43 project, EnergyPlus results were initially submitted for the June 2004 test cases, then 

submitted in June 2005 for the June 2005 test cases. Some early improvements to software to 

facilitate running the in-depth cases (see Section 2.4.4) indicated no or likely minor undetermined 

effects on results. Therefore, the June 2005 results are shown as they were submitted, except for 

the following adjustments to estimate results before improvements were made to the EnergyPlus 

model and an input error was corrected. The Case GC40b result was increased based on Section 

2.4.4.5; the Case GC55b result was decreased based on Section 2.4.4.6; results for cases GC40c 

and GC55c were decreased based on Section 2.4.4.4; results for cases GC60b and GC70b were 

reduced based on Section 2.4.4.1. 

• VA114: Results for this project were initially submitted for the June 2005 cases beginning in 

January 2006, after the code authors had begun adapting the ISO 13370 European standard 

ground heat transfer calculation method to VA114. As documented in Section 2.4.5.1, the 

adaptation of the ISO calculation was initiated because of large disagreements for the preliminary 

IEA SHC Task 22 tests. To estimate the VA114 results before ISO 13370 was adapted, initially 

submitted results were reduced by 70% per Section 2.4.5.1 for a steady-state and a steadyperiodic case with realistic interior surface coefficients (GC60b and GC70b, respectively). All 

other VA114 results are presented as initially submitted. 

• ESP-r/BASESIMP and BASECALC: Results were initially submitted for the June 2004 cases. 

However, too many of the specified boundary conditions could not be matched with these 

programs, so the June 2005 cases included “c”-series cases that specifically match those boundary 

conditions, as discussed in Section 2.3. As it was unclear how to convert preliminary results for 

Case GC30 to initial results for GC30c and NRCan’s modeler report does not indicate any 

software revisions were made based on preliminary results, the initially provided “c”-series 

results are presented as submitted. 

The results shown in Figures 2-22 and 2-24 indicate that there was initially a 9%–55% and 10%–55% 

disagreement among the steady-state and steady-periodic cases, respectively, for the floor conduction 

results, and that there was substantial scatter among initial program results for cases with shallow water 

table depth (GC55b) and large slab area (GC50b), and for case results that emphasize errors uncovered 

during the Task 22 cases (GC60b and GC70b). Here, disagreement is the difference between the 

maximum and minimum result for each case, divided by the mean of the results for each case ((maxmin)/mean). 

Figures 2-23 and 2-25 show that after correcting software errors with BESTEST diagnostics, the 

remaining disagreements among all results for steady-state and steady-periodic floor conduction are 1%–

16% and 7%–24%, respectively, with reduced scatter throughout. Agreement is also improved among the 

detailed numerical models, where disagreement ranges up to 12% were reduced to 0%–4% over the 

course of the project. This shows how the BESTEST method is used to diagnose and correct faulty 

algorithms in complex simulation programs. 

Regarding parametric sensitivities in the final results, the sensitivity to reducing interior surface heat 

transfer coefficient is substantial (see results for steady-state cases GC30b and GC60b in Figure 2-23). 

This is because a bare slab floor is specified for the test cases, so the interior surface heat transfer 

coefficient is effectively the primary insulation layer between the conditioned zone and all the floor slab 

and adjacent ground. Placing a carpet on the slab surface would be expected to reduce the sensitivity to 

interior surface coefficient somewhat. However, even with a carpet the amount of insulation between 

86 
conditioned zone air and the slab would be low, so the sensitivity underscores the importance of applying 

accurate interior surface coefficients when modeling ground-coupled heat transfer. Presumably the same 

is true for the exterior surface coefficient, although for this work varying it after varying the interior 

surface coefficient has likely obscured some of its significance (see GC65b versus GC60b in Figure 2-23) 

because overall thermal resistance was increased when interior surface coefficient was decreased for Case 

GC60b. 

Final ranges of disagreement are summarized in Table 2-7 for predictions of various outputs. The outputs 

are disaggregated for Case GC10a, the other steady-state cases (GC30a, GC30b, GC30c, GC60b, 

GC65b), and the steady-periodic cases (GC40a through GC80c, excluding GC60b and GC65b). Results 

are also disaggregated for the verified numerical-model results and the other simulation results. The 

results indicate very good agreement for the verified numerical-model results, within 5% for floor 

conduction in all cases. Disagreement of other simulation results using mid-level detailed models are up 

to 24%, which may be reasonable given the complexity of the modeling problem. The range of 

disagreement for peak loads differs little from that for annual loads, which is expected because solar gains 

are excluded from the test cases. The greatest range of annual floor conduction disagreement occurred for 

Case GC55b, which has the shallowest (2 m) deep ground temperature (or water table) depth and 

therefore the largest ratio of core-to-perimeter (deep ground temperature to air temperature) driven heat 

flow. Remaining disagreement issues for individual results are discussed in Section 2.4. 

Table 2-7. Ranges of Disagreement among Simulation Results 

Output 

Verified Numerical 

Models Other Simulations 

Case GC10a, Steady-State Floor 

Conduction (W or Wh/h) 

0.3% 0.5% (GHT only) 

Steady-State Floor Conduction, 

Other Cases (W or Wh/h) 

0.7%–4.2% 10%–16% 

Annual Steady-Periodic Floor 

Conduction (kWh/y) 

0.9%–3.5% 7%–24% 

Steady-Periodic Annual Peak Hour 

Floor Conduction (W or Wh/h) 

1.0%–4.2% 2%–18% 

Although disagreement among the verified numerical models is low for all cases, it disagreement is lower 

for Case GC10a than for cases where a mathematically derived closed-form analytical solution was not 

available. The reason for this is unclear, but could be the result of minor differences in node meshing 

schemes resulting from different soil domains modeled in GC10a versus the other cases. Anyhow, this 

agreement drift underscores the importance of using analytical solutions when available, and deriving 

new ones when possible. 

Based on results after several iterations of BESTESTing, and resulting model improvements, all the tested 

programs now appear to be generally reliable for modeling ground-coupled heat transfer related to slabon-grade construction, although remaining disagreements for specific models noted in Section 2.4 should 

be addressed. The verified numerical-model results may be used as a reference or benchmark against 

which other software can be tested. For applications where ground-coupled heat transfer is a major 

87 
component of a given simulation problem, the superior accuracy of the verified numerical models may 

justify adapting highly detailed models to more whole-building energy simulation programs, especially as 

computer hardware continues to improve and the detailed models become more user friendly. 

2.5.4 Test Cases for Future Work 

We suggest that additional work related to model testing and validation, outlined in the sections that 

follow, be considered. 

2.5.4.1 Additional Ground-Coupled Heat Transfer Cases 

This project developed a set of idealized in-depth diagnostic test cases for ground-coupled floor slab heat 

transfer models. The test cases allow comparison of models typically used with whole-building energy 

simulation programs to quasi-analytical solutions developed with state-of-the-art detailed 3-D numerical 

models. The test cases use an idealized uninsulated slab-in-grade configuration (see Figure 2-26). This 

simplified configuration is consistent with the analytical solution test case, is appropriate for developing 

robust ground-coupling test cases, is compatible with all the tested programs, and has facilitated the 

development of accurate detailed 3-D numerical-model results by minimizing chances for input errors 

that could occur with more detailed realistic geometry. The current cases provide the foundation for 

developing a numerical-model based secondary mathematical truth standard by transitioning from an 

analytically solvable case (GC10a) to other in-depth diagnostic cases that provide robust parametric 

sensitivity tests, using boundary conditions that are more typically applied by whole-building energy 

simulation programs. During this project, participants discussed other important test case configurations 

that could not be included with the current test cases because of resource constraints. These additional test 

cases would include: 

• A more realistic slab-on-grade configuration and realistic above-grade wall construction (see 

Figure 2-27)

• Slab material properties different from soil properties 

• Realistic full-year site weather data (e.g., TMY2), including robust climate sensitivity tests 

• Insulated cases that test horizontal and vertical insulation configurations (see Figure 2-27), and 

test sensitivity to variation of vertical depth, horizontal width, and insulation thickness 

• Other parametric sensitivity tests in a more realistic context, including variation of soil 

conductivity, slab aspect ratio, slab area, and water table depth 

• Maximized robustness of sensitivity tests within realistic construction extremes 

• Heated slab floors, having heating elements within or beneath the slab – the previously developed 

RADTEST (Achermann and Zweifel 2003) addresses radiant heating test cases, but does not 

address the ground-coupled heat transfer interaction 

• Similar in-depth diagnostic and realistic cases for basement constructions. 

A secondary mathematical truth standard enhances the ability to identify (and therefore diagnose) 

disagreements that may occur for tested simulation models. To facilitate continued use of numerical 

models for extending the set of results that may be used as a secondary mathematical truth standard, the 

following constraints would be applied to new in-depth test cases as appropriate: 

• The above-grade zone is adiabatic, except for the above-grade wall extended to a limited height 

above the floor slab. 

• Solar gains are excluded. 

• IR radiation exchange is suppressed. 

• Parametric variations are applied incrementally – both within the new test cases, and to transition 

from current test cases to new cases. 

88 
Figure 2-26. Current slab-in-grade configuration 

Figure 2-27. Slab-on-grade configuration for proposed additional test cases 

Grade

Above Grade Wall 

(UA = 0)

Foundation Wall 

(same properties as soil)

Soil

z

z

E

F

x

Slab IN Grade

(same properties as soil)

Grade

Slab

Footer

Sill Plate

Typical (e.g., R-11) 

Above Grade Wall

Foundation Wall

z

Soil

x x

z z

z Horizontal Edge 

Insulation

Vertical Exterior 

Edge Insulation

Includes vertical 

thermal break as 

shown x

89 
The ultimate goal of new test case development is to transition back to a more realistic set of test cases 

such as an updated version of the previous IEA SHC Task 22 ground-coupled heat transfer test cases 

(Deru, Judkoff, and Neymark 2003). These final cases would couple a realistic above-grade building 

construction with a realistic ground-coupled surface construction to test: 

• Effects of solar radiation on ground-coupled surfaces 

• Effects of IR radiation exchange on ground-coupled surfaces 

• Effects of calculated versus constant heat transfer coefficients 

• Interaction of floor slab thermal mass with dead-band and setback thermostat control 

• Walkout basement construction 

• Seasonally (or more frequently) varying soil properties and evapotranspiration, if enough models 

consider this. 

The final revised set of realistic test cases would also include results for detailed numerical models 

integrated with whole-building simulation programs where possible – e.g., the detailed models included 

with TRNSYS and SUNREL-GC can be readily integrated with their respective main programs. This 

would allow for continued use of detailed models that were tested for accuracy in preceding cases. Such 

detailed models could also be applied to the four realistic – but only coarsely diagnostic – slab and 

basement simplified model test cases included with HERS BESTEST (Judkoff and Neymark 1995b), for 

comparison with results of simplified models. However, such comparisons would require documenting 

detailed modeling assumptions that are not included in HERS BESTEST. 

The current “c”-series test cases provide examples of cases that were developed to conform with the 

constraints of specific models. Where there is a sufficient need and interest, additional test cases can be 

developed that are tailored to the constraints of other specific models. The need for such test cases could 

occur, for example, where a simplified model that has not been subjected to rigorous accuracy tests forms 

the basis of a codified standard calculation method. In general, it would be best for model authors to 

emphasize developing detailed, flexible ground-coupling models that can employ a great variety of 

realistic building configurations and parametric assumptions related to ground heat transfer. 

The 3-D analytical solution applying the rectangular steady-state boundary conditions of Case GC10a 

allowed us to establish a robust foundation for extension of that mathematical truth standard to other test 

cases by using a secondary mathematical truth standard that was developed with verified numerical 

models. The utility of this steady-state analytical solution generated interest in trying to find an analytical 

solution for a similar 3-D rectangular geometry problem with harmonic boundary conditions. A search for 

such a solution by one project participant was not successful (Crowley 2007). Given the ability to verify 

results of TRNSYS, FLUENT, and MATLAB within a narrow (0.3%–4.2%) range of disagreement for 

the current in-depth test cases, the urgency of obtaining additional analytical solutions was reduced. 

However, Table 2-7 does indicate increased disagreement among the verified numerical models for cases 

without analytical solutions, which underscores the importance of using analytical solutions when 

available. To establish an additional analytical solution as a further fundamental basis for verifying 

numerical-model results, it is worthwhile to consider additional research, perhaps through ASHRAE, to 

develop a solution for rectangular 3-D geometry with harmonic boundary conditions. 

2.5.4.2 Additional Building Thermal Fabric and Mechanical Equipment Test Cases 

Additional building thermal fabric and mechanical equipment model test cases for consideration to be 

developed in the future are summarized in HVAC BESTEST Volume 2 (Neymark and Judkoff 2004; 

Section 2.5.2). 

90 
2.6 Conclusions and Recommendations 

2.6.1 Conclusions 

2.6.1.1 Major Accomplishments 

The major accomplishments of this project were: 

• The IEA BESTEST building thermal fabric envelope tests were expanded to include in-depth 

diagnostic analytical verification test cases for ground-coupled heat transfer related to slab-ongrade construction. 

• A formal methodology was developed to facilitate using and verifying numerical models to 

establish a secondary mathematical truth standard; this method applies to the test case 

developement and to numerical model implementation, and allows quasi-analytical solutions to 

be developed for more realistic (less constrained) cases than exact analytical solutions allow. 

• A set of verified numerical-model results was developed for all test cases, using the newly 

developed methodology; this represents a secondary mathematical truth standard founded on the 

range of disagreement of the numerical-model results. 

• The accuracy of all models that participated in the field trials of the test cases was improved: 19 

errors were diagnosed and fixed; initial disagreement ranges of 9%–55% for the test cases were 

reduced to 1%–24% by applying the diagnostic logic of the test cases to expose problems with 

the models; initial disagreement ranges for only the numerical models were narrower (up to 

12%), and were similarly reduced to 0%–4% for the verified numerical-model results over the 

course of the project. 

With respect to the value of the test cases to software developers, one software developer/vendor 

participant made the following comment about this project: 

Without this IEA subtask for ground coupling, we would have had no means to check the 

results from our model, nor had a reason to make improvements to our model. There should 

be no question that the IEA subtask has improved the TRNSYS ground coupling model 

and, in doing so, has also provided energy modelers a greatly increased sense of confidence 

when modeling heat transfer to the ground (Thornton 2007b). 

2.6.1.2 Summary of Findings 

Test cases for in-depth diagnosis of ground-coupled heat transfer related to uninsulated slab-on-grade 

construction have been added to the IEA's method for systematically comparing whole-building energy 

software and determining the algorithms responsible for prediction differences. The new test cases use an 

idealized uninsulated slab-in-grade configuration. This simplified configuration is required by the 

analytical solution case, is appropriate for developing robust ground-coupling cases, is compatible with 

all the tested programs, and facilitated the development of accurate model results by minimizing chances 

for input errors. These cases, as they step away from the analytical solution, also test parametric 

sensitivities to variation of floor-slab aspect ratio, slab area, water table depth (constant deep ground 

temperature depth), slab-interior and ground-exterior surface heat transfer coefficients, and slab and 

ground thermal conductivity. 

This project developed an important methodological advance to extend the analytical verification method 

beyond the constraints inherent in classical analytical solutions. It allows a secondary mathematical truth 

standard to be developed in the form of a set of stand-alone detailed numerical models (quasi-analytical 

91 
solutions). Once verified against all available classical analytical solutions and compared with each other 

for cases that do not have exact analytical solutions, the set of verified numerical models can be used 

together to test other models as implemented in whole-building simulation programs. This allows for 

greatly enhanced diagnostic capability versus the purely comparative method, and allows somewhat more 

realistic boundary conditions to be used in the test cases than are possible with pure analytical solutions. 

This work applied an analytical solution result (Case GC10a) as a mathematical truth standard, and 

developed verified numerical-model results as a secondary mathematical truth standard for all test cases. 

The final range of disagreement among the verified numerical-model results is much narrower than that 

among the other simulation results, which improved the diagnostic capability of the cases. Therefore, where 

there is a disagreeing simulation result for a given test, there is a much stronger possibility of an algorithmic 

problem, coding error, or input error than when results are compared only with other simulation programs. 

The procedure has been field-tested with a number of building energy simulation programs from around the 

world. The method has proven effective at isolating the sources of predictive differences. The diagnostic 

procedures revealed bugs, faulty algorithms, limitations, and input errors in all simulation models tested in 

this study. This includes the three detailed 3-D numerical models that were verified as quasi-analytical 

solutions – TRNSYS, DIT’s model using MATLAB, and PAAET’s model using FLUENT – along with the 

other tested simulation programs – BASECALC, BASESIMP, EnergyPlus, GHT/SUNREL-GC, and 

VA114 (which adapted the ISO-13370 European standard ground heat transfer calculation). A number of 

important technology advances were made as a result of running the test cases: 

• The detailed numerical-methods modelers used the analytical solution to improve their models – 

e.g., a TRNSYS node meshing refinement (finer mesh near perimeter boundaries) resulted in a 

10% improvement versus the analytical solution. 

• Three participating stand-alone 3-D numerical models showed excellent agreement with the 

analytical solution and with each other for the remaining cases; these verified numerical-model 

results form a secondary mathematical truth standard based on their range of disagreement. 

• The high level of agreement among the verified numerical models allowed diagnosis of errors in 

other mid-level detailed models integrated with whole-building energy simulation software, some 

of which may have been missed without the secondary mathematical truth standard. 

• Of 24 found disagreements, 19 were diagnosed and fixed, 3 are planned for investigation by the 

software authors, and 2 were judged as acceptable by the authors of mid-level detailed models 

(after they had fixed previous disagreements); Table 2-8 summarizes notable examples of error 

trapping – supporting details are provided in Section 2.4. 

Many errors listed in Table 2-8 were significant, with greater than 20% floor conduction effect for several 

cases in this test suite. For unpublished preliminary in-depth cases developed during IEA SHC Task 22 

(which spawned the current cases), two participants documented 270% and 70%–100% effects of model 

improvements on floor conduction dominated heating loads. In other instances for individual programs 

applying the current in-depth cases, some errors had relatively minor (< 2%) effect on floor conduction. 

Where a program had multiple errors of smaller magnitude, such errors did not necessarily compensate each 

other, and may have been cumulative in some cases. Therefore, correcting the minor and major errors was 

important. 

After correcting software errors using BESTEST diagnostics, the remaining disagreements of floor 

conduction results are 0.3%–4.2% for the verified numerical models with very little scatter among them, 

and 1%–24% for the other simulation programs. This shows how the BESTEST method is used to 

diagnose and correct faulty algorithms in complex simulation programs. 

92 
Table 2-8. Summary of Software Problems Found Using IEA BESTEST Slab-On-Grade Cases 

Modela Error Descriptiona % Floor Conduction Effect 

or Disagreementa,b Resolution

BASECALC Input error 1%–5% (“c”-series cases) Fixed 

BASECALC Perimeter heat flow disagreement 9% (GC45c) No changef

BASESIMP/ESP-r Test configurations fall outside range of 

parameter variations allowed by correlations 

21% (GC80c) 

1%–4% (other “c” cases) 

Fixed 

DIT/MATLAB 

 

Surface convection modeling by DIT 1%–4% (GC30b, GC30c, 

GC60b, GC65b) 

Fixed 

DIT/MATLAB Slab edge loss modeling by DIT 0.3% (GC30a) Fixed 

DIT/MATLAB Near-surface temperature reporting by DIT No effect on floor conduction Fixed 

EnergyPlus User cannot input floor slab interior surface 

coefficient 

270% (Task 22 Case GC180) Fixed 

EnergyPlus User cannot define deep ground boundary 

temperature (Tdg) 

No effect on test results 

(Tdg = annual average ODB) 

Fixed 

EnergyPlus User cannot define ground surface h,ext 

(h,ext calculated from wind speed) 

Not isolated by participant, 

probably minor effect 

Fixed 

EnergyPlus Unclear documentation regarding inputs for 

ground depth and far-field dimension 

4%, 7% (GC40c, GC70c) 

Simulation crash (GC55b) 

Fixed 

EnergyPlus Input error related to manual interface of 

Slab subprogram and main EnergyPlus 

35%–40% (GC40) Fixedc

EnergyPlus User cannot define ground depth 35% (GC55b v. GC55) Fixed 

EnergyPlus Disagreement for variation of ground 

surface heat transfer coefficient 

18% (GC65b) Authors 

notified 

EnergyPlus Disagreement for variation of ground depth 15% (GC55b) Authors 

notified 

GHT/SUNREL-GC Integration of GHT model with SUNREL-GC 5% (GC30b v.GC30) 

8% (GC40b v.GC40) 

Fixed 

GHT/SUNREL-GC Disagreements versus verified numerical 

models 

7%–10% (“a”-series cases) 

5%–8% (“b”-series cases) 

Authors 

notified 

PAAET/FLUENT PAAET modeling error 0.7% (GC30b) Fixed 

PAAET/FLUENT Two output reporting issues by FLUENT No effect on overall floor 

conduction 

Fixedd

TRNSYS First noding algorithm improvement 10% (GC10) Fixed 

TRNSYS Second noding algorithm improvement 2% (GC10a) Fixed 

TRNSYS Third noding algorithm improvement 0.4% (GC10a) 

1%–2% (GC30a–GC80c) 

Fixed 

VA114/ISO-13370 One-dimensional conduction modeling 100%, 70% (preliminary Task 

22 cases GC100 and GC180) 

Fixede

VA114/ISO-13370 Insensitive to variation of ground depth 29%, 49% (GC50b, GC55b) Fixed 

VA114/ISO-13370 Late time of occurrence for peak heat flow Peak delayed 700, 300–500 

hours (GC55b, other cases) 

No changef

a Acronyms and abbreviations used in this column are defined in Section 2.7. b Effects are for floor conduction unless otherwise noted; specific cases relevant to the described effects are included in 

parentheses. For disagreements listed as fixed, listed percentage values are the effect of the change for new results versus 

previous results for a given model; otherwise, percentage values are remaining disagreement versus verified numerical models. c Program developers later included example floor model inputs to main EnergyPlus as output from the Slab subprogram; however, 

better automation of interface between the EnergyPlus subprogram and main engine is recommended. d Fixed in later version of FLUENT before this testing. e Adapted ISO-13370 European standard ground heat transfer calculation method. f Software developer indicates this disagreement is acceptable for this model. 

93 
Based on results after several iterations of BESTESTing, and resulting model improvements, all tested 

programs now appear to be generally reliable for modeling ground-coupled heat transfer related to slabon-grade construction, although some remaining disagreements (discussed in Section 2.4) should be 

addressed. The verified numerical-model results may be used as a reference or benchmark against which 

other software can be tested. For applications where ground-coupled heat transfer is a major component 

of a given simulation problem, the superior accuracy of the verified numerical models may justify 

adapting highly detailed models to more whole-building energy simulation programs, especially as 

computer hardware continues to improve and the detailed models become more user friendly. 

Based on this work and previous work of Task 22, there are a number of recommended areas for further 

investigation with respect to developing additional validation test cases for modeling ground coupled heat 

transfer. These are described in detail in Section 2.5.4.1. For the longer term we hope to develop test 

cases that emphasize special modeling issues associated with more complex building types and HVAC 

systems as discussed in Section 2.5.4.2. 

2.6.1.3 Advantages of BESTEST Methodology 

Similar to previous test suites that applied the BESTEST method, these new cases have a variety of uses, 

including: 

• Comparing output from building energy simulation programs to a set of analytical and quasianalytical solutions that constitute a reliable set of theoretical results given the underlying physical 

assumptions in the case definitions 

• Comparing several building energy simulation programs to determine the degree of disagreement 

among them 

• Diagnosing the algorithmic sources of prediction differences among several building energy 

simulation programs 

• Comparing predictions from other building energy simulation programs to the analytical solution, 

verified numerical model results, and simulation results in this report 

• Checking a program against a previous version of itself after the internal code has been modified, to 

ensure that only the intended changes actually resulted 

• Checking a program against itself after a single algorithmic change to understand the sensitivity 

between algorithms. 

An advantage of the BESTEST methodology is that a program is examined over a broad range of 

parametric interactions based on a variety of output types, minimizing the possibility that problems are 

concealed by compensating errors. Performing the tests resulted in quality improvements to all slab-ongrade heat transfer models and building energy simulation programs used in the field trials. Although the 

advancement of the state-of-the-art in ground heat transfer modeling is relatively recent, some bugs may 

well have been present for several years. The fact that they have just now been uncovered shows the 

power of BESTEST and suggests the importance of continuing to develop formalized validation and 

diagnostic methods. Only after coding bugs have been eliminated can the assumptions and 

approximations in the algorithms be evaluated. 

Checking a building energy simulation program for the first time with the BESTEST in-depth slab-on-grade 

heat transfer test cases requires about one person-week for an experienced user, not including improvements 

to the software, if necessary. Subsequent program checks are faster because input files may be reused. 

Because the simulation programs have taken many years to produce, the new BESTEST cases provide a 

94 
very cost-effective way of testing them. As we continue to develop new test cases, we will adhere to the 

principle of parsimony so the entire suite of BESTEST cases may be implemented by users with a 

reasonable time commitment. 

2.6.2 Recommendations 

2.6.2.1 Adaptation of Test Procedures for ANSI/ASHRAE Standard 140 

The work presented in this report, other work of IEA SHC Task 34/ECBCS Annex 43, and the work that 

preceded it in IEA SHC Tasks 8, 12, and 22 are important for two reasons: (1) the methods have been 

extremely successful at correcting software errors in advanced building energy simulation programs 

throughout the world; and (2) the methods are finding their way into industry by being adopted as the 

theoretical basis for formalized standard methods of test and software certification procedures; in this sense 

the work may be thought of as pre-normative research. 

Along with the overall validation methodology (Judkoff et al. 2008; Judkoff 1988; Judkoff and Neymark 

2006) – that has recently been added to the ASHRAE Handbook of Fundamentals (ASHRAE 2005), the 

following test suites, developed in conjunction with IEA, have been code-language adapted and formally 

approved as standard test methods, ANSI/ASHRAE Standard 140-2007, Standard Method of Test for the 

Evaluation of Building Energy Analysis Computer Programs (ANSI/ASHRAE 2007): 

• IEA BESTEST, building thermal fabric comparative tests (Judkoff and Neymark 1995a) 

• HVAC BESTEST Volume 1, unitary cooling equipment analytical verification tests (Neymark 

and Judkoff 2002) 

• HVAC BESTEST Volume 2, unitary cooling equipment comparative tests (Neymark and Judkoff 

2004) 

• HVAC BESTEST fuel-fired furnace analytical verification and comparative tests (Purdy and 

Beausoleil-Morrison 2003). 

Within the BESTEST/Standard 140 structure is room to add new test cases. BESTEST is better developed 

in areas related to energy flows and energy storage in the architectural fabric of the building. BESTEST 

work related to mechanical equipment is still in its early phases in that there are many kinds and 

configurations of mechanical systems to test. 

The new in-depth slab-on-grade ground heat transfer test cases described in this report are planned for 

inclusion in Standard 140. Additionally, HERS BESTEST (Judkoff and Neymark 1995b) is being codelanguage adapted for future inclusion with ASHRAE Standard 140 (SSPC-140 2008). Other completed 

test suites not yet included in ANSI/ASHRAE Standard 140 (ANSI/ASHRAE 2007) that have been 

developed within IEA SHC Task 34/ECBCS Annex 43 and IEA SHC Task 22, and will be considered for 

addition to Standard 140, include:

• IEA BESTEST Multi-Zone Non-Airflow In-Depth Cases (Neymark, Judkoff, et al. 2008) 

• BESTEST Airflow Cases (Utsumi and Mitamura 2008) 

• Shading/Daylighting/Load Interaction Empirical Validation Tests (Loutzenhiser, Manz, and 

Maxwell 2007) 

• Chilled Water and Hot Water Mechanical Equipment and Control Comparative and Empirical 

Validation Tests (Felsmann 2008) 

• Double-Skin Façade Comparative and Empirical Validation Tests (Kalyanova and Heiselberg 

2008) 

95 
• RADTEST Radiant Heating and Cooling Test Cases for hydronic systems (Achermann and 

Zweifel 2003). 

Other test suites developed outside IEA research that are near-term candidates for inclusion with 

ASHRAE Standard 140 include: 

• ASHRAE RP-865, Development of Accuracy Tests for Mechanical System Simulation (Yuill and 

Haberl 2002) 

• ASHRAE RP-1052, Development of an Analytical Verification Test Suite for Whole Building 

Energy Simulation Programs – Building Fabric (Spitler, Rees, and Xiao 2001) 

• Mechanical equipment test cases for low-rise residential construction included in, Procedures for 

Verification of International Energy Conservation Code Performance Path Calculation Tools 

(RESNET 2007). 

2.6.2.2 Closing Remarks 

Standard 140 and the BESTEST reports that comprise the test suites contained therein, are being referenced 

and used by a growing number of code promulagation authorities throughout the world. ASHRAE Standard 

90.1 (ANSI/ASHRAE/IESNA 2007, 2005), which is ASHRAE’s consensus energy code for commercial 

buildings and for non-low-rise residential buildings, requires that software used for demonstrating 

performance compliance with Standard 90.1 be tested using ASHRAE Standard 140-2004 (ANSI/ASHRAE 

2004a). Similarly, software used for calculating energy savings for energy-efficient commercial building tax 

deductions in the United States must be tested with Standard 140-2007. (IRS 2008) DOE currently lists 10 

building energy simulation programs as qualified for this purpose, by having been tested with Standard 140. 

(DOE 2008) IEA BESTEST is also being used for simulation certification tests in The Netherlands (ISSO 

2003), Australia (SEDA 2003; Pears 1998), New Zealand (Donn 2004), and Portugal (Maldonado 2005). As 

part of their building energy performance assessments under the European Community’s Energy 

Performance Directive (European Union 2002), Austria, Denmark, Greece, and The Netherlands are using a 

new software tool that includes algorithms that have been checked with BESTEST (Balaras, Poel, and van 

Crutchen 2005). Also, CEN has used BESTEST to check its reference cooling load calculation general 

criteria of prEN ISO 13791 (CEN 2004a) and simplified methods of prEN ISO 13792 (CEN 2004b; Millet 

2003) In the United States, the National Association of State Energy Officials (NASEO) Residential Energy 

Services Network (RESNET) has adopted Home Energy Rating System (HERS) BESTEST (Judkoff and 

Neymark 1995b) as the basis for certifying software to be used for home energy rating systems under the 

NASEO/RESNET national accreditation standard (NASEO/RESNET 2006). These citations indicate the 

importance of validation methods for improving the state-of-the-art in building energy simulation software, 

and for helping to certify such software for use with building energy codes, building energy tax credits, 

home energy rating standards, and other building energy incentive programs. 

A growing body of evidence indicates that the BESTEST procedures are becoming part of software 

developers’ normal in-house quality control efforts. Use of the BESTEST procedures has been documented 

by many software developers in the United States and elsewhere, including the developers of prominent 

programs such as DOE-2.1E, DOE-2.2, EnergyPlus, eQUEST, HAP (Carrier Corp.), TRACE (Trane), 

TRNSYS, ESP-r (United Kingdom), HOT3000 (Canada), VA114 (The Netherlands), and many others. A 

recent report compared 20 whole-building energy simulation tools (Crawley et al. 2005). The report 

indicates that 19 of the 20 tools reviewed have been tested with at least one of the four BESTEST 

procedures included in ANSI/ASHRAE Standard 140-2007, four have been tested with three procedures, 

two have been tested with all four procedures, and four have also been tested with HERS BESTEST, which 

is currently being adapted for Standard 140. Additional examples of the importance of software testing 

include: 

96 
• The number of programs listed as having qualified for calculating energy savings for the energyefficient commercial building tax deductions in the United States, which require testing with 

ASHRAE Standard 140, increased from 1 to 10 between June 2006 and March 2008 

• Software developers’ use of Standard 140 and BESTEST, along with other validation tests, is 

documented on the DOE Building Energy Software Tools Directory (DOE 2008) 

• At least one software developer has automated use of BESTEST within its software for testing 

new versions (Strachan, Kokogiannakis, and Macdonald 2005) 

• Researchers in other countries have translated previous BESTEST work into Dutch, German, and 

Japanese (ISSO 2003; Neymark et al. 2003; Utsumi et al. 2006a, 2006b) 

• We have received more than 1000 requests for the various BESTEST reports. 

Along with this, the simplicity, diagnostic power, and building physics background content of BESTEST 

are evidenced by the BESTEST procedures being used as teaching tools for simulation courses at 

universities in the United States and Europe. 

Computer scientists universally accept the merits of software testing. A well-known rule of thumb is that 

in a typical programming project more than 50% of the total cost is expended in testing the program or 

system being developed (Myers 2004). Of this, about 20% of development time goes toward system 

testing (McConnell 2004). Because new energy-related technologies are continually being introduced into 

the buildings market, there will always be a need to further develop simulation models, combined with a 

substantial program of testing and validation. Such an effort should contain all the elements of an overall 

validation methodology (Judkoff and Neymark 2006; ASHRAE 2005, Chp. 32), including: 

• Analytical verification 

• Comparative testing and diagnostics 

• Empirical validation. 

Future work should therefore: 

• Continue to produce a standard set of analytical tests. 

• Develop a set of diagnostic comparative tests that emphasize the modeling issues important in large 

commercial buildings, including more tests for heating, ventilating, and air-conditioning systems, 

and other mechanical equipment including on-site power generation equipment. 

• Develop a sequentially ordered series of high-quality data sets for empirical validation. 

Continued support of model development and validation activities is essential because occupied buildings 

are not amenable to classical controlled, repeatable experiments. The few buildings that are truly useful 

for empirical validation studies have been designed primarily as test facilities. The energy, comfort, and 

lighting performance of buildings depend on the interactions among a large number of transfer 

mechanisms, components, and systems. Simulation is the only practical way to bring a systems 

integration problem of this magnitude within the grasp of designers. A growing body of literature and 

activity demonstrates the importance of simulation tools for greatly reducing the energy intensity of 

buildings through better design (e.g., Torcellini, Hayter, and Judkoff 1999; IBPSA 2005; GARD 

Analytics 2007). As building energy simulation programs are more widely used – such as in the United 

States. for establishing LEED ratings (USGBC 2007) and federal tax deductions, in Europe to comply 

with the European Performance Directive, in Australia to comply with greenhouse gas emission ratings, 

etc. – the design and engineering communities must continue to have confidence in the quality of these 

programs. Such confidence and quality are best established and maintained by combining a rigorous 

development and validation effort with user-friendly interfaces. 

97 
The work described here represents a good start in the effort to develop carefully validated building energy 

simulation tools. Continued development and validation of whole-building energy simulation programs are 

two of the most important activities meriting the support of national energy research programs. DOE and the 

IEA executive committees for Solar Heating and Cooling and for Energy Conservation in Buildings and 

Community Systems should diligently consider future collaborations that would best support this essential 

research area.

Finally, the authors wish to acknowledge that the expertise available through IEA and the dedication of 

the participants were essential to the success of this project. Over the 4-year field trial effort, there were 

several revisions to the BESTEST specifications and subsequent re-executions of the computer 

simulations. This iterative process led to the refining of the new BESTEST cases, and the results of the 

tests led to improving and debugging the simulation models. The process underscores the leveraging of 

resources for the IEA countries participating in this project. Such extensive field trials, and resulting 

enhancements to the tests, were much more cost effective with the participation of the IEA SHC Task 34/ 

ECBCS Annex 43 experts. 

2.7 Abbreviations and Acronyms for Parts II and III 

These acronyms are used in Sections 2.2 through 2.6 and in Part III. 

Adiab adiabatic 

ANSI American National Standards Institute 

AR aspect ratio 

ASHRAE American Society of Heating, Refrigerating and Air-Conditioning Engineers 

BESTEST Building Energy Simulation Test and Diagnostic Method 

CEN European Committee for Standardization 

CETC CANMET Energy Technology Centre, Natural Resources Canada 

CSIRO Commonwealth Scientific and Industrial Research Organisation 

DIT Dublin Institute of Technology 

DOE U.S. Department of Energy 

E deep ground depth 

ECBCS Energy Conservation in Buildings and Community Systems Programme (of the IEA) 

ESRU Energy Systems Research Unit, University of Strathclyde 

F far field dimension 

GARD GARD Analytics 

h surface heat transfer coefficient 

HERS Home Energy Rating System 

HVAC heating, ventilating, and air-conditioning 

h,int interior surface heat transfer coefficient 

h,ext exterior surface heat transfer coefficient 

IBPSA International Building Performance Simulation Association 

98 
IEA International Energy Agency 

IEA 34/43 International Energy Agency joint Solar Heating and Cooling Programme Task 34 and 

Energy Conservation in Buildings and Community Systems Programme Annex 43 

IESNA Illuminating Engineering Society of North America 

Inf. infinity 

ISO International Organization for Standardization 

ISO 13370 European Standard EN ISO 13370: Thermal performance of buildings – Heat transfer via the 

ground – Calculation methods 

ISSO Instituut voor Studie en Stimulering van Onderzoek op het Gebied van Gebouwinstallaties 

(The Netherlands) 

k slab/soil thermal conductivity 

LBNL Lawrence Berkeley National Laboratory 

LEED Leadership in Energy and Environmental Design 

Lin dT linearly varying perimeter boundary surface temperature (see Case GC10a, Section 1.3.2.1) 

Max maximum 

Min minimum 

NASEO National Association of State Energy Officials 

NRCan Natural Resources Canada 

NREL National Renewable Energy Laboratory 

ODB outdoor dry-bulb temperature 

PAAET Public Authority for Applied Education and Training 

prEN project Norme Européenne (draft European Standard) 

R thermal resistance 

RADTEST radiant heating and cooling test cases 

RESNET Residential Energy Services Network 

SEDA Sustainable Energy Development Authority (Australia) 

SHC Solar Heating and Cooling Programme (of the IEA) 

Soln. solution 

sp steady-periodic 

ss steady-state 

SSPC Standing Standard Project Committee (of ASHRAE) 

Tdg, Tdg deep ground temperature 

TESS Thermal Energy System Specialists 

TMY2 Typical Meteorological Year 2 

UA thermal conductance 

USGBC U.S. Green Buildings Council 

U.S. IRS United States Internal Revenue Service 

v. versus 

99 
VABI VABI Software BV 

x variable dimension along x-axis 

z variable dimension along z-axis 

1-D one-dimensional 

2-D two-dimensional 

3-D three-dimensional 

2.8 References for Parts II and III 

Achermann, M.; Zweifel, G. (2003). RADTEST Radiant Heating and Cooling Test Cases. Horw-Lucerne, 

Switzerland: Lucerne School of Engineering and Architecture, University of Applied Sciences of Central 

Switzerland. www.iea-shc.org/task22/reports/RADTEST_final.pdf. 

ANSI/ASHRAE Standard 140-2004. (2004a). Standard Method of Test for the Evaluation of Building 

Energy Analysis Computer Programs. Atlanta, Georgia, US: American Society of Heating, Refrigerating 

and Air-Conditioning Engineers. 

ANSI/ASHRAE Standard 140-2004. (2004b). Addendum b. Standard Method of Test for the Evaluation 

of Building Energy Analysis Computer Programs. Atlanta, Georgia, US: American Society of Heating, 

Refrigerating and Air-Conditioning Engineers. 

ANSI/ASHRAE Standard 140-2007. (2007). Standard Method of Test for the Evaluation of Building 

Energy Analysis Computer Programs. Atlanta, Georgia, US: American Society of Heating, Refrigerating 

and Air-Conditioning Engineers. 

ANSI/ASHRAE/IESNA Standard 90.1-2007. (2007). Energy Standard for Buildings Except Low-Rise 

Residential Buildings. Atlanta, Georgia, US: American Society of Heating, Refrigerating and AirConditioning Engineers. References ANSI/ASHRAE Standard 140-2004. 

ANSI/ASHRAE/IESNA Standard 90.1-2004, Addendum L, Energy Standard for Buildings Except LowRise Residential Buildings. (2005). Atlanta, GA: American Society of Heating, Refrigerating and AirConditioning Engineers. References ANSI/ASHRAE Standard 140-2004. 

ASHRAE. (2005). 2005 Handbook of Fundamentals, Atlanta, Georgia, US: American Society of Heating, 

Refrigerating and Air-Conditioning Engineers. 

Balaras, C.A.; Poel, B.; van Crutchen, G. (2005). Software for Energy Performance Assessment of 

Existing Dwellings. IBPSA News, Volume 15, Number 1. International Building Performance Simulation 

Association, April 2005. 

Beausoleil-Morrison, I. (1996). "BASECALC : A Software Tool for Modeling Residential- TM 

Foundation Heat Losses.” Third Canadian Conference on Computing in Civil and Building 

Engineering. Montreal. pp. 117–126. 

Beausoleil-Morrison, I. (1999). BASESIMP ESP-r implantation (Fortran code). Ottawa, Canada: Natural 

Resources Canada. 

100 
Beausoleil-Morrison, I.; Mitalas, G. (1997). “BASESIMP: A Residential-Foundation Heat-Loss 

Algorithm for Incorporating into Whole-Building Energy-Analysis Programs”, Building Simulation ’97, 

(2) 1-8, International Building Performance Simulation Association, Prague Czech Republic. 

Ben-Nakhi, A. (2006). Private communications with J. Neymark. Kuwait, State of Kuwait: Public 

Authority for Applied Education and Training. May 2006. 

CEN. (2004a). prEN ISO 13791. Thermal Performance of Buildings – Calculation of Internal 

Temperatures of a Room In Summer without Mechanical Cooling – General Criteria and Validation 

Procedures. Final Draft. Comité Européen de la Normalisation, Brussels. 

CEN. (2004b). prEN ISO 13792. Thermal Performance of Buildings – Calculation of Internal 

Temperatures of a Room In Summer without Mechanical Cooling – Simplified Methods. Final Draft. 

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102 
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104 
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105 
2.9 APPENDIX II: Simulation Modeler Reports 

In Appendix II, we present reports written by the modelers for each simulation program. The modelers were 

asked to document: 

• Modeling assumptions (required inputs not explicitly described in the test specification) 

• Modeling options (alternative modeling techniques) 

• Difficulties experienced in developing input files for the test cases with their programs 

• Demonstration of appropriate level of modeling detail 

• Bugs, faulty algorithms, documentation problems, and input errors uncovered during the field trials 

• Source code or input modifications made because of the diagnostic results 

• Comments on agreement or disagreement of results compared to other simulation results 

• Any odd results obtained with their programs 

• Sensitivity studies conducted to further understand the sources of differences between their 

programs and the others 

• Conclusions and recommendations about their simulation models, the test specification, or both. 

Modelers also filled out a pro-forma description that defines allowable ranges of inputs for geometry and 

material properties related to slab-on-grade construction. 

106 
Appendix II-A

Modeler Report for BESTEST Cases GC10a-GC80c 

TRNSYS Version 16.1 

by 

Jeff Thornton 

Thermal Energy System Specialists, LLC 

United States 

 

September 2007 

1. Introduction

TRNSYS is a modular system simulation tool that has been widely used in the study of buildings, renewable 

energy technologies, and HVAC systems. The program was originally written by the Solar Energy 

Laboratory at the University of Wisconsin; but recently is maintained, supported, and distributed by a 

consortium of international companies and government agencies. TRNSYS Version 16.1 was used for the 

most recent analysis as well as an extended library of TRNSYS components written by Thermal Energy 

System Specialists (TESS) LLC of Madison, WI. The ground coupling models used for this analysis are 

part of the commercially available TESS ground-coupling library for TRNSYS. 

The particular model that was used for this analysis is a part of a larger suite of slab-to-soil heat transfer 

models written by TESS for the TRNSYS simulation package that differ only in application. The core 

solution algorithm used for the suite of models is identical. For example, there are models for slab-on-grade 

situations, slab-in-grade situations, slabs that interact with detailed building models that calculate the radiant 

exchange between surfaces, slabs that interact with the simpler building models where only the zone air 

temperature is available, models where there is not a slab but simply a resistive cover over the ground 

surface, versions where the foundation walls (and insulation) are accounted for, etc. 

In the IEA test procedure, the slab, soil, and foundation walls have identical thermal properties with no 

insulation beneath the slab or on the edges of the slab. The slab is assumed to be very thin and surrounded 

by adiabatic walls (all cases but GC10, which imposes a conductive boundary). The radiant exchange from 

the slab to the zone is ignored in the test cases. With these restrictions in place, we chose one of our models 

that best fit the requirements of these tests. 

With the slab having the same thermal properties as the soil, being very thin, and communicating with the 

zone through convective exchange only, we were able to use one of our simpler models for these tests. The 

model that we chose simulates an exposed floor with a conductive covering that isolates the zone air from 

the soil. In these test cases, the resistance of the covering was set very small to mimic the test conditions. 

The routine models the heat transfer from a horizontal surface to the soil beneath the surface. The heat 

transfer is assumed to be conductive only and moisture effects are not accounted for in the model. The model 

relies on a 3-dimensional rectangular finite difference representation of the soil and solves the resulting 

interdependent differential equations using a simple iterative method. The governing differential equations 

imposed by the energy balance on each soil node are solved using an implicit methodology; ensuring that the 

solution is stable over all ranges of simulation time steps. 

107 
One of the philosophies of the TRNSYS simulation program is that individual component models should be 

formulated as generically as possible such that they may be re-used in other applications. This slab model is 

no exception. 

Due to its implicit formulation, the model allows very high surface heat transfer coefficients (i.e., addresses 

large Biot Number issues) without the calculation instabilities that plague many of the other soil models 

currently being studied. This can be seen by the almost identical results from the constant surface 

temperature condition and the high convection coefficient condition shown later in this report. Each of the 

soil nodes at the surface conducts to the “local surface temperature” and not directly to the ambient or zone 

temperature. The “local surface temperature” is typically calculated from an energy balance on a massless, 

opaque plane located between the air and the soil node. This solution methodology requires another set of 

coupled iterative calculations within the model – but allows us quite a bit more freedom with the model – a 

requirement for a well-formulated TRNSYS model. The surface temperature can be calculated from an 

energy balance (just described), set from a long term average surface temperature correlation (Kasuda 1965), 

or provided to the model as an input (for example from a swimming pool model or parking lot model, etc.) 

The soil volume surrounding the slab in the x, y, and z directions (Cartesian coordinate system) is referred to 

as the near field. The near field soil is assumed to be affected by the heat transfer from the slab into the soil. 

Nodes contained in the near field can vary in size in all three dimensions, typically becoming larger as they 

get farther from the edges/corners of the slab or get farther from the surface. The user controls the size and 

number of the nodes by providing parameters to the model for the noding algorithm, as described later in this 

document. The user also controls the size/volume of the near field by providing parameters to the model 

specifying the distance away from the edge of the slab that the soil is unaffected by the slab (far field 

distance), and the distance beneath the slab that the soil is unaffected by the slab (deep earth distance). 

The near field is in turn surrounded by the far field, which is assumed to be an infinite energy sink/source 

(energy transfer with the far field does not result in a temperature change of the far-field). Like the near field 

nodes, the sizes of the far-field nodes typically increase as they get further from the soil surface. The 

boundary between the near field and far field may also be specified as adiabatic. The soil beneath the near 

field (below the deep earth boundary) is also assumed to be unaffected by the slab and may also be specified 

as an adiabatic boundary. The temperature of the far-field nodes can be calculated based on an energy 

balance (not a function of the near field temperatures but solely of the surface and deep earth temperatures) 

or can be specified by the Kasuda correlation (temperature a function of the time of year and distance below 

the surface). The deep earth temperature can also be an input to the model (for high water movement for 

example) or calculated from the Kasuda approach. 

2. Modeling Assumptions

No assumptions beyond those imposed by the test were noted. 

3. Modeling Options

The ground-coupling models may be operated independently of the building model (one of the benefits of 

TRNSYS) and, unless otherwise noted, were left uncoupled from the building model. By uncoupling the 

ground model from the building model, the speed of the simulations was increased as there are no iterative 

calculations between the building and the ground models. The test cases called for a fully-mixed zone-air 

condition with idealized controls to maintain the zone air temperature at the prescribed values. The intent of 

this specification was to mimic a constant zone air temperature – possible in the TRNSYS environment by 

simply providing the desired temperature to the ground model as an input for the zone air temperature 

(typically connected to the zone air temperature model output from the building). 

108 
A simple building project with coupling to the soil model is shown below to illustrate the iterative nature of 

the solution. 

As the test procedure either specified the soil surface conditions or the ambient temperature along with either 

the zone air temperature or slab surface temperature, the coupling of the ground model to the building was 

not required. Instead a temperature profile could be connected to the ground model to simplify things as 

shown in the figure below. 

The ground coupling models, and TRNSYS in general may be operated at timesteps ranging from 1/100th of 

a second to 1 hour. For these tests, as there is not an iterative solution required between component models, 

the simulations were run with a 1-hour timestep. 

109 
4. Modeling Difficulties

The original models were not set up to allow for a conductive wall as called for in test case GC10. The 

models allowed us to insulate the ground surface surrounding the slab for a user-specified width (as called 

for in test case GC30) but had no mechanism for imposing a linear variation between the slab temperature 

(Ti) and the ground surface temperature (To) over the specified width (W). As the analytical solution 

provided us with a solid test case for our modeling assumptions, we created a slightly modified version of 

the standard model that attempted to meet the criteria imposed by test case GC10. In the original slab model, 

the user has an option to specify the surface temperature of the ground; set to 10°C for the entire ground 

surface for this test. However, being the model developer, we were able to modify a version of the source 

code and set the ground surface temperatures for the nodes representing the width (W) around the slab to 

have a linear variation from 30°C to 10°C. In this way the conductive boundary approach specified by 

GC10 is modeled and we should be able to get a fairly good estimate to the analytical solution. 

5. Demonstration of Appropriate Level of Modeling Detail

 For Case GC10 only, demonstrate the current level of modeling detail yields negligible (= 0.1%) 

change in results versus a lesser level of detail, including for: 

• deep ground boundary depth and far-field boundary distance 

We ran a series of test cases for the GC10 specification (using a moderately noded soil) to study the 

impact of far-field and deep-earth distances on the slab-to-soil heat transfer rate. The results are presented 

below in tables showing the heat transfer rate at the end of the 10th year of operation and showing the 

percent difference between each combination of deep earth and far-field distances as compared to the 40 

m × 40 m case. 

The results show that we could have run with a deep earth distance of 30 m and a far-field distance of 20 

m and met the 0.1% criteria for submittal. However with our expanding noding size scheme in the model, 

we were able to run at 40 m × 40 m without a significant change in simulation speed as compared to the 

30 m × 20 m case. The results presented in the summary sections of this report for TRNSYS for the 

GC10a case utilize a denser noding than the results presented here and also utilize 40 m x 40 m 

boundaries. It should also be noted that the boundaries for these tests were assumed to be conductive 

boundaries and not adiabatic boundaries. 

10 20 30 40

10 2,411.34 2,459.04 2,408.91 2,408.78

20 2,406.67 2,458.39 2,403.29 2,403.10

30 2,406.50 2,458.38 2,403.05 2,402.85

40 2,406.49 2,458.38 2,403.04 2,402.84

Far Field Distance (m)

Slab Heat Transfer 

(Watts)

Deep Earth Distance (m)

110 
10 20 30 40

10 2.34% 0.35% 0.25% 0.25%

20 2.31% 0.16% 0.02% 0.01%

30 2.31% 0.15% 0.01% 0.00%

40 2.31% 0.15% 0.01% 0.00%

Percent Change from 

40 x 40 Case Far Field Distance (m)

Deep Earth Distance (m)

 

 For Case GC10 only, demonstrate the current level of modeling detail yields negligible (= 0.1%) 

change in results versus a lesser level of detail, including for 

• duration of simulation (tsim) 

Using the submittal results for test case GC10a (heavily-noded, 40 m × 40 m boundary), the slab heat 

transfer as a function of time is shown graphically and numerically below. 

111 
0

500

1,000

1,500

2,000

2,500

3,000

1 2 3 4 5 6 7 8 9 10

Year of Analysis

Slab Heat Transfer Rate (W)

0.01%

0.10%

1.00%

10.00%

100.00%

% Change from Previous Year (Log Scale)

Slab Heat Transfer Rate (W)

% Difference from Previous Year

Year 

Slab 

Heat 

Transfer 

(W) 

% 

Change 

1 2,519.46 100.00% 

2 2,467.79 2.05% 

3 2,451.21 0.67% 

4 2,441.96 0.38% 

5 2,436.12 0.24% 

6 2,432.16 0.16% 

7 2,429.33 0.12% 

8 2,427.23 0.09% 

9 2,425.63 0.07% 

10 2,424.37 0.05% 

Although the slab heat transfer quickly stabilizes after only a few years, it should be pointed out that all 

heat transfers in the ground have not stabilized – even after 10 years. The following plot shows the heat 

transfer rates as a function of time. Notice that the amount of energy storage is decreasing, but still nonzero – indicating steady-state has not been fully reached. The bottom boundary and side boundary heat 

transfer rates are also increasing as the 10th year is reached. 

112 
-

500

1,000

1,500

2,000

2,500

3,000

0 1 2 3 4 5 6 7 8 9 10

Year

Heat Transfer (W)

Slab

Bottom Boundary

Ground Surface

Side Boundary

Stored

 For Case GC10 only, demonstrate the current level of modeling detail yields negligible (= 0.1%) 

change in results versus a lesser level of detail, including for: 

• convergence tolerance 

As our model relies on an implicit and iterative approach to solve for the nodal temperatures and heat 

flows at each simulation timestep, the convergence tolerance may be a factor in the results. The model 

will iterate at each timestep until every calculated nodal temperature (which affects each surrounding 

nodal temperature) changes by less than the convergence tolerance from the previous iteration. However, 

we found that for the steady-state GC10a test case that the tolerance only affected the soil energy balance 

at each timestep and not the long-term (near steady-state) heat transfer rates as shown below:

Convergence 

Tolerance (C)

% Difference 

from Previous

 N/A 0.00001

 0.00010 0.02%

 0.00100 0.01%

 0.01000 0.00%

 0.10000 0.00%

 1.00000 0.00%

While it may seem counterintuitive that the percent difference actually decreases as the tolerance gets 

larger we believe that this is actually correct. With a large tolerance, the temperatures of the nodes aren’t 

updated as often each time step, but are still done at least once each time step. After 10 years of 

operation, the nodal temperatures are not changing more than about 0.01°C per hour, resulting in no 

change in slab heat transfer as we loosen the convergence tolerance further. For the submitted test cases 

we ran with a convergence tolerance of 0.001°C. 

113 
 For Case GC10 only, demonstrate the current level of modeling detail yields negligible (= 0.1%) 

change in results versus a lesser level of detail, including for: 

• numerical methods mesh. 

The TRNSYS model relies on an algorithm that increases the sizes of the nodes in the x, y, and zdirections outwards and downwards from the edges of the slab and away from the surface boundary. 

1 * − = i

i Nom XSizeSize

Where i = 1 corresponds to the node nearest the edge of the slab or surface, SizeNom is the size of the 

smallest node (typically 1 inch for these cases) and X is a scalar (typically 1.2 to 2.0). Changing the size 

of X from 2.0 to 1.2 significantly increases the number of nodes. For a 40 m × 40 m boundary, changing 

the scalar from 2.0 down to 1.2 increases the total number of nodes by a factor of 18 for a 1-inch sized 

smallest node. 

The heat transfer as a function of the number of nodes (for a smallest node size of 1 inch) and the percent 

difference from the analytical solution for each scalar value are show below. 

Scalar Value % Difference 

from 

Delsante 

2.0 4.5% 

1.8 3.4% 

1.6 2.2% 

1.4 1.1% 

1.3 0.6% 

1.2 0.2% 

114 
2,000

2,050

2,100

2,150

2,200

2,250

2,300

2,350

2,400

2,450

2,500

0 10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 100,000

Total Number of Nodes

Slab Heat Transfer (W)

TRNSYS Results

Delsante Solution

6. Software Errors Discovered, and/or Comparison between Different Versions of the Same 

Software, and/or Lessons Learned Regarding Use of Detailed Models

At the onset of this IEA task, our component models for soil heat transfer were brand new and had not yet 

been extensively tested or reviewed. It was only at the urging of the IEA task leaders that we agreed to 

submit our results for this project. They felt that having a detailed but flexible model in the test process 

would not only provide the project participants with another set of baseline results but may also ultimately 

improve the model itself. They were right. 

We have changed our model several times during the process, mostly minor cosmetic changes to make the 

model easier to use or improving the output capabilities of the program. However, we did improve the 

noding algorithm substantially from its earliest incarnation. The original model employed a user-specified 

number of nodes along the slab and in the near field (X and Y directions) as well as a user-specified number 

of nodes in the depth direction. Adjacent nodes in the near field increased in size by a factor of 2.0 from the 

edges of the slab outwards and downwards. The soil nodes directly beneath the slab surface were assumed to 

have constant X and Y dimensions (uniformly noded) with the user controlling the number of nodes in each 

direction. While we were aware that this uniform noding scheme under the slab was far from ideal, we felt 

that the change would be somewhat small and that the heat transfer would be limited by the amount of nodes 

in the soil beyond the slab. We were also concerned with the simulation speed slowdown that we were 

noticing as we began to heavily node the soil beneath the slab. 

The original preliminary model, applied prior to the January 2005 initial TRNSYS results submittal, had the 

following nodal settings: 

115 
• The entire slab was modeled, not just one-fourth of the slab as in later versions 

• The size of the nodes directly under the slab in the X and Y-directions was uniform 

• The size of the nodes directly under the slab in the depth direction (Z) increased by a factor 

of 2 for each node. 

• The sizes of the nodes in the X, Y, and Z directions for the nodes not directly under the slab 

changed by a factor of 2 as the nodes proceed farther from the slab edge and deeper from 

the soil surface. 

• The size of the smallest node in the X, Y, and Z directions was calculated as a function of 

the number of nodes allowed in each direction and the distance from the slab to the far-field 

and deep-earth boundaries. 

Given its preliminary nature, we were not surprised that this early model had a nearly 12% disagreement 

versus the analytical solution. For the January 2005 field-trial results submittal, the assumption of uniformly 

sized nodes under the slab was changed to a user-specified number of nodes under the slab with the nodes 

growing in size by a factor of 2 as they progressed inwards, outwards and downwards from the edges of the 

slab. As shown below (see results labeled 1/14/05), this improvement caused a 10% increase in floor 

conduction versus the original node mesh, but still had a 3% disagreement with the analytical solution. 

 Steady-State Analytical Verification, Case GC10

qfloor % difference versus

(W) Analytical Solution

Analytical Soln. 2561 --

TRNSYS (Initial Results) 2261 -11.71%

TRNSYS (Results of 1/14/05) 2486 -2.93%

We could have easily increased the number of uniformly spaced slab nodes to compensate, but with an 

alarming increase in simulation time. For the same size largest node under the slab, the increasing size 

algorithm results in significantly more nodes than the uniform noding scheme at a cost of significant 

simulation time. It should be noted that the January 2005 submittal utilized very small nodes near the edges 

of the slab – smaller even than the 1-inch nodes used in latter submissions (but with a larger scalar as 

discussed below). 

For the June 2005 submittal we thought that creating an automatic noding scheme with a few user-specified 

parameters was preferable to the user having to enter the number of the nodes in the x, y, and z directions 

(certainly the new approach is less flexible but easier to use). With this in mind we programmed an 

algorithm that uses a 

1 * − = i

i Nom XSizeSize

approach, where SizeNom is the size of the smallest node (typically 1 inch), X is the scalar (typically 1.2 to 2) 

and i is a nodal indicator (1 = next to the slab/surface). The algorithm also limits the size of i; keeping 

identical size nodes beyond a fixed point. This algorithm groups small nodes close to the edges and soil 

surface and increases the sizes of the nodes as they progress away from these edges. 

To combat the slowdown issue, we removed some of the flexibility of the original model; which had allowed 

the user to have non-rectangular slab geometries. By imposing a rectangular geometry we were able to 

utilize symmetry to allow us to only model one fourth of the slab, significantly reducing the simulation times 

and allowing us to run with a higher nodal density than previous submittals. 

116 
We submitted the June 2005 set with the following specifications: 

• SizeNom = 1 inch 

• X = 1.5 to 2 depending on the test 

• Maximum i = 10 

Based on the results of June 2005 and the new one-fourth approach, the TRNSYS model node meshing was 

further revised so that the mesh size increases by a factor of 1.2 to 1.3 moving away from the slab edge, and 

the size of node i is allowed to increase without limit. The difference in mesh sizing between the meshing 

schemes is shown in the figure below. 

-

0.5000

1.0000

1.5000

2.0000

2.5000

0 5 10 15 20 25 30

Node Number

Size (m)

Old Scheme at 1.5,10

New scheme at 1.2

The newly modified algorithm allowed us to run with a similar number of nodes using a scalar of 1.2 to 1.3 

than the previous cases which were run with a scalar of 1.5 for most cases for some of the larger-boundary 

tests. 

We submitted the May 2006 set with the following specifications: 

• SizeNom = 1 inch 

• X = 1.2 to 1.3 depending on the test 

• Maximum i = infinity 

The three TRNSYS results sets produced for the project are summarized in the table below. Note that there 

are specification differences for cases GC30 and GC30a, and GC40 and GC40a, where the “a”-series cases 

specify kground = 1.9 and constant temperature surface boundaries, and the preliminary-series cases specify 

kground = 2.0 along with interior and exterior surface coefficients of h = 5000 W/m2K. The difference in 

ground conductivity should cause reduced floor conduction in the “a”-series cases versus the preliminary 

117 
cases, while the effect of varying the surface boundary condition should be negligible as h = 5000 W/m2K 

approximates a constant-temperature surface boundary condition. However, the TRNSYS model noding 

scheme was also changed between January 2005 and June 2005, further affecting the results. 

TRNSYS results summary

Submittal Date 1/14/2005 6/21/2005 5/23/2006

Noding Scheme "x (2)" Full slab "x (1.5)" 1/4 Slab "x (1.2-3)" 1/4 Slab

 Steady-State Analytical Verification

 GC10 GC10a

qfloor del % v. qfloor del % v. qfloor del % v.

(W) AnnSoln (W) AnnSoln (W) AnnSoln

Analytical Soln. 2561 n/a 2433 n/a 2433 n/a

TRNSYS 2486 -2.93% 2417 -0.64% 2427 -0.24%

 Steady-State Cases

qfloor del % v. qfloor del % v. qfloor del % v.

(W) previous (W) previous (W) previous

GC30 & GC30a 2620 n/a 2606 -0.52% 2642 1.34%

GC30b 2494 n/a 2533 1.53%

GC30c 2104 n/a 2137 1.56%

GC60b 2085 n/a 2113 1.36%

GC65b 1965 n/a 1994 1.43%

 Harmonic Cases

Qfloor del % v. Qfloor del % v. Qfloor del % v.

(kWh/y) previous (kWh/y) previous (kWh/y) previous

GC40 & GC40a 22994 n/a 22831 -0.71% 23033 0.88%

GC40b 21852 n/a 22099 1.12%

GC45b 32405 n/a 32758 1.08%

GC55b 34952 n/a 35075 0.35%

GC70b 17214 n/a 17396 1.05%

GC80b 5970 n/a 6029 0.97%

GC40c 18425 n/a 18649 1.20%

GC45c 26735 n/a 27004 1.00%

GC55c 19120 n/a 20760 7.90%

GC80c 9086 n/a 9192 1.16%

The results from the June 2005 submittal show an uncharacteristic pattern/result for the GC55c test case that 

was pointed out by the IEA task leaders. We tried to go back and see if we could replicate the result or 

explain the differences that were noted, but we have been unable to unearth the cause of the discrepancy. It 

is likely a wrong parameter entered for that test case, an unfinished simulation that was reported, or user 

error entering the results into the spreadsheet. The May 2006 submittal does not show the same behavior 

and compares favorably to the other test cases. 

After the June 2005 submittal we were asked to comment on the differences between the FLUENT results 

and the TRNSYS results for the soil surface temperatures. While the energy flows were nearly identical 

between the two detailed models, the surface temperature plots were very different. The reason, as it turns 

out, was simple. The TRNSYS results were being reported for the true surface condition while the FLUENT 

results were being reported for the node/element just beneath the surface. For example, in test case GC10a 

118 
the specification calls for an exterior soil surface temperature of 10°C, an interior surface temperature of 

30°C and a linear temperature profile between 10°C and 30°C for the area beneath the exterior wall. The 

plots of the TRNSYS results for that test case show exactly that temperature profile while the FLUENT 

results show deviations from that profile that are especially noticeable for the area underneath the exterior 

wall. However, when we plot the TRNSYS results for the node directly beneath the surface (and not the 

surface temperature) versus the FLUENT results for the test cases we find near-identical results – confirming 

our suspicions about the differences. 

The surface temperature results were especially pronounced after the June 2005 submittal for the GC30 test 

cases – with the TRNSYS results showing an odd behavior under the wall. For reference, the GC30 test case 

uses a non-constant surface temperature condition. The results were again due to the definition of the 

surface temperatures. The TRNSYS results again showed the surface temperatures, but for the area beneath 

the wall we were forced to use the temperatures of the nodes directly under the wall – and not the surface 

temperatures – as they could not be calculated for the adiabatic boundary specified beneath the wall. So the 

plots show surface temperatures on both sides of the wall, and temperatures 1 node down beneath the wall, 

which causes an inconsistency in the plot that was noticed by the task leaders. When the temperatures of the 

nodes directly beneath the surface are instead plotted and compared to the FLUENT results the graphs are 

nearly identical. 

Another surface temperature anomaly (corner effects) noticed by the task leaders for the GC65 test case 

turned out to be an error in the algorithm we used to calculate the interpolated surface temperatures in the 

post-processing spreadsheet and not an error in the model itself. 

7. Results

Our model matches up extremely well with the other verified detailed 3-D modeling programs (FLUENT 

and MATLAB) in both surface temperature profiles and slab heat transfer for all test cases. 

8. Other (optional) 

To assist with development of the test specification for some of the other less flexible modeling programs 

(the “b” and “c” test cases), a number of sensitivity tests requested by NREL were run. With the flexibility 

of our model, these analyses were quite easy to model, requiring very little preparation time. Some of the 

more interesting results of these tests are discussed below. These sensitivity tests do not necessarily apply all 

parameters in the final test specification, so results are not expected to exactly match final or interim 

TRNSYS results shown elsewhere. 

119 
 Deep Ground and Far Field Dimension Sensitivity Tests 

Figure 2A-1 and Tables 2A-1 and 2A-2 show the impacts of far field and deep earth distances as well as the 

impact of the convection coefficients on the steady-state slab heat transfer rate for preliminary Case GC30 

(using very high surface coefficients). Based on this output “a”-series depth and far-field dimensions of 30 m 

and 20 m, respectively, were applied in the test specification. 

7000

7500

8000

8500

9000

9500

10000

10500

11000

0 5 10 15 20 25 30 35 40 45

Deep Earth Distance (m)

Slab Heat Transfer Rate (kJ/h)

Far-Field = 40m

Far-Field = 30m

Far-Field = 20m

Far-Field = 10m

Far-Field = 5m

Figure 2A-1. Impact of deep earth and far-field dimensions on slab heat transfer rate, 

Case GC30

 Table 2A-1. Varied Depth for 40 m Far Field Table 2A-2 Varied Far Field for 30 m Depth 

Deep 

Earth (m)

Far-Field 

(m)

Slab Heat 

Transfer 

(kJ/h)

Change v. 

30m/40m 

(%)

30 40 9071.2

30 30 9071.3 0.00%

30 20 9070.1 -0.01%

30 10 9040.9 -0.33%

30 5 8873.1 -2.18%

Deep 

Earth (m)

Far-Field 

(m)

Slab Heat 

Transfer 

(kJ/h)

Change v. 

40m/40m 

(%)

40 40 9069.0

30 40 9071.2 0.02%

20 40 9091.8 0.25%

10 40 9312.7 2.69%

5 40 10254.4 13.07%

To establish a far-field dimension (F) for the “b”-series cases (h = 100 W/m2

K), far-field dimensions were 

varied for ground depth = 15 m. Based on results of Table 2A-3, far-field dimension of 15m was chosen 

for the “b”-series cases. Results variation for F = 15 versus F = 8 (specified for the “c”-series cases) is 

also shown. 

120 
Table 2A-3 Variation of Far-Field for 30m Depth

Slab Heat Change v.

Far-Field Transfer Rate Previous Detail

(m) (kJ/h) (%)

8 8726

10 8737 0.13%

12 8741 0.05%

15 8746 0.06%

20 8744 -0.02%

 Surface Coefficient Sensitivity Tests 

The effect of surface heat transfer coefficients on floor conduction was analyzed. Figure 2A-2 indicates slab 

heat transfer versus exterior heat transfer coefficient for Case GC30, and shows a 2% decrease in floor 

conduction for h = 100 W/m2

K versus an idealized exterior high heat transfer coefficient that approximates a 

constant temperature surface boundary condition (i.e., h > 5000 W/m2

K). If both interior and exterior heat 

transfer coefficients are set to h = 100 W/m2

K, the slab heat transfer decrease is 4% versus idealized 

boundary conditions. Note for units in the figure slab heat transfer is in kJ/h and heat transfer coefficient is in 

kJ/(h·m2

K), whereas the test specification uses W and W/m2K respectively. 

Figure 2A-3 shows how Case GC30 slab heat transfer changes when interior and exterior heat transfer 

coefficients are varied separately and together, for h ≤ 100 W/m2

K; the result for the constant temperature 

boundary condition is the dashed line (asymptote as h increases). 

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

1 10 100 1,000 10,000 100,000

Exterior Heat Transfer Coefficient (kJ/h.m2.K)

Steady State Slab Heat Transfer Rate (kJ/h)

GC-30 Test Case with Identical Interior and 

Exterior Convection Coefficients (h=5000 

W/m2.K)

Blue line is result for constant Temperature 

interior slab and exterior soil surfaces

GC30 test case with identical interior and 

exterior convection coefficients (h = 5000 

W/m2K)

q @ h = 100 W/m2K

Variation of exterior surface only results in 2% 

variation v const T boundary, as shown above. 

Varying both interior and exterior boundaries 

resulted in 4% variation:

q @ constant T: 9066 kJ/h

q @ h = 100 W/m2K: 8658 kJ/h.

Figure 2A-2. Impact of exterior heat transfer coefficient on Case GC30 slab heat transfer results 

121 
( )

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

0 20 40 60 80 100 1

Convection Coefficient (kJ/h.m2.K)

Steady-State Slab Heat Transfer (kJ/h) 

20

Constant Surface Temperatures (Infinite h's)

Identical Interior and Exterior Coefficients

Infinite Exterior Coefficient, Varying Interior Coefficient

Infinite Interior Coefficient, Varying Exterior Coefficient

About 12% variation at 

h,int = h,ext = 100 kJ/m2

K 

(27.8 W/m2

K) 

Figure 2A-3. Slab heat transfer as a function of the surface coefficients, TRNSYS Case GC30 

9. Conclusions and Recommendations

 Conclusions about your test results and/or IEA BESTEST in-depth diagnostic cases for ground 

coupled heat transfer related to slab-on-grade construction. Recommendations regarding future 

improvements to your software and/or this test specification. 

1. We’re excited to see that the results from our model match very closely with the published results 

from FLUENT and MATLAB for all cases and with GHT-SUNREL for many of the test cases. The 

fact that the three reference-standard programs can closely agree on these test cases gives an 

increased sense of confidence to all participants when comparing to the reference results. 

2. The results for our GC10a simulation show a less than 1% difference compared to the analytical 

solution. 

3. We’re convinced that the extra effort we put forth to make the model as flexible as possible paid off 

when we were able to run all of the test cases without having to “tweak” the model parameters 

and/or assumptions to mimic some of the test conditions. This flexibility also allowed us to assist 

the task leaders in assessing the impact of test specifications for the “b” and “c” test cases. 

4. Without this IEA subtask for ground coupling, we would have had no means to check the results 

from our model, nor had a reason to make improvements to our model. There should be no question 

that the IEA subtask has improved the TRNSYS ground coupling model and, in doing so, has also 

provided energy modelers a greatly increased sense of confidence when modeling heat transfer to 

the ground. 

 Recommendations 

Another analytical test that could easily be added to this project is the case of 1-D heat transfer using the 

conditions specified in GC40. Have the edges of the slab be heavily insulated in the depth direction to the 

122 
123 

location of the deep earth boundary (effectively setting F to zero). Referring to Figure 1-2 of Part I the 

steady state solution is then simply qslab = ksoil * B * L * (Tia-Tdg) / E. This is one of the very first test 

cases we ran when creating our model.

 

10. References 

Kasuda, T.; Archenbach, P.R. (1965). Earth Temperature and Thermal Diffusivity at Selected Stations 

in the United States. ASHRAE Transactions, 71 (1).
Model Geometry and Thermal Property Allowed Inputs (pro forma)

Model and Version:

Horizontal Vertic

Foundation Above Grade Edge Interior 

Slab Wall Footer Soil Sill Plate Wall Insulation Insula

GEOMETRY*

Floor Slab In (below) Grade ("yes" or "no") yes n/a n/a n/a n/a n/a n/a n/a 

Floor Slab On (above) Grade ("yes" or "no") yes n/a n/a n/a n/a n/a n/a n/a 

Floor Slab Minimum Thickness (cm) >0 n/a n/a n/a n/a n/a n/a n/a 

Floor Slab Maximum Thickness (cm) +Infinity n/a n/a n/a n/a n/a n/a n/a 

Minimum x- Thickness or Width (cm) n/a >0 0 n/a c(see 0 

Maximum x -Thickness or Width (cm) n/a +Infinity b (see below) n/a below) 0 

Minimum z -Thickness (cm) n/a n/a 0 n/a n/a 0 n/a 

Maximum z -Thickness (cm) n/a n/a +Infinity n/a n/a 0 n/a 

Minimum Bottom-Edge Depth Below Grade (z , cm) 00 0 n/a n/a n/a n/a

Maximum Bottom-Edge Depth Below Grade (z , cm) +Infinity +Infinity +Infinity n/a n/a n/a n/a c (s

Minimum Top-Edge Height Above Grade (z , cm) 0 >0 n/a n/a n/a n/a n/a

Maximum Top-Edge Height Above Grade (z , cm) +Infinity * (see below) n/a n/a n/a n/a n/a c (s

Minimum Soil Depth (E, m) n/a n/a n/a >0 n/a n/a n/a n/a 

Maximum Soil Depth (E, m) n/a n/a n/a +Infinity n/a n/a n/a n/a 

Minimum Soil Far-Field Distance (F, m) n/a n/a n/a >0 n/a n/a n/a n/a 

Maximum Soil Far-Field Distance (F, m) n/a n/a n/a +Infinity n/a n/a n/a n/a 

THERMAL PROPERTIES*

Minimum Conductivity (W/(mK)) >0 >0 >0 >0 0 0 

Maximum Conductivity (W/(mK)) +Infinity +Infinity +Infinity +Infinity 0 0 

Minimum R-Value (m2K/W)) **   **  00 

Maximum R-Value (m2K/W)) **   **  +Infinity +Infin

Minimum Density (kg/m3) >0 >0 >0 >0 0 0 

Maximum Density (kg/m3) +Infinity +Infinity +Infinity +Infinity 0 0 

Minimum Specific Heat (kJ/(kgK)) >0 >0 >0 >0 0 0 

Maximum Specific Heat (kJ/(kgK)) +Infinity +Infinity +Infinity +Infinity 0 0 

COMMENTS

Uninsulated detail (Figure A-1) ok? ("yes" or "no") yesa

Insulated detail (Figure A-2) ok? ("yes" or "no") yesa

If no, include additional assumptions of your model a the ground model does not directly apply above the top edge of the slab including sill plate, walls 

not covered here (add rows as needed) limits for above grade components are those typical to the TRNSYS building type

b restricted to the width (and material) of the foundation wall

Include other clarfications and/or comments here c insulation is only allowed adjacent to high-mass sections (ie cannot extend below the foundation 

(add rows as needed) insulation modeled as an additional massless resistance located on the boundary between two no

e.g.,: R = dx(i)/2./Conductivity(i,j,k) + Rinsulation + dx(i-1)/2./Conductivity(i-1,j,k)

 note that this equation is an example for 1 surface along the x-axis; there are 6 equations for ea one for each boundary.

NOTES"n/a": not applicable* If a listed input does not apply to your model, enter "0" in the relevant cells.** For below grade high-mass components, only list R-value input limits if there is some difference versus what would be calculated based on listed 

 conductivity and thickness limits

a (see below)

TRNSYS v16 with Optional TESS Component Libraries Insulation C

Below-Grade High-Mass Components Low-Mass Components

124 
Appendix II-B 

Modeler Report for BESTEST Cases GC10a-GC80c 

FLUENT Version 6.0.20 

by 

Dr. Abdullatif Ben-Nakhi, Associate Professor 

College of Technological Studies – Public Authority for Applied Education and Training 

(PAAET), Kuwait 

Edited by Joel Neymark, J. Neymark & Associates, United States 

 

September 2007 

1. Introduction 

Modeling Software: FLUENT 6.0.20, by Fluent Incorporated, Centerra Resource Park, 10 

Cavendish Court, Lebanon, NH 03766 

• The model is independent of a whole-building simulation program. However, it requires a 

meshing tool. GAMBIT is commonly used to build and mesh models for FLUENT. 

• In the current work, the ground is modeled without the building. The building is represented by a 

thermal boundary surface (e.g., fixed surface temperature, convective surface, etc.). 

• Any positive time step is acceptable in principle; however, numerical stabilities should be 

respected. In the current work, the time step for all transient simulations was 1 hour. 

• FLUENT is a state-of-the-art computer program for modeling fluid flow and heat transfer in 

complex geometries. In the current work, only heat transfer in simple geometries is considered. It 

was concluded that the post-processing facilities in FLUENT 6.0 are not optimal for the current 

project purposes, although the post-processing facilities in FLUENT are highly efficient for fluid 

flow problems. 

 

2. Modeling Assumptions

FLUENT allows input of the linearly varying perimeter surface temperature boundary condition of 

GC10a. In all cases, it was necessary to model only one quarter of the domain, as the problem is 

symmetric. See Appendix A of this report for discussion of range of modeling possible with FLUENT. 

Because analysis with FLUENT is done independently of a whole-building energy simulation program, 

outside surface temperatures are provided directly as boundary conditions. For the periodic cases the 

equation describing ODB variation provided in the test specification was used as basis to write a UDF 

(user defined function) within FLUENT to explicitly and directly set the outside surface temperature for 

Case GC40a, and to set the outside air temperature for the other periodic cases. The outside surface 

temperatures provided are produced by FLUENT via monitoring the temperature of the center of the 

outside surface (i.e., at the mid-distance between the perimeter and far-field surface). Because of 

limitations in FLUENT 6.0’s built-in output reporting capabilities, it was not possible to monitor outside 

ambient temperature when a convective boundary is defined. However, the ODB UDF was validated by 

monitoring the outside surface temperature in GC40a, which defines the outside surface temperature. 

125 
3. Modeling Options

FLUENT offers two major types of solvers: steady-state and transient. For all steady-state cases, the 

steady-state solver was used, which does not consider density and/or heat capacity in the governing 

equations. There is no time step in this solver; a steady-state run consists of several iterations (not time 

steps) until it converges (i.e., the governing equations are valid). This steady-state solver should give 

faster and more accurate results than steady-state results using the dynamic solver for many time steps. 

4. Modeling Difficulties

The periodic cases require very long start-up period (i.e., several years). This is mainly due to the large 

thermal mass associated with the ground (i.e., domain). In order to overcome this problem, two options 

were implemented. In the first option, the temperature distribution at the end of simulation of another case 

of equivalent dimensions was used as the initial condition. When that was not available, the second option 

was used, in which the steady-state solution of the active periodic case was used as the initial condition 

for the problem. The steady-state solution for the active periodic case was created by replacing the 

periodic temperature with a steady temperature of 10°C. 

 

5. Demonstration of Appropriate Level of Modeling Detail 

The figures below show the final grids that were employed. For example, Figure 2B-1 (“inside-m0p06-

r1p10”) shows the structured mesh for the floor slab, where “m0p06” means mesh size for inside slab and 

perimeter is 0.06 m (i.e., uniform mesh size throughout both surfaces), and “r1p10” means mesh size 

increases in the x, y, and z directions with a ratio of 1.10 outside the internal and perimeter surfaces. 

Mesh size increase is shown, for example, in Figures 2B-2 (“outside-m0p06-r1p10”) and 2B-4 (“deepm0p06-r1p10”).

Figure 2B-1. (“inside-m0p06-r1p10”): mesh for inside slab surface; plan view of the 

slab-only showing uniform grid 

126 
Note the gradual increase in 

mesh size away from the 

floor slab. 

Floor slab here, as enlarged 

in Figure 2B-1 (“insidem0p06-r1p10”) 

Perimeter mesh here, as 

enlarged in Figure 2B-3 

(“perimeter-m0p06-r1p10”) 

Figure 2B-2 (“outside-m0p06-r1p10”): mesh for outside boundary surface; plan view 

Figure 2B-3 (“perimeter-m0p06-r1p10”): uniform mesh for perimeter surface boundary; plan view 

127 
wall 

inside outside

outside 

inside 

wall 

Figure 2B-4 (“deep-m0p06-r1p10”): structured mesh for deep ground boundary (plan view of 

bottom surface grid at GC10a deep ground depth of 40 meters)

Figure 2B-4 (“deep-m0p06-r1p10”) is a horizontal section drawing indicating node structure at the deep 

ground boundary depth of 40 m for Case GC10a. In this figure “inside,” “wall,” and “outside” indicate 

the relative locations of the slab, perimeter wall, and soil respectively at the surface (see Figure 2B-2 

[“outside-m0p06-r1p10]); at the 40 m depth there is only soil, and no slab or perimeter wall. The same 

horizontal mesh structure continues from the surface to the deep ground depth, however, the distance 

between nodes increases in the vertical direction. This is shown in Figure 2B-5 (“far-m0p06-r1p10”), 

which indicates an isometric view (looking downward through the top surface) of only the far-field mesh 

structure for the bounding vertical planes descending from the slab/soil top surface to the deep ground 

depth. This results in an implemented mesh that is non-uniform (i.e., mesh size changes in space 

dimension, such as x-direction), orthogonal (mesh lines intersect perpendicularly), and structured (each 3-

D cell is connected to only one 3-D cell in each of the 6 directions (6 cells in total); and the indices (i.e., 

node number) of the adjacent nodes do not need to be saved as each adjacent node index can be 

determined based on the ordered geometry. For unstructured mesh the neighboring indices should be 

saved, as cells are not arranged in arrays. 

128 
wall 

inside 

outside 

Deep ground 

Figure 2B-5 (“far-m0p06-r1p10”): mesh for far field boundary, isometric view (looking downward 

from the surface) of the far-field mesh structure for the bounding vertical planes descending from 

the surface to the deep ground depth

Note in Figure 2B-5 (“far-m0p06-r1p10”): At the deep ground level Figure 2B-4 (“deep-m0p06-r1p10”) fits 

in the yellow square labeled as “deep ground”. At the surface level Figure 2B-2 (“outside-m0p06-r1p10”) 

fits in the green square labeled “outside”, and blue and red lines identify the slab and perimeter wall 

boundaries, respectively. 

Figure 2B-6 (“deep-uns-m0p04-r1p10”) is an earlier unstructured mesh version of the deep ground boundary 

structured mesh of Figure 2B-4 (“deep-m0p06-r1p10”). Several mesh approaches and densities were 

examined. The structured mesh was implemented because of the faster simulation compared to unstructured 

mesh such as the one shown below. 

129 
Figure 2B-6 (“deep-uns-m0p04-r1p10”): unstructured mesh for deep ground 

surface boundary 

Demonstration of appropriate level of modeling detail is summarized as follows. 

Case gc10a: 

The results shown below are for 40 m deep-ground distance and 40 m far-field distance. As only onequarter of the domain is modeled, the values provided are for the results of the model multiplied by 4. 

Run

No. 

Case Name Flux 

(Watt) 

Result 

Quality 

Number of 

Nodes 

1 gc10a-e40-f40-m0p12-r1p10 2405.2 Good 322959 

2 gc10a-e40-f40-m0p08-r1p10 2418.9 Better 629563 

3 gc10a-e40-f40-m0p06-r1p10 2424.5 Best 999045 

analytical solution 2432.6 

The relation between the flux increase and increase in number of nodes indicates that the target or exact 

solution for flux should be greater than 2424.5 W for the run where deep ground distance (e-distance) is 

40 m and far field distance (f-distance) is 40 m. The “m0p06-r1p10” mesh yields a heat flow result 0.2% 

greater than the previous level of detail (“m0p08-r1p10”), and is within 0.3% of the analytical solution. 

Deep ground distance and far-field distance (amount of soil domain to model) were established based on 

the following results. 

130 
Run

No. 

Case Name Flux 

(Watt) 

Result 

Quality 

Number of 

Nodes 

4 gc10a-e30-f20-m0p06-r1p10 2423.4 Better 846888 

3 gc10a-e40-f40-m0p06-r1p10 2424.5 Best 999045 

analytical solution 2432.6 

The 0.04% variation going from Run No. 4 to Run No. 3 indicates that increasing the soil depth beyond 

40 m for depth and far-field dimensions can only have negligible effect, and upon consideration of runs 

No. 1 and No.2 suggests that to achieve better agreement with the analytical solution, one should apply a 

more dense mesh (if practical). 

Case gc30a: 

The results shown below are for 30 m deep ground distance and 20 m far field distance. 

Run 

No. 

Case Name Flux 

(Watt) 

Result Quality Number of 

Nodes 

5 gc30a-e30-f20-m0p12-r1p05 2501.9 Good 529254 

6 gc30a-e30-f20-m0p08-r1p05 2558.4 Better 1080288 

7 gc30a-e30-f20-m0p06-r1p10 2585.3 Best 846888 

The mesh of Run No. 6 is better than for Run No. 5 in that the wall mesh size for Run No. 6 is 0.08 m 

while it is 0.12 m for Run No. 5. The rate of mesh size increase away from the wall is 1.05 for both Runs 

No. 5 and No. 6. Due to memory limitation Run No. 7 was modeled with mesh increase ratio of 1.10 

while the wall mesh size is 0.06 m. Time constraints prevented simulation of an additional run with wall 

mesh size of 0.04 m and mesh increase ratio of 1.10. Had this more detailed run been performed, the 

result would probably be somewhat greater than 2585.3 W (and possibly a bit closer agreement with 

TRNSYS [2641.7 W] than the current 2% difference). 

Regarding sufficient duration of simulation, results are provided showing the difference in the results for 

each year of the simulation. The results below give an example of this for GC40a, where 5 years were 

simulated for a detailed mesh utilizing double precision and 1087849 nodes. 

1st Year 2nd Year 

% change 

v. prior 

year 

3rd Year

% change 

v. prior 

year 

4th Year

% change 

v. prior 

year 

5th Year

% change 

v. prior 

year 

min (W) 578.0642 548.5512 5.38 542.4594 1.12 540.065 0.44 538.8389 0.23 

max (W) 23183.79 777.7612 2880.84 765.9149 1.55 762.2567 0.48 760.5798 0.22 

average (W) 772.9901 660.9343 16.95 653.5455 1.13 650.8789 0.41 649.559 0.20 

sum (kW) 6771.394 5789.785 16.95 5725.058 1.13 5701.699 0.41 5690.137 0.20 

6. Software Errors Discovered, and/or Comparison between Different Versions of the Same 

Software, and/or Lessons Learned regarding Use of Detailed Models

Two output reporting issues occurred in FLUENT 6.0, as follows: 

131 
a. FLUENT permits monitoring variables or their residuals in many forms (i.e., integral, maximum, 

minimum, mean, etc) during the simulation. Many of the post-processing utilities are available for 

monitoring during simulation per time step or iteration. For dynamic (i.e., transient) cases, the project 

output requires heat flux through inside slab per each time step of 3600 s (1 hr) period. This can be 

achieved by monitoring the integrated value of heat flux over all cells of the inside slab. However, when 

this option was invoked, it was noticed that the last monitored value of heat flux through inside slab 

differs from that obtained for the same variable via the post-processing utilities. The total heat flux 

through inside slab can be obtained in two ways from the post-processing utilities: 1) via report “fluxes”, 

2) via report “surface integrals”. These two post-processing methods for calculating total heat flux 

through inside slab produced the same value that is different from that provided by the monitoring utility, 

which is based on automatically calling report “surface integrals” at the end of each time step and 

appending the value in a specified file. This issue occurs only when we want to monitor one of the 

coplanar surfaces, for example, the slab, perimeter, and outside surfaces, which are all encompassed by a 

single plane at the same level (top surface) and have similar slope (in this case horizontal). This may be 

an interpolation-related issue because there are nodes at adjacent surfaces having different boundary 

conditions. For example, when FLUENT performs integration over the inside slab, it uses values of nodes 

adjacent to the inside slab (i.e., the perimeter surface, which has a different boundary condition). This 

issue was bypassed by defining a post-processing surface (dummy surface used for data presentation 

purposes) that exactly overlaps the inside slab. The monitored heat flux through the created dummy 

surface matched the heat flux values provided by both post-processing utilities. This may be because 

FLUENT works with dummy surfaces in isolation as defined by the user, without investigating what is 

adjacent to the dummy surface. On the other hand, the outside temperature was monitored using only one 

node temperature. FLUENT facilitates monitoring the minimum, maximum, mean (or some other 

statistical forms) of temperature throughout the outside surface. A dummy (i.e., post-processing utility) 

point was defined that is located at the outside surface level (z dimension) and at the mid-distance 

between the perimeter and far field surface (x and y dimensions). The temperature of this dummy point 

was monitored as the outside surface temperature. 

b. There is a bug in FLUENT that produces diagonal surface temperature profile results twice (i.e., each 

node value is reported twice within a single file). FLUENT facilitates two types of lines for postprocessing purposes: “line” and “rake”. “Line” was used for reporting the temperature profile across the 

diagonal of the upper surface of the domain. The values reported across the “line” are at actual nodes of 

the domain mesh. It is possible to work-around the double reporting issue by using the “rake” option, 

which allows specifying the number of reporting points at equal spacing. However, “rake” produces 

interpolated values at the specified points instead of exact node values. 

As discussed above, it was possible to work around these reporting issues to obtain proper outputs. 

FLUENT Inc. investigated the above reporting errors and confirmed that both existed in FLUENT 6.0. They 

noted that both errors were already fixed for FLUENT 6.2, and that at the time of this writing FLUENT is 

currently at version 6.3.26. (Watve 2006) 

7. Results

• Floor conduction for Case GC10a is within 0.33% of the analytical solution. 

• For all other cases floor conduction results for FLUENT, TRNSYS, and MATLAB models are 

within 0.7%–4.2% of each other. 

• Phase shift for peak floor conduction versus minimum ODB is consistent with the TRNSYS and 

132 
MATLAB models in all cases. 

If there were not practical limits for mesh detail using the PC computer available for this project, it may be 

possible to further reduce the disagreement versus the analytical solution, and obtain greater precision for the 

other results.

8. Other 

Because of output limitations FLUENT does not allow precise reporting of the GC10a surface 

temperatures unless mesh density is increased beyond PC capabilities, which is not possible for this 

project. Figure 2B-7 shows that interpolated FLUENT surface temperatures for Case GC10a disagree 

with the TRNSYS surface temperatures. Figure 2B-8 shows TRNSYS temperatures for just below the 

surface agree with interpolated FLUENT results. As TRNSYS and FLUENT heat flow results are both 

within 0.4% of the GC10a analytical solution, and their sensitivities to variation of boundary conditions 

for Case GC30a appear to have good agreement, FLUENT output is consistent with correctly input 

boundary conditions for GC10a. 

 

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

TRNSYS Steady-State Surface Temperatures (Y=0, thru center of edge)

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

552 576 600 624 648 672

Distance from Slab Center (cm)

Temperature (°C)

TRNSYS-GC10a FLUENT-GC10a TRNSYS-GC30a FLUENT-GC30a

FLUENT outputs interpolated 

temperature values

Figure 2B-7. 

133 
IEA BESTEST Ground Coupling: In-Depth Floor Slab - GC10a 

Steady-State Just-Below-Surface Temperatures (Y=0, thru edge center)

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

552 576 600 624 648 672

Distance from Slab Center (cm)

Temperature (°C)

TRNSYS-GC10a FLUENT-GC10a

FLUENT outputs interpolated 

temperature values

TRNSYS values for just 

below surface

Figure 2B-8. 

The above results represent the static temperature or total temperature as defined below. Inner-surface 

wall temperature and outer-surface wall temperature results were also submitted, but are not shown here. 

Outer and inner temperatures are reported at cell centers not nodes, so they cannot give exact surface 

temperature results for the nodes at x = 600 cm and x = 624 cm. Based on the FLUENT User’s Guide the 

temperatures differ as follows. For incompressible flows total temperature equals static temperature, 

where static temperature is the temperature moving with the fluid (in this solid conduction case, the fluid 

is not moving). Inner-surface wall temperature is the temperature of a bounding wall surface on the side 

(surface) of the wall away from an adjacent fluid, while outer-surface wall temperature is the temperature 

of a bounding wall surface on the side of the wall surface adjacent to the fluid. In this case a zerothickness wall was used for defining the surface boundary so that inner-surface wall temperature = outersurface wall temperature. 

In summary 

• For solids, static temperature should equal to total temperature. 

• Total temperature is available at boundary nodes. 

• Inner and outer temperatures are available at cell centers. 

Further documentation is included in the FLUENT User’s Guide cited in the references; see Sections 25.8.2 

and 27.1.2, and Table 27.3.4 of the FLUENT User’s Guide. 

9. Conclusions and Recommendations 

[Editor’s note: no comments were provided here by PAAET.] 

134 
10. References 

Fluent Inc. (2001). Fluent 6.0 User’s Guide, Lebanon, New Hampshire, US: Fluent Incorporated. 

Watve, A. (2006). Fluent Incorporated. Private communications with A. Nakhi and J. Neymark, Nov-Dec 

2006. 

Appendix A: Model Geometry and Thermal Property Allowed Inputs 

In principle, there is no limitation for the geometry from FLUENT, so the pro-forma table and 

accompanying figures are not included. Of course, dimensions should be positive. The practical limitation 

for number of cells (or nodes) is dependent on the computer capabilities. That is, the bigger the RAM the 

larger number of nodes that can be handled. The array size and related run time of the FLUENT program 

(i.e., executable) is dynamic and is dependent on the number of nodes and variables to be simulated. The 

executable increases the array size as requested by the problem in hand. FLUENT incorporates dynamic 

storage, hence, limits are set by computer capabilities. There is no limitation for properties in FLUENT 

other than to avoid numerical instabilities. 

135 
Appendix II-C 

Modeler Report for BESTEST Cases GC10a-GC80c 

MATLAB 7.0.4.365 (R14) Service Pack 2 

by 

Michael Crowley 

Dublin Institute of Technology 

Republic of Ireland 

 

September 2007 

1. Introduction

The software package used for this work was MATLAB 7.0.4.365 (R14) Service Pack 2 written by The 

MathWorks, Inc., Massachusetts, United States of America. It is a general purpose mathematical package 

and is independent of building energy simulation. A series of ground-coupled heat transfer programs was 

prepared specifically for this task using the high-level language within MATLAB, which includes an 

extensive catalog of built-in functions. Functions for interpolation and the solution of linear algebraic 

equations (LAE) and ordinary differential equations (ODE) were of most use for the present work. A large 

part of the work of these functions is matrix processing and MATLAB is considered ‘state-of-the-art’ for 

matrix computation – incorporating the LAPACK and BLAS libraries (The MathWorks, Inc. 2007). 

Each of MATLAB’s built-in ODE solvers forms an estimate of the error for the proposed time step and, if 

necessary, varies the length of the step to keep the error close to the specified tolerance. At each step, the 

error e in each nodal temperature T satisfies e ≤ ( × T AbsTol,RelTolmax ). A relative tolerance (RelTol) 

of 10-5 and an absolute tolerance (AbsTol) of 10-8 were used here. Fixed time steps, if large, can lead to 

excessive error where the solution changes rapidly and, if small, can be unnecessarily accurate (slow) for a 

large part of the interval of integration. MATLAB does not offer fixed step size as an option. 

MATLAB includes a range of direct and iterative solvers for linear algebraic equations. Direct methods were 

used exclusively here (for steady state problems) because they are generally more accurate and more reliable 

than iterative solvers (Heath 2002). Direct solvers (all based on Gaussian elimination) produce exact 

solutions in the absence of rounding error. Since MATLAB calculates in double precision, results can 

therefore be expected to be many orders of magnitude more accurate than the specified precision for this 

project unless the matrix of coefficients is ill-conditioned. MATLAB tests for this circumstance and issues a 

warning if necessary. All of the foregoing concerns rounding error. Truncation error is, of course, separately 

present and is reduced by decreasing the space increment. 

The test problems are very large (approaching 106

 nodes/equations for the required precision) and this would 

usually necessitate the use of iterative methods on the PC available for the work (HP Compaq D330; 

Pentium 4, 2.8 GHz; 512 MB RAM). In order to use direct solution methods operating entirely within fast 

memory (RAM), two steps were taken. Memory was increased to 4 GB, of which 1 GB was reserved for the 

operating system. Also, the problems were programmed taking maximum advantage of symmetry. Three 

geometric symmetries are present in most of the problems and consequently only one-eighth of the problem 

domain need be considered. The system matrix is not fully symmetric and so no further efficiencies of this 

type are available. The matrix is, however, very sparse and this allowed two further efficiencies: (i) 

MATLAB can be programmed to store just the nonzero elements of a matrix, thus freeing up RAM for other 

136 
uses and (ii) MATLAB’s direct solvers take advantage of sparsity in that they do minimal wasteful 

processing of zero valued matrix elements (as well as minimizing fill-in during the elimination stage). 

2. Modeling Assumptions

The modeling assumptions and inputs used were as described in the Test Specification and as shown in 

Table 2C-1 with the following exceptions: 

Hourly ambient temperature data was provided as part of a weather file for the harmonic test cases. These 

data are normally interpolated within building energy models that produce output at less than hourly 

intervals. Some building energy models use linear interpolation, others use smoother functions. The 

programs prepared here include the harmonic function in Section 1.3.1.2.3 of the Test Specification (i.e. a 

cosine modulating a cosine) which was coded as a smooth function of time down to the limits of double 

precision accuracy (approx. 10-15 seconds). This is close to perfect interpolation and may be considered the 

ideal to be aspired to in building energy models. Including a simpler interpolation method (or none) may bias 

the test toward those using that specific (less than perfect) method. For the purpose of comparison, hourly 

integrated heat flow calculations were carried out for a small sample of ambient temperatures from the 

weather file (1 June, hours 1-24) using (i) the hourly temperatures as provided (no interpolation) and (ii) the 

smooth cosine function (perfect interpolation). The maximum difference was 0.8%, occurring at hour 4. The 

inclusion of even a simple interpolation routine would be expected to reduce this difference. 

The Test Specification assumes that dynamic models (DM) will be used for the steady-state cases and that 

these models will be run to steady state to obtain the desired results. Since the boundary conditions do not 

change over time, these cases are more appropriately modeled using algebraic equations, i.e. steady-state 

models (SSM), which require just one application of an appropriate solver. SSMs are much quicker than 

DMs, in this case many orders of magnitude quicker, because the test cases are large (many nodes), 

moderately stiff and require exceptionally long integration intervals. 

3. Modeling Approach

The models prepared here are 3-D finite difference approximations to the Heat Diffusion Equation. The 

SSMs include a second-order centered difference approximation to the space derivatives and the DMs 

include, in addition, a third-order forward difference representation of the time derivative. As such, they are 

all capable of converging (Fletcher 1991) onto their respective exact solutions provided the issues of 

stiffness, stability, matrix condition (and even the accumulation of the minute rounding error over some of 

the lengthy integration intervals to be discussed below) are dealt with correctly – and, of course, assuming 

sufficient computing power is available. The specific solvers employed were as follows: (i) a sparse LU 

decomposition method of the analyse/factorise/solve variety (Davis 2004) was applied to the LAEs arising 

in the SSMs, (ii) an explicit numerical method (Bogacki and Shampine 1989) was used to solve the ODEs 

presented in the DMs; the problems were not stiff enough to justify the costly matrix processing associated 

with implicit methods. 

All the programs used here include mesh spacings that are independently variable in the x-direction (which, 

due to symmetry, includes the y-direction for problems with square perimeter boundaries) and the 

z-direction. The spacings are denser near to the perimeter boundary and a different spacing factor is used 

inside (fxL0) and outside (fxF0) the perimeter, and a third spacing factor (fz0) for the z-direction. Grid 

spacings increase by approximately these factors as the distance from the perimeter boundary increases; the 

program adjusts the factors slightly so that a whole number of grid spacings fits within the available 

dimension (L, F, or E). The initial grid spacings in the vicinity of the perimeter are dx0 in the x and y 

directions and dz0 in the z direction. Two of the test cases (GC45b and GC45c) have rectangular rather than 

137 
square perimeter boundaries and so further grid spacing parameters were required for the y direction. They 

were tied to the existing parameters in the following way. The number of space increments in the y direction 

was made equal to the number in the x direction both inside and outside the perimeter boundary (Figure 2C1). Outside the boundary, temperature gradients in the x and y directions are similar whereas inside the 

boundary, the rate of change of temperature along the very large y-dimension can be expected to be small. 

The chosen grid spacings are compatible with these expectations. The number of space increments within 

the perimeter boundary dimension (W) is the same in both directions. 

W 

W 

y 

x 

wall 

B/2 F 

L/2 

F 

Figure 2C-1 Mesh pattern for cases GC45b and GC45c; one-fourth of domain modeled 

In broad terms, the values of these parameters, together with E and F defining the extent of the modeled soil 

volume, were varied to minimize the error for Case GC10a within the constraints of the available PC. The 

final steady state heat loss through the floor slab was noted and compared with the analytical solution 

(Delsante et al. 1983). Dimensions E and F were then reduced to the values for Case GC30a and the small 

increase in computer resources was used to refine the grid further. This was the final opportunity to compare 

the analytical and finite difference solutions. The (perimeter) boundary conditions were next changed to 

those for Case GC30a – the SSM was otherwise unchanged – and the model was run to produce results. 

Most subsequent models, both SSMs and DMs, share this same mesh density (i.e. dx0, dz0, fxL0, fxF0, and 

fz0); the exceptions being GC45b and GC45c discussed above and the very large slab case, GC50b. DMs 

were evolved from SSMs by including mass and replacing the LAE solver with an ODE solver. DMs were 

initially tested by running them to quasi-steady state and comparing the averaged outcome with that of a 

SSM for the same problem; the results differed typically by 0.005% or less. In the case of GC10a, the quasisteady output of the DM can be compared with the exact solution. Further tests of SSMs and DMs are 

described in Section 6. 

138 
The space traversed by varying the seven parameters (dx0, dz0, fxL0, fxF0, fz0, E, and F) is complex and 

discontinuous. The manual optimization described above is clearly not perfect and could possibly be 

improved by the use of formal methods. Nevertheless, those results which are verifiable were found to be 

well within specification, indicating that the level of discretization was at least adequate. 

4. Modeling Options

Since bespoke programs were prepared specifically for this task, the question of options does not arise. All 

aspects were modeled as specified insofar as the finite difference domain allows. The three types of 

boundary condition (isothermal, adiabatic and convective), for example, were explicitly and separately 

modeled. Convective surface coefficients behaved well, even at large values. Unwanted aspects such as 

radiation and moisture played no part because they were not included in the model. 

5. Modeling Difficulties

 No difficulties were experienced with the use of the Test Specification or the values specified therein. The 

major modeling difficulty arose out of the nature of the test problems themselves. Following the construction 

of the early DMs (GC30a and GC40a), a first principles method (Crowley and Hashmi 2000) was used to 

establish the pre-conditioning period for the system. This is identical to (i) the longest thermal time constant 

for the system and (ii) the time necessary to reach a quasi-steady state. It was needed to determine the 

required interval of integration. It was estimated by calculating the time taken for the slowest transient 

solution of the nodal equation set to decay to 0.1% of its initial value. The period found was 28.25 years – an 

exceptionally long one in the context of building energy simulation. 

Reduced runs were next carried out to estimate the real time required for a 30-40 year interval of integration 

and it was found to be 1–2 months on the available PC described in Section 1. Because of the number of test 

runs and confirming runs required, this would have taken the work well beyond the time scale for the 

project. Initially it was decided to increase the grid spacings in the DMs by a factor of five so that 40 years of 

simulated time could be processed overnight. However, this led to a 2% discrepancy between the averaged 

output of GC40a and the result for GC30a, its steady-state counterpart. This was greater than the difference 

for TRNSYS and FLUENT (< 0.6% variation) so, instead, four more PCs of similar specification were 

equipped to work on the project and a 10-year integration interval was investigated (using the original high 

mesh density). It was found that the results for 10-year runs were well within the principal error tolerance 

specified, that is, that there be at most 0.1% variation in floor heat loss between the last hour of each of the 

final two simulated years. This finding does not appear probable in the light of the very long preconditioning period but the apparent contradiction can be understood as follows: (i) performance is judged 

on floor heat flow rate which involves just a small fraction of the total number of nodal temperatures solved 

for in each simulation run and (ii) the initial conditions used here for each dynamic test run were just the 

solution temperatures for the corresponding steady state run. Since the average of the harmonically varying 

ambient temperature used in the DMs is the same as the outdoor temperature used in the SSMs, this meant 

that the nodes furthest from the surface (and therefore slowest to respond) were already close to their quasisteady temperatures. 

6. Demonstration of Appropriate Level of Modeling Detail

The Test Specification calls for supplementary test runs to confirm that the principal result for each of the 

cases is close to optimal. This is demonstrated by varying problem parameters and confirming minimal 

sensitivity of results to these changes. The prescribed changes are as follows: 

139 
(i) Reduce the integration interval by one year (does not apply to SSMs). 

(ii) Reduce the volume of soil modeled (applies to case GC10a only). 

(iii) Reduce the mesh density (i.e. reduce the number of nodes used). 

(iv) Increase the error tolerance or convergence tolerance used in the solver (does not apply to 

LAE solver used in SSMs here). 

The specified maximum allowable variation in floor slab heat loss is 0.1% for any of these changes. A 5% 

change in the above parameters was, where possible, used in the confirmatory runs here, i.e. 50 times the 

permitted change in floor heat loss. For (ii) and (iii) the number of nodes was reduced by 5% – by 

reducing E and F simultaneously in the case of (ii). For (iv) the tolerance variables RelTol and AbsTol 

were each increased by 5%. Because the dynamic runs took so long, sensitivity tests (iii) and (iv) were 

usually carried out together. For the same reason, not all of the cases were tested in this way; the chosen 

cases are representative problem types. 

The test results are presented in Table 2C-1. The optimal runs are identified and the parameters varied in 

each of the confirmatory runs are highlighted. In every case, the change in floor slab heat loss was much 

less than the permitted 0.1%. 

Table 2C-1. Optimal and Confirmatory Runs for Selected Cases 

Case F 

(m) 

E 

(m) 

dx0 

(m) 

dz0 

(m) 

fxL0 fxF0 fz0 Number 

of nodes 

Floor slab 

heat loss 

Comments 

GC10a* 150 300 0.020 0.012 1.150 1.495 1.150 892,552 2431.82 W Optimal run. 

GC10a 120 240 0.020 0.012 1.150 1.495 1.150 849,120 2431.60 W 0.009% change. 

GC10a 150 300 0.020 0.012 1.155 1.5015 1.155 849,120 2431.54 W 0.012% change. 

GC30a 20 30 0.015 0.0090 1.135 1.4755 1.135 840,840 2694.99 W Optimal run. 

GC30a 20 30 0.016 0.0096 1.135 1.4755 1.135 798,720 2694.87 W 0.004% change. 

GC40a 20 30 0.015 0.0090 1.135 1.4755 1.135 840,840 23,608.9 kWh/y Optimal run, 

(10 year run). 

GC40a 20 30 0.015 0.0090 1.135 1.4755 1.135 840,840 23,609.1 kWh/y 0.001% change, 

(9 year run). 

GC40a# 20 30 0.016 0.0096 1.135 1.4755 1.135 798,720 23,607.8 kWh/y 0.005% change, 

(10 year run). 

GC45b 15 15 0.020 0.012 1.135 1.4755 1.135 410,000 33,483.5 kWh/y Optimal run, 

(10 year run). 

GC45b 15 15 0.020 0.012 1.135 1.4755 1.135 410,000 33,483.5 kWh/y 0.000% change, 

(9 year run). 

GC45b# 15 15 0.020 0.012 1.138 1.4794 1.138 384,160 33,479.2 kWh/y 0.013% change, 

(10 year run). 

GC65b 15 15 0.015 0.0090 1.135 1.4755 1.135 715,520 2003.66 W Optimal run. 

GC65b 15 15 0.015 0.0090 1.140 1.4820 1.140 677,376 2003.50 W 0.008% change. 

GC80b 15 15 0.015 0.0090 1.135 1.4755 1.135 715,520 6151.43 kWh/y Optimal run, 

(10 year run). 

GC80b 15 15 0.015 0.0090 1.135 1.4755 1.135 715,520 6151.53 kWh/y 0.002% change, 

(9 year run). 

GC80b# 15 15 0.015 0.0090 1.140 1.4820 1.140 677,376 6150.86 kWh/y 0.009% change, 

(10 year run). 

*Analytical solution is 2432.60 W. #Error tolerance for ODE solver was increased by 5%. 

140 
7. Software Errors Discovered, and/or Comparison between Different Versions of the Same 

Software, and/or Lessons Learned regarding Use of Detailed Models

Two programming errors were discovered in the course of this work, both by comparing the output with the 

results of others. A 3-D interpolation function was initially used to produce, for each steady-state case, two 

lines of sub-surface temperatures emanating from the origin (Test Specification, Fig. 1-4). The results were 

very different to the output produced by others (Fig. 2C-2). When a 1-D interpolation function was used (the 

required interpolation points being collinear with the sub-surface nodes) the results were very much in 

agreement with the other participants (Fig. 2C-3). The nature of the problem was not established with 

certainty. MATLAB’s 3-D function interpolates using 64 neighboring points. It may be utilizing 

unrepresentative nodal temperatures considering the small scale of the perimeter boundary and the large 

temperature gradients in its vicinity. 

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

552 576 600 624 648 672

Distance from Slab Center (cm)

Temperature (°C)

TRNSYS-GC30b FLUENT-GC30b MATLAB-GC30b

TRNSYS-GC60b FLUENT-GC60b MATLAB-GC60b

TRNSYS-GC65b FLUENT-GC65b MATLAB-GC65b

Figure 2C-2 Interpolated subsurface temperatures through corner (3-D interpolation) 

141 
0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

552 576 600 624 648 672

Distance from Slab Center (cm)

Temperature (°C)

TRNSYS-GC30b FLUENT-GC30b MATLAB-GC30b

TRNSYS-GC60b FLUENT-GC60b MATLAB-GC60b

TRNSYS-GC65b FLUENT-GC65b MATLAB-GC65b

Figure 2C-3 Interpolated subsurface temperatures through corner (1-D interpolation) 

Another programming error became apparent when convective boundary conditions were first introduced. 

MATLAB’s floor heat loss predictions for cases GC30b, GC30c, GC60b, and GC65b were initially 3%–5% 

higher than those of TRNSYS and FLUENT. An error in the modeling of convection within the edge loss 

routine was quickly located and corrected (Table 2C-2). The edge loss subprogram models floor heat loss 

just inside the perimeter boundary. 

Finally, a minor improvement (in interpolation again) was included in the edge loss routine before the 

lengthy dynamic runs were undertaken. This resulted in a 0.3% change in the result for GC30a but a 0.002% 

deterioration in that of GC10a (Table 2C-3). 

Table 2C-2. Effects of Error Related to Convection Modeling within Edge Loss Routine 

Case F 

(m) 

E 

(m) 

dx0 

(m) 

dz0 

(m) 

fxL0 fxF0 fz0 Number 

of nodes 

Floor slab 

heat loss 

Comments 

GC30b 15 15 0.015 0.009 1.135 1.4755 1.135 715,520 2591.92 W Before correction 

GC30b 15 15 0.015 0.009 1.135 1.4755 1.135 715,520 2569.97 W After correction 

GC30c 8 15 0.015 0.009 1.135 1.4755 1.135 693,504 2240.66 W Before correction 

GC30c 8 15 0.015 0.009 1.135 1.4755 1.135 693,504 2154.48 W After correction 

GC60b 15 15 0.015 0.009 1.135 1.4755 1.135 715,520 2212.15 W Before correction 

GC60b 15 15 0.015 0.009 1.135 1.4755 1.135 715,520 2128.28 W After correction 

GC65b 15 15 0.015 0.009 1.135 1.4755 1.135 715,520 2079.09 W Before correction 

GC65b 15 15 0.015 0.009 1.135 1.4755 1.135 715,520 2003.66 W After correction 

142 
Table 2C-3. Effects of Interpolation Improvement in Edge Loss Routine 

Case F 

(m) 

E 

(m) 

dx0 

(m) 

dz0 

(m) 

fxL0 fxF0 fz0 Number 

of nodes 

Floor slab 

heat loss 

Comments 

GC10a* 150 300 0.020 0.012 1.150 1.495 1.150 892,552 2431.87 W Before improvement 

GC10a* 150 300 0.020 0.012 1.150 1.495 1.150 892,552 2431.82 W After improvement 

GC30a 20 30 0.015 0.009 1.135 1.4755 1.135 840,840 2686.33 W Before improvement 

GC30a 20 30 0.015 0.009 1.135 1.4755 1.135 840,840 2694.99 W After improvement 

*Analytical solution is 2432.60 W. 

8. Results

The results produced by MATLAB are in good agreement with those of TRNSYS and FLUENT. All three 

programs are within 0.3% of the known exact solution for case GC10a. Each of them underpredicts the floor 

heat loss, with MATLAB producing the highest heat flow of the three. For most other cases MATLAB 

predicts slightly higher heat flow rates also – typically about 2% higher. This may be attributable to the 

denser mesh used in MATLAB, but this has not been confirmed. 

9. Conclusions and Recommendations

All of the test cases included here are concerned with steady- or quasi-steady state solutions – even for the 

dynamic problems. Dynamic performance is not severely tested, for example, by step changes in the load. 

To do this one needs analytical solutions for dynamic cases but these are generally not available. Almost as 

useful are what can be termed converged solutions (Crowley 2006). These can be generated to arbitrary 

accuracy for dynamic problems of realistic scale and complexity. 

The very lengthy thermal time constants (discussed in Section 5) for ground coupled heat transfer problems 

such as slab in/on grade (also basements, labyrinth cooling systems etc) have serious consequences for the 

HVAC design and simulation communities when this heat transfer mode is a significant fraction of the total 

thermal load. Normally one discards the initial output of a simulation run, that is, the output calculated 

during the pre-conditioning period – which is defined to be the simulation time required to allow the 

temperatures of all nodes to converge to values which are no longer affected by their arbitrarily chosen 

initial values. If the pre-conditioning period is decades in duration, then load predictions are inaccurate for a 

significant fraction of the building life unless initial conditions are directly measured – using bore-holes for 

example. Typical subsurface temperature profiles are of little use on most sites which will have been 

disturbed by site excavation during the construction phase and probably by road works, pipe laying and 

construction of adjacent buildings prior to that. 

10. References 

Bogacki, P. and Shampine, L.F., 1989. A 3(2) pair of Runge-Kutta formulas. Appl. Math. Lett., 2 (4), 321-

325. 

Crowley, M.E., 2006. Validation of solution methods for building energy simulation. Proceedings of eSim 

2006: 4th Biennial Building Performance Simulation Conference, University of Toronto, Canada, 173-180. 

Crowley, M.E., Hashmi, M.S.J., 2000. Improved direct solver for building energy simulation. Proc. CIBSE 

A: Building Serv. Eng. Res. Technol., 21 (3), 167-173. 

143 
Davis, T. A., 2004. Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method. ACM 

Trans. Math. Software, 30 (2), 196-199. 

Delsante, A.E., Stokes, A.N., and Walsh, P.J., 1983. Application of Fourier transforms to periodic heat flow 

into the ground under a building. Int. J. Heat Mass Transfer, 26 (1) 121-132. 

Fletcher, C.A.J., 1991. Computational techniques for fluid dynamics, Vol. 1. (2nd ed.) Berlin: SpringerVerlag. 

Heath, M.T., 2002. Scientific computing; An introductory survey. (2nd ed.) Boston: McGraw-Hill. 

The MathWorks, Inc., 2007. Getting started with MATLAB. Massachusetts: The MathWorks, Inc. 

Modeler Report Appendix A 

Model Geometry and Thermal Property Allowed Inputs (pro forma) 

Figures 2CA-1 and 2CA-2 define components and dimensions used in Table 2CA-1. 

Figure 2CA-1. Uninsulated slab detail 

Grade

Slab

Uninsulated Slab 

Footer

Sill Plate

Above Grade Wall

Foundation Wall

Detail (no scale)

Soil

x

z

z

z

z

z

E

F

x

x

x

z

144 
145 

Figure 2CA-2. Insulated slab detail 

Grade

Slab

Footer

Sill Plate

Above Grade Wall

Foundation Wall

Soil

Insulated Slab Detail 

(no scale)

z

x

x

z

x

z z

z

Horizontal Edge 

Insulation

Vertical Interior 

Edge Insulation

Vertical Exterior 

Edge Insulation
Table 2CA-1. Model Geometry and Thermal Property Allowed Inputs (pro forma) 

Model and Version MATLAB 7.0.4.365 (R14) Service Pack 2

Foundation Above Grade Horizont

Slab Wall Footer Soil Sill Plate Wall Edge 

GEOMETRY*

Floor Slab In (below) Grade ("yes" or "no") yes n/a n/a n/a n/a n/a n/a 

Floor Slab On (above) Grade ("yes" or "no") no n/a n/a n/a n/a n/a n/a 

Floor Slab Minimum Thickness (cm) 0 n/a n/a n/a n/a n/a n/a 

Floor Slab Maximum Thickness (cm) 0 n/a n/a n/a n/a n/a n/a 

Minimum x-Thickness or Width (cm) n/a 24 0 n/a 24 24 0 

Maximum 

x-Thickness or Width (cm) n/a 24 0 n/a 24 24 0 

Minimum 

z-Thickness (cm) n/a n/a 0 n/a 0 n/a 0 

Maximum 

z-Thickness (cm) n/a n/a 0 n/a 0 n/a 0 

Minimum Bottom-Edge Depth Below Grade (

z, cm) 0 0 0 n/a n/a n/a n/a 

Maximum Bottom-Edge Depth Below Grade (

z, cm) 0 0 0 n/a n/a n/a n/a 

Minimum Top-Edge Height Above Grade (

z, cm) 0 0 n/a n/a n/a n/a n/a 

Maximum Top-Edge Height Above Grade (

z, cm) 0 0 n/a n/a n/a n/a n/a 

Minimum Soil Depth (E, m) n/a n/a n/a 2 n/a n/a n/a 

Maximum Soil Depth (E, m) n/a n/a n/a 300 n/a n/a n/a 

Minimum Soil Far-Field Distance (F, m) n/a n/a n/a 8 n/a n/a n/a 

Maximum Soil Far-Field Distance (F, m) n/a n/a n/a 150 n/a n/a n/a 

THERMAL PROPERTIES*

Minimum Conductivity (W/(mK)) 0.5 0 0 0.5 0 0 0 

Maximum Conductivity (W/(mK)) 1.9 0 0 1.9 0 0 0 

Minimum R-Value (m2K/W)) 0** 0** 0** 0** 0 0 0 

Maximum R-Value (m2K/W)) 0** 0** 0** 0** 0 0 0 

Minimum Density (kg/m3

) 1490 0 0 1490 0 0 0 

Maximum Density (kg/m3

) 1490 0 0 1490 0 0 0 

Minimum Specific Heat (kJ/(kgK)) 1800 0 0 1800 0 0 0 

Maximum Specific Heat (kJ/(kgK)) 1800 0 0 1800 0 0 0 

146 
147 

Uninsulated detail (Figure [2C]A-1) ok? ("yes" or

"no")

 no 

Insulated detail (Figure [2C]A-2) ok? ("yes" or "no") no 

If no, include additional assumptions of

your model not covered here

 My models were much simpler than shown. They included a slab in grfoundation or insulation. Since the slab and soil were both considered density and specific heat, slab thickness was irrelevant. Boundary conexterior and the perimeter boundary surface were input directly into the of large convection coefficients (to simulate isothermal boundary condinecessary. For the same reason a building zone was not necessary anmodel. 

NOTES “n/a”: not applicable * If a listed input does not apply to your model, enter "0" in the relevant cells ** For below grade high-mass components, only list R-value input limits if there is some difference versus what wou

on listed conductivity and thickness limits
148 

Appendix II-D 

Modeler Report for BESTEST Cases GC10a-GC80c 

EnergyPlus Version 2.0.0.025 

by 

Robert Henninger and Michael Witte 

GARD Analytics, Inc. 

United States 

 

September 2007 

1. Introduction 

Software: EnergyPlus Version 2.0.0.025 

Authoring Organization: Lawrence Berkeley National Laboratory, U.S. Department of Energy; 

 University of Illinois 

Authoring Country: USA 

This report describes the modeling methodology and results for the testing done for the Proposed IEA 

BESTEST In-Depth Diagnostic Cases for Ground-Coupled Heat Transfer Related to Slab-on-Grade 

Construction, which were simulated using the EnergyPlus software. The specifications for the test suite 

are described in Proposed IEA BESTEST In-Depth Diagnostic Cases for Ground-Coupled Heat Transfer 

Related to Slab-on-Grade Conduction, IEA SHC Task 34/Annex 43, March 2006 (referred to as the 

BESTEST Indepth G-C specification in this report). 

 

2. Modeling Methodology 

The difficulty behind linking ground heat transfer calculations to EnergyPlus is the fact that the 

conduction calculations in EnergyPlus (and in DOE–2 and BLAST before it) are 1-D and the ground heat 

transfer calculations are 2-D or 3-D. This causes severe modeling problems irrespective of the methods 

being used for the ground heat transfer calculation. The basic heat balance based zone model of 

EnergyPlus has to be considered as the foundation for building energy simulation at the present time and 

for some time in the future. Thus, it is necessary to be able to relate ground heat transfer calculations to 

that model. 

The heat balance zone model considers a single room or thermal zone in a building and performs a heat 

balance on it. A fundamental modeling assumption is that the faces of the enclosure are isothermal 

planes. A ground heat transfer calculation usually considers an entire building and the earth that 

surrounds it, resulting in non-isothermal face planes where there is ground contact. While it is not 

impossible to imagine multi-zone, whole-building models that include the surrounding earth and nonisothermal building surfaces, such models will not be practical for some time in the future, and their 

usefulness even then is not clear. 
149 

The EnergyPlus development team addressed this question and decided that the most reasonable first step 

would be to partially decouple the ground heat transfer calculation from the thermal zone calculation. 

The most important parameter for the zone calculation is the outside face temperature of the building 

surface that is in contact with the ground. Thus, this becomes a reasonable “separation plane” for the two 

calculations. It was further decided that the current usage of monthly average ground temperature was 

reasonable for this separation plane temperature as well, since the time scales of the building heat transfer 

processes are so much shorter than those of the ground heat transfer processes. 

Using the separation plane premise, the 3D ground heat transfer programs for slabs developed by 

Bahnfleth (1989, 1990) were modified by Clements (2002) to produce outside face temperatures. The 

program has been modified to permit separate monthly average inside temperatures as input. The 

program produces outside face temperature for the core area and the perimeter area of the slab. It also 

produces the overall weighted average surface temperature based on the perimeter and core areas used in 

the calculation. 

The independent EnergyPlus Slab program requires the use of the EnergyPlus whole-building simulation 

program in order to determine the space heating or cooling load and resultant space temperature for each 

time step of the simulation. Only In-Depth Tests GC30b, GC40b, GC45b, GC50b, GC55b, GC60b, 

GC65b, GC70b, GC80b, GC30c, GC40c, GC45c, GC55c and GC80c were simulated with EnergyPlus. 

Each of these cases was simulated using the autogrid feature of the EnergyPlus Slab program. 

The simulation of ground-coupled heat transfer is a two-step process with EnergyPlus. First, for each of 

the BESTEST G-C in-depth cases that were modeled, the characteristics and properties of the soil and 

slab along with boundary conditions, indoor film coefficients, and monthly average indoor temperature 

setpoint were input to the EnergyPlus Slab program, which is an auxiliary program that is part of the 

EnergyPlus suite. Using the slab Area-to-Perimeter (A/P) ratio defined by the user, the Slab program 

generates an equivalent slab with appropriate perimeter and core areas and simulates the slab heat transfer 

for a period of years until the temperature convergence tolerance is reached. A set of monthly slab 

perimeter and core temperatures at the ground-slab interface and heat fluxes are output as shown in tables 

below. The second step then is to create the EnergyPlus whole building model (IDF file), which includes 

the monthly average ground temperature values from the Slab program analysis. In the EnergyPlus IDF 

file these monthly temperatures are input as part of the GROUNDTEMPERATURES object. The whole 

building simulation is then performed using a one zone building where all surfaces except for the floor 

were adiabatic. This analysis process is then repeated for each case to be analyzed. 

The monthly temperatures calculated by the Slab program for various cases are summarized in the tables 

below. The temperatures listed in the column labeled “Taverage” were used by EnergyPlus to simulate 

heat transfer between the slab and the zone interior space. It should be noted that the total slab area 

(perimeter area + core area) presented in the tables below will not necessarily agree with the total slab 

area specified for each case in the BESTEST Indepth G-C specification. This is particularly noticeable 

for Cases GC45b and GC45c. The EnergyPlus Slab program requests that the user input the A/P ratio for 

each case and not the dimensions or area of the slab. The EnergyPlus Slab program then constructs a 

square slab with an equivalent A/P ratio and then performs its analysis to determine the ground/slab 

interface temperatures. For those cases where the specification calls for a slab with dimensions of 12 m × 

12 m (Cases GC30, GC 40, GC55, GC60, GC65, and GC70), the total floor area used by the Slab 

program happens to be approximately 144 m2

. For the other cases however, where the specification calls 

for a rectangular floor (Case GC45 with a 36 m × 4 m floor and Case GC 50 with a 80 m × 80 m floor), 

the floor area used by EnergyPlus is not that called for in the specification. The resulting ground/slab 
150 

interface temperatures calculated by the Slab program for these last two cases should be reliable since 

they are based on a floor with the same A/P ratio. The resulting monthly ground/slab interface 

temperatures (identified in the tables below as (TAverage) are then specified in EnergyPlus along with the 

actual slab dimensions from the specification for each test case. EnergyPlus then performs simulations 

based on the correct slab area. 

Cases GC30b – Steady-State Comparative Test Base Case 

Monthly Slab Outside Face Temperatures, C and Heat Fluxes(loss), W/(m^2)

Perimeter Area: 79.00 Core Area: 64

Month TAverage TPerimeter TCore TInside AverageFlux PerimeterFlux CoreFlux

1 28.57 27.99 29.31 30 18.39 25.94 8.95

2 28.57 27.99 29.31 30 18.39 25.94 8.95

3 28.57 27.99 29.31 30 18.39 25.94 8.95

4 28.57 27.99 29.31 30 18.39 25.94 8.95

5 28.57 27.99 29.31 30 18.39 25.94 8.95

6 28.57 27.99 29.31 30 18.39 25.94 8.95

7 28.57 27.99 29.31 30 18.38 25.94 8.95

8 28.57 27.99 29.31 30 18.38 25.94 8.95

9 28.57 27.99 29.31 30 18.38 25.94 8.94

10 28.57 27.99 29.31 30 18.38 25.94 8.95

11 28.57 27.99 29.31 30 18.38 25.94 8.94

12 28.57 27.99 29.31 30 18.38 25.93 8.95

Convergence has been gained.

Case GC40b – Harmonic Variation of Ambient Temperature 

Monthly Slab Outside Face Temperatures, C and Heat Fluxes(loss), W/(m^2)

Perimeter Area: 79.00 Core Area: 64

Month TAverage TPerimeter TCore TInside AverageFlux PerimeterFlux CoreFlux

1 28.39 27.66 29.30 30 20.73 30.11 8.00

2 28.38 27.65 29.29 30 20.92 30.32 9.16

3 28.41 27.72 29.28 30 20.46 29.41 9.28

4 28.49 27.86 29.28 30 19.46 27.57 9.31

5 28.59 28.04 29.28 30 18.17 25.31 9.25

6 28.68 28.20 29.29 30 16.95 23.22 9.11

7 28.75 28.30 29.31 30 16.12 21.87 8.92

8 28.77 28.32 29.32 30 15.90 21.63 8.74

9 28.73 28.25 29.33 30 16.36 22.55 8.63

10 28.65 28.11 29.33 30 17.38 24.40 8.59

11 28.55 27.93 29.33 30 18.67 26.68 8.66

12 28.46 27.77 29.32 30 19.89 28.76 8.80

Convergence has been gained.
151 

Case GC45b – Aspect Ratio 

Monthly Slab Outside Face Temperatures, C and Heat Fluxes(loss), W/(m^2)

Perimeter Area: 41.60 Core Area: 10.24

Month TAverage TPerimeter TCore TInside AverageFlux PerimeterFlux CoreFlux

1 27.65 27.32 28.99 30 30.30 34.58 12.95

2 27.62 27.29 28.97 30 30.59 34.85 13.32

3 27.68 27.37 28.95 30 29.83 33.84 13.54

4 27.81 27.53 28.95 30 28.16 31.75 13.55

5 27.98 27.74 28.96 30 26.04 29.17 13.34

6 28.13 27.92 28.99 30 24.04 26.76 12.96

7 28.24 28.04 29.03 30 22.69 25.19 12.52

8 28.26 28.07 29.06 30 22.36 24.88 12.12

9 28.20 27.99 29.08 30 23.14 25.91 11.90

10 28.07 27.83 29.08 30 24.83 28.01 11.89

11 27.91 27.62 29.06 30 26.96 30.61 12.11

12 27.75 27.44 29.03 30 28.96 33.01 12.49

Convergence has been gained.

Case GC50b – Large Slab 

Monthly Slab Outside Face Temperatures, C and Heat Fluxes(loss), W/(m^2)

Perimeter Area: 624.00 Core Area: 5776.00

Month TAverage TPerimeter TCore TInside AverageFlux PerimeterFlux CoreFlux

1 29.52 28.03 29.69 30 6.13 25.35 4.05

2 29.52 28.02 29.68 30 6.16 25.51 4.07

3 29.53 28.08 29.68 30 6.09 24.71 4.08

4 29.54 28.21 29.68 30 5.94 23.11 4.09

5 29.55 28.36 29.68 30 5.74 21.15 4.08

6 29.57 28.50 29.68 30 5.56 19.36 4.06

7 29.58 28.59 29.69 30 5.43 18.21 4.04

8 29.58 28.60 29.69 30 5.39 18.02 4.02

9 29.58 28.54 29.69 30 5.46 18.84 4.01

10 29.56 28.41 29.69 30 5.61 20.45 4.01

11 29.55 28.26 29.69 30 5.81 22.42 4.02

12 29.53 28.12 29.69 30 5.99 24.21 4.03

Convergence has been gained.

Case GC55b – Shallow Deep Ground Temperature 

Monthly Slab Outside Face Temperatures, C and Heat Fluxes(loss), W/(m^2)

Perimeter Area: 79.00 Core Area: 64.00

Month TAverage TPerimeter TCore TInside AverageFlux PerimeterFlux CoreFlux

1 27.38 26.82 28.09 30 33.69 40.99 24.55

2 27.40 26.84 28.09 30 33.54 40.74 24.55

3 27.44 26.92 28.10 30 32.91 39.62 24.54

4 27.52 27.06 28.10 30 31.94 37.88 24.50

5 27.60 27.20 28.10 30 30.88 36.02 24.46

6 27.67 27.32 28.10 30 30.04 34.53 24.42

7 27.70 27.38 28.11 30 29.62 33.81 24.40

8 27.69 27.36 28.11 30 29.76 34.05 24.39

9 27.64 27.27 28.11 30 30.40 35.20 24.41

10 27.56 27.13 28.10 30 31.38 36.93 24.44

11 27.48 26.99 28.10 30 32.44 38.80 24.48

12 27.42 26.87 28.10 30 33.28 40.29 24.52

Convergence has been gained.
152 

Case GC60b – Steady State with Typical Interior Surface Convective Coefficient 

Monthly Slab Outside Face Temperatures, C and Heat Fluxes(loss), W/(m^2)

Perimeter Area: 79.00 Core Area: 64.00

Month TAverage TPerimeter TCore TInside AverageFlux PerimeterFlux CoreFlux

1 27.02 25.86 28.45 30 15.43 21.38 7.99

2 27.02 25.86 28.45 30 15.43 21.38 7.99

3 27.02 25.86 28.46 30 15.43 21.38 7.99

4 27.02 25.86 28.45 30 15.43 21.38 7.99

5 27.02 25.86 28.46 30 15.43 21.38 7.99

6 27.02 25.86 28.46 30 15.43 21.38 7.98

7 27.02 25.87 28.46 30 15.43 21.38 7.99

8 27.02 25.87 28.46 30 15.43 21.38 7.99

9 27.02 25.86 28.46 30 15.42 21.38 7.98

10 27.02 25.87 28.46 30 15.43 21.38 7.99

11 27.02 25.87 28.46 30 15.42 21.38 7.98

12 27.02 25.87 28.46 30 15.43 21.38 7.99

Convergence has been gained.

Case GC65b – Steady State with Typical Interior and Exterior Surface Convective Coefficients 

Monthly Slab Outside Face Temperatures, C and Heat Fluxes(loss), W/(m^2)

Perimeter Area: 79.00 Core Area: 64.00

Month TAverage TPerimeter TCore TInside AverageFlux PerimeterFlux CoreFlux

1 27.83 27.14 28.68 30 11.24 14.78 6.82

2 27.83 27.14 28.68 30 11.24 14.78 6.82

3 27.83 27.14 28.68 30 11.24 14.77 6.81

4 27.83 27.14 28.68 30 11.24 14.77 6.81

5 27.83 27.14 28.68 30 11.24 14.77 6.81

6 27.83 27.14 28.68 30 11.23 14.77 6.81

7 27.83 27.14 28.68 30 11.23 14.77 6.81

8 27.83 27.14 28.68 30 11.23 14.77 6.81

9 27.83 27.14 28.68 30 11.23 14.77 6.81

10 27.83 27.14 28.68 30 11.23 14.77 6.81

11 27.83 27.14 28.68 30 11.23 14.77 6.81

12 27.83 27.14 28.68 30 11.23 14.77 6.81

Convergence has been gained.

Case GC70b – Harmonic Variation of Ambient Temperature with Typical Interior and Exterior 

Surface Convective Coefficients 

Monthly Slab Outside Face Temperatures, C and Heat Fluxes(loss), W/(m^2)

Perimeter Area: 79.00 Core Area: 64.00

Month TAverage TPerimeter TCore TInside AverageFlux PerimeterFlux CoreFlux

1 27.46 26.56 28.60 30 13.11 17.80 7.24

2 27.44 26.53 28.58 30 13.23 17.96 7.32

3 27.46 26.58 28.57 30 13.12 17.71 7.38

4 27.52 26.69 28.57 30 12.80 17.12 7.40

5 27.61 26.83 28.57 30 12.38 16.38 7.38

6 27.69 26.97 28.58 30 11.96 15.67 7.32

7 27.75 27.07 28.60 30 11.63 15.13 7.25

8 27.78 27.12 28.61 30 11.46 14.89 7.17

9 27.77 27.09 28.63 30 11.50 15.02 7.11

10 27.72 26.99 28.63 30 11.78 15.55 7.07

11 27.63 26.83 28.63 30 12.24 16.36 7.09

12 27.54 26.67 28.62 30 12.73 17.19 7.15

Convergence has been gained.
153 

Case GC80b – Reduced Slab and Ground Conductivity 

Monthly Slab Outside Face Temperatures, C and Heat Fluxes(loss), W/(m^2)

Perimeter Area: 79.00 Core Area: 64.00

Month TAverage TPerim eter TCore TInside AverageFlux PerimeterFlux CoreFlux

1 28.60 27.95 29.41 30 5.26 7.69 2.21

2 28.58 27.92 29.41 30 5.31 7.79 2.22

3 28.60 27.96 29.40 30 5.24 7.65 2.24

4 28.65 28.05 29.40 30 5.05 7.30 2.25

5 28.72 28.17 29.40 30 4.80 6.84 2.25

6 28.79 28.30 29.40 30 4.55 6.38 2.25

7 28.84 28.38 29.40 30 4.36 6.06 2.24

8 28.85 28.41 29.41 30 4.30 5.95 2.23

9 28.83 28.37 29.41 30 4.37 6.09 2.21

10 28.78 28.28 29.41 30 4.56 6.44 2.20

11 28.71 28.16 29.41 30 4.81 6.90 2.20

12 28.65 28.04 29.41 30 5.07 7.36 2.20

Convergence has been gained.

Cases GC30c – Steady-State Comparative Test Base Case with Baseimp 

Monthly Slab Outside Face Temperatures, C and Heat Fluxes(loss), W/(m^2)

Perimeter Area: 79.00 Core Area: 64

Month TAverage TPerimeter TCore TInside AverageFlux PerimeterFlux CoreFlux

1 26.90 25.67 28.43 30 16.05 22.41 8.11

2 26.90 25.67 28.43 30 16.05 22.41 8.11

3 26.90 25.67 28.43 30 16.05 22.41 8.11

4 26.90 25.67 28.43 30 16.05 22.40 8.11

5 26.90 25.67 28.43 30 16.05 22.40 8.10

6 26.90 25.67 28.43 30 16.05 22.40 8.10

7 26.90 25.67 28.43 30 16.05 22.40 8.10

8 26.90 25.67 28.43 30 16.05 22.40 8.10

9 26.90 25.67 28.43 30 16.05 22.40 8.10

10 26.90 25.67 28.43 30 16.05 22.40 8.10

11 26.90 25.67 28.43 30 16.05 22.40 8.10

12 26.90 25.67 28.43 30 16.04 22.40 8.10

Convergence has been gained.

Case GC40c – Harmonic Variation of Direct-Input Exterior Surface Temperature with Baseimp 

Boundary Conditions 

Monthly Slab Outside Face Temperatures, C and Heat Fluxes(loss), W/(m^2)

Perimeter Area: 79.00 Core Area: 64

Month TAverage TPerimeter TCore TInside AverageFlux PerimeterFlux CoreFlux

1 26.47 24.91 28.41 30 18.26 26.31 8.20

2 26.44 24.89 28.38 30 18.40 26.42 8.37

3 26.53 25.07 28.36 30 17.94 25.51 8.48

4 26.72 25.40 28.36 30 16.97 23.76 8.49

5 26.95 25.81 28.38 30 15.76 21.66 8.40

6 27.17 26.18 28.41 30 14.63 19.75 8.23

7 27.31 26.41 28.45 30 13.88 18.57 8.03

8 27.35 26.44 28.48 30 13.72 18.42 7.85

9 27.25 26.26 28.50 30 14.19 19.36 7.73

10 27.07 25.91 28.51 30 15.17 21.12 7.72

11 26.83 25.51 28.49 30 16.38 23.24 7.82

12 26.61 25.14 28.46 30 17.51 25.13 7.99

Convergence has been gained.
154 

Case GC45c – Aspect Ratio with Baseimp Boundary Conditions 

Monthly Slab Outside Face Temperatures, C and Heat Fluxes(loss), W/(m^2)

Perimeter Area: 41.60 Core Area: 10.24

Month TAverage TPerimeter TCore TInside AverageFlux PerimeterFlux CoreFlux

1 24.90 24.21 27.70 30 26.35 29.91 11.90

2 24.86 24.18 27.63 30 26.55 30.07 12.27

3 25.01 24.38 27.59 30 25.78 29.06 12.46

4 25.32 24.76 27.60 30 24.19 27.09 12.42

5 25.70 25.22 27.65 30 22.21 24.69 12.14

6 26.06 25.64 27.74 30 20.38 22.52 11.71

7 26.29 25.91 27.83 30 19.19 21.15 11.24

8 26.33 25.95 27.90 30 18.96 20.96 10.85

9 26.18 25.75 27.94 30 19.76 21.00 10.65

10 25.87 25.36 27.93 30 21.36 23.99 10.71

11 25.48 24.90 27.88 30 23.35 26.39 10.99

12 25.13 24.48 27.79 30 25.17 28.55 11.42

Convergence has been gained.

Case GC55c – Shallow Deep Ground Temperature with Baseimp Boundary Conditions 

Monthly Slab Outside Face Temperatures, C and Heat Fluxes(loss), W/(m^2)

Perimeter Area: 79.00 Core Area: 64.00

Month TAverage TPerimeter TCore TInside AverageFlux PerimeterFlux CoreFlux

1 26.09 24.58 27.98 30 20.21 28.01 10.45

2 26.07 24.56 27.94 30 20.34 28.11 10.63

3 26.16 24.75 27.93 30 19.84 27.15 10.71

4 26.36 25.10 27.93 30 18.82 25.33 10.68

5 26.61 25.52 27.96 30 17.55 23.16 10.54

6 26.83 25.90 28.00 30 16.37 21.21 10.32

7 26.98 26.13 28.05 30 15.60 20.00 10.09

8 27.01 26.15 28.08 30 15.45 19.88 9.91

9 26.91 25.96 28.10 30 15.96 20.87 9.82

10 26.71 25.61 28.09 30 16.99 22.70 9.86

11 26.47 25.19 28.07 30 18.27 24.88 10.00

12 26.24 24.81 28.02 30 19.44 26.82 10.22

Convergence has been gained.

Case GC80c – Reduced Slab and Ground Conductivity with Baseimp Boundary Conditions 

Monthly Slab Outside Face Temperatures, C and Heat Fluxes(loss), W/(m^2)

Perimeter Area: 79.00 Core Area: 64.00

Month TAverage TPerim eter TCore TInside AverageFlux PerimeterFlux CoreFlux

1 27.52 26.35 28.99 30 8.95 13.18 3.66

2 27.50 26.32 28.98 30 9.02 13.28 3.70

3 27.56 26.43 28.97 30 8.83 12.90 3.73

4 27.67 26.64 28.96 30 8.41 12.13 3.75

5 27.82 26.90 28.96 30 7.88 11.18 3.75

6 27.96 27.15 28.97 30 7.37 10.29 3.73

7 28.05 27.31 28.98 30 7.03 9.71 3.69

8 28.07 27.34 28.99 30 6.95 9.60 3.65

9 28.02 27.23 29.00 30 7.15 9.98 3.61

10 27.90 27.02 29.01 30 7.57 10.76 3.59

11 27.75 26.75 29.01 30 8.11 11.72 3.59

12 27.62 26.51 28.00 30 8.61 12.60 3.61

Convergence has been gained.
155 

3. Modeling Difficulties 

The boundary condition of zero-vertical heat flux implied for the soil surface just beneath the adiabatic 

exterior walls of the conditioned zone, as specified in the BESTEST Indepth G-C specification, was not 

modeled by the EnergyPlus Slab program. The slab program does not have the capability to model this 

effect. The slab configuration used in the slab program is a slab-in-grade model. That is, the slab top 

surface is assumed to be level with the outside earth surface. The modeling capabilities of the EnergyPlus 

Slab program are shown in Figure 2D-1. The insulation layers are optional and were not required for any 

of the G-C test cases. With the EnergyPlus Slab program the entire slab top surface is exposed to the 

interior zone condition. 

Figure 2D-1 Slab-in-grade illustration 

4. Modeling Assumptions 

Over the duration of this ground-coupling test suite development in which EnergyPlus first participated in 

December 2004, the EnergyPlus auxiliary Slab program has had two upgrades with changes as 

summarized below: 

• May 2003 Original version used to report results in EnergyPlus Modeler Report dated 

December 2004 

• April 2005 Enhanced to allow optional user inputs for the lower deep boundary temperature 

and exterior ground heat transfer coefficient and was used to report revised results presented in 

EnergyPlus Modeler Report dated June 2005. Changes were also made to the gridding scheme to 

include stability considerations and eliminate “floating overflow” and “array bounds” errors. A 

scheduling feature was added to the OtherSideCoefficients object in EnergyPlus 1.2.2 to allow 

the separate simulation of perimeter and core portions of slab floors. 

• March 2006 Enhanced to allow user input of the lower deep boundary depth and was used to 

report revised results presented in EnergyPlus Modeler Report dated March 2006. To make it 

easier for the user to separately simulate the perimeter and core areas of floor slabs in 

EnergyPlus, example inputs (IDF) for using the EnergyPlus OtherSideCoefficients object to 

simulate the perimeter and core of floor slabs were added to the Slab program output. 
156 

Several of the inputs required by the EnergyPlus Slab program to simulate the In-Depth G-C test cases 

are highlighted below. 

1) Ground surface albedo for snow and no snow conditions – both set to 0.0 

2) Ground surface emissivity for snow and no snow conditions – both set to 0.000001 

3) Ground surface roughness for snow and no snow conditions – both set to 0.000001 

4) Slab thickness - The EnergyPlus Slab program requires the user to specify the thickness of 

the slab. For the results reported in the EnergyPlus Modeler Report dated December 2004, 

the slab thickness was set to 0.1524 m (6 inch). In accordance with the G-C In-Depth 

specification released in June 2005 where it was requested that the thinnest slab allowable be 

used, all cases were revised to use a slab with thickness of 0.1285 m (5 inch). 

5) Surface evapotranspiration – set to FALSE (off) 

6) Convergence tolerance – The Slab program iterations continue until the temperature change 

of all modes are less than this value. For all test cases the convergence tolerance was set to 

0.1°C. 

7) For all cases the grid autosizing option was used. 

8) For Cases GC30c, GC40c, GC45c and GC80c the exterior ground surface temperature could 

not be fixed as required by the Indepth G-C specification. To approximate this condition, as 

suggested in the specification, the exterior ground convective coefficient was set to 100 

W/m2-K. 

5. Appropriate Modeling Detail 

The accuracy of results produced by the EnergyPlus Slab program are controlled by the Convergence 

Tolerance input parameter specified by the user. Annual simulations by the EnergyPlus Slab program 

continue until the change in temperature for all nodes of the grid are less than this convergence tolerance. 

 For all of the cases simulated as part of this test suite, the convergence tolerance was set to 0.1 C. 

Convergence for the cases that ran successfully occurred within the following time periods: 

 Case GC30b 7 years 

 Case GC40b 7 years 

 Case GC45b 7 years 

 Case GC50b 8 years 

 Case GC55b 3 years 

 Case GC60b 7 years 

 Case GC65b 8 years 

 Case GC70b 7 years 

 Case GC80b 16 years 

 Case GC30c 6 years 

 Case GC40c 6 years 

 Case GC45c 6 years 

 Case GC55c 3 years 

 Case GC80c 10 years 
157 

6. Enhancements to EnergyPlus 

As was discussed in Section 4, a series of enhancements had to be made to the EnergyPlus Slab program 

in order to accommodate the range of variable testing required by the BESTEST In-Depth G-C 

specification. The extreme range of some of these variables would never be seen in real buildings but are 

convenient for controlled comparative testing. A summary of these enhancements and their impact on 

results is presented below. 

• User definition of a specific lower deep boundary temperature. This capability was required to 

ensure that all programs participating in the BESTEST In-Depth G-C comparative testing 

exercise were using the same deep boundary temperature. Previous to this enhancement, this 

temperature was calculated for the user by the EnergyPlus Slab program and set to the annual 

mean outdoor dry-bulb temperature as determined from data on the weather file. Since the lower 

deep boundary temperature required by the specification was 10°C for all test cases and each of 

the weather files used as part of the test suite already had annual mean ambient dry-bulb air 

temperatures of 10°C, use of this new capability did not change any of the test results. 

• User definition of ground surface heat transfer coefficient. This capability was required to ensure 

that all programs participating in the BESTEST In-Depth G-C comparative testing exercise were 

using the same the same ground heat transfer coefficient. Most test cases the In-Depth G-C 

specification required that this parameter be set to 100 W/(m2

K), a value far higher than typically 

seen in real situations. Cases GC65b and GC70b, however, required that this parameter be set at 

11.95 W/(m2

K). In the original version of the EnergyPlus Slab program the user did not have the 

option of defining this parameter but rather it was calculated internally by the program as a 

function of the ambient temperature and wind speed from the weather file. Subsequent to this 

enhancement the ground heat transfer coefficient for each test case was set by input to that 

required by the specification. 

• User definition of the lower deep boundary depth, including allowing the automated gridding 

option for various depths. This capability was required because the In-Depth G-C specification 

requested the simulation of shallow as well as deep boundary depths ranging from 2 m to 30 m. 

Previous to this enhancement, when the A/P ratio was 4.25 or less the deep boundary depth was 

automatically set to 15 m and if greater than 4.25 it was set to 20 m. In reality, once you reach 

20 m there would be no change in results beyond that distance. For all test cases except GC55b 

and GC55c, the deep boundary depth specified is 15 m, and since for all cases except GC50b the 

A/P ratio is less than 4.25, this new capability affected only 3 of the 14 of the test cases modeled 

by EnergyPlus. 

• With earlier versions of the Slab program documentation there was some confusion about the 

input parameter “Distance from edge of slab to domain edge.” It was unclear if this was the 

horizontal far field distance or the deep boundary depth. Later documentation changes cleared 

this up. 
158 

7. Results 

Results for this round of testing with EnergyPlus 2.0.0.025 for the cases modeled are shown below. Some 

of the requested output results were not available from the EnergyPlus Slab program. 

Software: Version: Date:

 Steady State Cases GC10 Only

qfloor qzone Tzone tsim Qcumulative E F

(W) (W) (°C) (hours) (kWh) (m) (m)

GC10a n/a n/a n/a

GC30a

GC30b 2652 2652 30 61320 69706

GC30c 2308 2308 30 52560 60652

GC60b 2219 2219 30 61320 58304

GC65b 1616 1616 30 70080 42457

 Harmonic Cases

 Annual Sums and Means Annual Hourly Integrated Maxima and Minima 

Qfloor Qzone Tzone,mean tsim qfloor,max qzone,max TODB,min (first occurrence) Number of hours 

(kWh/y) (kWh/y) (°C) (hours) (W) Date Hour (W) Date Hour (°C) Date Hour at TODB,min 

GC40a

GC40b 23204 23204 30 61320 3005 02/02 03:00 3005 02/02 03:00 2.0375 01/08 04:00 15

GC45b 33415 33415 30 61320 4415 02/02 04:00 4415 02/02 04:00 2.0375 01/08 04:00 15

GC50b 324257 324257 30 70080 39570 01/01 01:00 39570 01/01 01:00 2.0375 01/08 04:00 15

GC55b 39932 39932 30 26280 4860 01/01 01:00 4860 01/01 01:00 2.0375 01/08 04:00 15

GC70b 15553 15553 30 61320 1906 02/03 08:00 1906 02/03 08:00 2.0375 01/08 04:00 15

GC80b 6059 6059 30 140160 766 02/04 02:00 766 02/04 02:00 2.0375 01/08 04:00 15

GC40c 20255 20255 30 52560 2650 02/03 11:00 2650 02/03 11:00 2.0375 01/08 04:00 15

GC45c 28707 28707 30 52560 3827 02/03 07:00 3827 02/03 07:00 2.0375 01/08 04:00 15

GC55c 22570 22570 30 26280 2926 02/03 11:00 2926 02/03 11:00 2.0375 01/08 04:00 15

GC80c 10073 10073 30 87600 1300 02/05 05:00 1300 02/05 05:00 2.0375 01/08 04:00 15

 EnergyPlus 2.0.0.025 Oct. 9, 2007

8. Other 

One issue that came up in the early stages of the work was a disagreement for the results of GC40-GC30, 

see Figures 2D-2 and 2D-3 below. This disagreement was traced to an input error where the monthly slab 

perimeter temperatures output by the slab model were input to EnergyPlus, rather than the monthly 

average (of perimeter and core) slab temperatures. Figure 2D-4 indicates corrected results, which show a 

roughly 45% decrease in floor conduction versus Figure 2D-3. A simultaneous secondary effect on these 

results is the difference between the specified ideal (infinite) surface coefficients of Case GC40 and 

surface coefficients of 100 W/m2

K for Case GC40b. This secondary effect can account for at most a 4%–

5% variation based on FLUENT, SUNREL-GC and TRNSYS results for cases GC40a and GC40b, and is 

probably less because for Case GC40 EnergyPlus did not run for interior surface coefficient > 180 

W/m2

K. Another secondary effect is variation of soil conductivity from 2.0 W/mK for Case GC40 to 1.9 

W/mK for Case GC40b, which should have about a 5% effect on all model results. Therefore, the effect 

of correcting the input error is estimated at about a 35–40% decrease for floor conduction (i.e., 45% – 

(5% for reduced conductivity) – (a few % for reduced surface coefficient). 
159 

-500

0

500

1000

1500

2000

GC30-GC10,

perimeter b.c.

GC40*-GC30,

dynamics

GC30-GC60,

hint

GC60-GC65,

hext

GC30-GC65,

hint & hext

GC70*-GC65,

dyn & films

Floor Heat Flow (W or Wh/h)

Eplus/GARD

EnergyPlus sensitivity for GC40-GC30 

should be zero, like the other programs.

GHT/NREL SUNREL/NREL TRNSYS-ind/TESS

Figure 2D-2. EnergyPlus GC40-GC30 disagreement, February 2005 

0

5000

10000

15000

20000

25000

30000

35000

40000

GC40, base case 

ideal films

GC45, aspect ratio GC50, large slab GC55, shallow

ground depth

GC70, hint=1

hext=17

Floor Heat Flow (kWh)

Eplus/GARD

•EnergyPlus 45% disagreement with SUNREL and TRNSYS 

for steady-periodic cases GC40 (base)

•Problem traced to input error.

GHT/NREL SUNREL/NREL TRNSYS-ind/TESS

Figure 2D-3. EnergyPlus GC40 disagreement, February 2005
160 

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

GC40a, ideal films GC40b, h=100 GC45b, AR=36x4 GC50b, large

slab/10

GC55b, 2m

depth

GC70b, hint=7.95,

hext=11.95

GC80b, k=0.5

Floor Heat Flow (kWh)

TRNSYS-ind/TESS

EnergyPlus 

improved result

GHT/NREL SUNREL/NREL

FLUENT/Nakhi Eplus/GARD VA114-ISO13370/VABI

Figure 2D-4. EnergyPlus input error correction, shown with April 2006 results

9. Conclusions 

The results and comparisons for several ground-coupling programs that participated in the IEA BESTEST 

Ground-Coupling exercise were presented by Joel Neymark at a meeting in Quebec City, Canada on June 

26, 2006 (Neymark 2006b). From those results it appeared that the EnergyPlus results compared to other 

programs were overly sensitive to exterior ground heat transfer coefficient and ground deep boundary 

depth. As is suggested by Neymark, much of this increased sensitivity with the EnergyPlus groundcoupling model is probably due to the EnergyPlus Slab program’s shorter heat flow path around the 

exterior wall which would overestimate the slab perimeter heat flow. These EnergyPlus Slab program 

sensitivities will be further examined by the EnergyPlus development team. 
161 

10. References 

Bahnfleth, W.P. 1989. Three Dimensional Modeling of Heat Transfer from Slab Floors. Ph.D. 

diss., also published as USACERL TM E-89/11, University of Illinois. 

Bahnfleth, W.P. and C.O. Pedersen. 1990. A Three Dimensional Numerical Study of Slab-onGrade Heat Transfer. ASHRAE Transactions Pt. 2, 96:61-72. 

Clements, Edward, 2004, Three Dimensional Foundation Heat Transfer Modules for WholeBuilding Energy Analysis, MS Thesis, Pennsylvania State University. 

EnergyPlus 2006. U.S. Department of Energy, Energy Efficiency and Renewable Energy, Office 

of Building Technologies. www.energyplus.gov

Ground Heat Transfer in EnergyPlus, Auxiliary EnergyPlus Programs, pgs 65-81, September 20, 

2006. 

Neymark, J., and R. Judkoff. 2006a. Proposed IEA BESTEST In-Depth Diagnostic Cases for 

Ground Coupled Heat Transfer Related to Slab-on-Grade Construction, IEA SHC Task 34/ 

Annex 43, National Renewable Energy Laboratory, Golden, Colorado, March 2006. 

Neymark, J. 2006b. PowerPoint Presentation titled IEA BESTEST Ground Coupling Review, 

June 26, 2006 
Model Geometry and Thermal Property Allowed Inputs (pro forma)

Model and Version:

Horizontal Vertica

Foundation Above Grade Edge Interior Ed

Slab Wall Footer Soil Sill Plate Wall Insulation Insulatio

GEOMETRY*

Floor Slab In (below) Grade ("yes" or "no") yes n/a n/a n/a n/a n/a n/a n/a 

Floor Slab On (above) Grade ("yes" or "no") no n/a n/a n/a n/a n/a n/a n/a 

Floor Slab Minimum Thickness (cm) set by stab n/a n/a n/a n/a n/a n/a n/a 

Floor Slab Maximum Thickness (cm) 15m n/a n/a n/a n/a n/a n/a n/a 

Minimum x-Thickness or Width (cm) n/a 0 0 n/a 0 0 0 0 

Maximum x-Thickness or Width (cm) n/a 0 0 n/a 0 0 200 0 

Minimum z -Thickness (cm) n/a n/a 0 n/a 0 n/a 0 n/a 

Maximum z -Thickness (cm) n/a n/a 0 n/a 0 n/a 0 n/a 

Minimum Bottom-Edge Depth Below Grade (z , cm) set by stab 0 0 n/a n/a n/a n/a 20 

Maximum Bottom-Edge Depth Below Grade (z , cm) 1500 0 0 n/a n/a n/a n/a 300 

Minimum Top-Edge Height Above Grade (z , cm) 0 0 n/a n/a n/a n/a n/a 0 

Maximum Top-Edge Height Above Grade (z , cm) 0 0 n/a n/a n/a n/a n/a 0 

Minimum Soil Depth (E, m) n/a n/a n/a 0 n/a n/a n/a n/a 

Maximum Soil Depth (E, m) n/a n/a n/a 15 n/a n/a n/a n/a 

Minimum Soil Far-Field Distance (F, m) n/a n/a n/a 0 n/a n/a n/a n/a 

Maximum Soil Far-Field Distance (F, m) n/a n/a n/a 15 n/a n/a n/a n/a 

THERMAL PROPERTIES*

Minimum Conductivity (W/(mK)) 0 0 0 0 0 0 0 

Maximum Conductivity (W/(mK)) 0 0 0 0 0 0 0 

Minimum R-Value (m2K/W))0 0 0 0 0 0 0 0 

Maximum R-Value (m2K/W))0 0 0 0 0 0 0 0 

Minimum Density (kg/m3)0 0000 00 

Maximum Density (kg/m3)0 0000 00 

Minimum Specific Heat (kJ/(kgK)) 0 0 0 0 0 0 0 

Maximum Specific Heat (kJ/(kgK)) 0 0 0 0 0 0 0 

COMMENTS

Uninsulated detail (Figure A-1) ok? ("yes" or "no") yes

Insulated detail (Figure A-2) ok? ("yes" or "no") yes

If no, include additional assumptions of your model 

not covered here (add rows as needed)

Include other clarfications and/or comments here Many of the limits are set by stability considerations and can not be specified in isolation. 

(add rows as needed)

NOTES"n/a": not applicable* If a listed input does not apply to your model, enter "0" in the relevant cells.** For below grade high-mass components, only list R-value input limits if there is some difference versus what would be calculated ba conductivity and thickness limits

EnergyPlus Auxiliary Slab Program Insulation Com

Below-Grade High-Mass Components Low-Mass Components

162 
163 

 

Appendix II-E 

Modeler Report for BESTEST Cases GC10a-GC80c 

BASECALC Version 1.0e and BASESIMP/ESP-r 

by 

Hajo Ribberink, Patrice Pinel1

 and Ian Beausoleil-Morrison2

CANMET Energy Technology Centre, Natural Resources Canada 

Canada 

 

January 2007 

1. BASECALC V1.0e 

Results file: GC-InDepth-Out-0606a_Basecalc.xls 

1.1. Introduction

BASECALC is an independent basement heat losses evaluation software developed by NRCan. 

The genesis of the BASECALC technique was the National Research Council of Canada’s Mitalas method. 

Mitalas utilized mainframe computers to perform finite-element analyses of a large number of basements and 

analyzed the results to produce a series of basement heat-loss factors. BASECALC incorporates the finiteelement approach used by Mitalas to generate his basement heat-loss factors but allows modeling of exact 

insulation configurations, basement geometries, and site conditions, thus improving accuracy. 

The solution is obtained by performing three 2-D finite element simulations and using corner correction 

factors to obtain quasi-3D solutions. First, a finite element run calculates the above-grade heat losses (Qag). A 

steady state run is then performed to obtain the below grade average heat losses (Qbg,avg). Finally, a transient 

3-year run is used to evaluate the below-grade variable heat losses (Qbg,variable). 

The finite element solutions have the form S2dFE-AG, S2dFE-BG,avg, S2dFE-BG,var where: 

• S2dFE-AG = calculated above grade heat loss factor (W/m°C) 

• S2dFE-BG,avg = calculated below grade average heat loss factor (W/m°C) 

• S2dFE-BG,var = calculated below grade variable heat loss factor (W/m°C) 

These solutions are then converted into three dimensional parametric heat loss factors using the corner 

correction method: 

• Sagr = S2dFE ,ag * [2(L+W)] (1) 

• Sbg,avg = S2dFE,avg * [2(L-W) + 4W*Fc,avg] (2) 

• Sbg,var = S2dFE,var * [2(L-W) + 4W*Fc,var] (3) 

1

Mr. Pinel is no longer with Natural Resources Canada. 2

Mr. Beausoleil-Morrison has recently moved to Carleton University, Canada. 
164 

Where: 

• L = length of the basement (m) 

• W = width of the basement (m) 

• Fc = corner correction factor evaluated from the correlations of the corner correction method 

• Sag = calculated above grade heat loss factor (W/°C) 

• Sbg,avg = calculated below grade average heat loss factor (W/°C) 

• Sbg,var = calculated below grade variable heat loss factor (W/°C) 

These factors are then converted into fluxes for any weather conditions by using: 

Qag,i = Sag (Tbasement – Ta,i) (4) 

Qbg,avg = Sbg,avg (Tbasement – Tg,avg) (5) 

Qbg,var,I = Sbg,var Tg,amp cos(2π/365 middledayi + phase – Ps) (6) 

 

Where: 

• Qag,i = above grade heat losses for month I (W) 

• Qbg,avg = average below grade heat losses (W) 

• Qbg,var,i = variable below grade heat losses for month i (W) 

• Ta,i = the ambient outdoor temperature for month i (°C) 

• Tg,avg = annually averaged ground surface temperature (°C) 

• Tg,amp = amplitude of the annual variation of the ground surface temperature (°C) 

• Tbasement = basement temperature (°C) 

• middledayi = number of days from the beginning of the year to the middle of month i (days) 

• phase = phase lag, (B – phase) is the lag between the coldest ground surface temperature and 

the largest heat losses (radians) 

• Ps = phase lag of ground surface temperature cosine (radians) 

Finally, the total heat losses from the basement for month i is calculated using: 

Qbasement,i = Qag,i + Qbg,avg + Qbg,var,i (7) 

The BASECALC software returns monthly values of above and below grade heat losses but the parametric 

heat loss factors can be adapted to approximate heat losses using a smaller time scale. 

1.2. Modeling Assumptions 

The modeling assumptions and boundary conditions BASECALC uses for calculating heat losses to the 

ground are illustrated in Figures 2E-1 and 2E-2. 
165 

deepground 

depth 

8 m 

Tg,avg

Tambient

Tg, surface

adiabatic 

adiabatic 

water table (constant temperature)

Figure 2E-1 BASECALC heat loss model boundary conditions 

Grade

Above Grade Wall

Above Grade 

Wall

BASECALC:

Soil

Slab IN Grade Detail 

(no scale)

200 cm

5 cm

E

F

x

Floor Slab z

Not separately defined:

• Footer

• Sill Plate

Above ground wall bottom 

edge depth = slab top edge 

depth

Footer

Footer only defined for indicating 

location of thermal breaks. Modeled 

in BASECALC as soil

Grade

Above Grade Wall

Above Grade 

Wall

BASECALC:

Slab IN Grade Detail 

Soil

(no scale)

200 cm

5 cm

E

F

x

Floor Slab

Not separately defined:

• Footer

• Sill Plate

Above ground wall bottom 

edge depth = slab top edge 

depth

z

Footer

Footer only defined for indicating 

location of thermal breaks. Modeled 

in BASECALC as soil

Figure 2E-2 BASECALC slab in grade details (uninsulated) 
166 

For heat losses to the deeper underground, BASECALC assumes a constant temperature (Tg,avg) at a water 

table depth (E) of 5 m–20 m (user input). An adiabatic boundary condition is used at a far field distance (F) 

of 8 m. 

BASECALC assumes a uniform air temperature inside the basement. From there, a 7.95 W/m2°C coefficient 

is used to evaluate convection and radiation at the inside face of the floor and walls and a 14.196 W/m2°C 

convection/radiation coefficient is used at the outside face of the walls. No heat transfer is calculated at the 

basement ceiling. 

BASECALC requires a minimum slab thickness (z) of 5 cm. This value is used in all calculations. The slab 

must have at least 5cm ground above in the interior slab surface level in order for the finite elements 

calculation method to converge on a solution. This should not result in a large difference in the solution 

compared to a real slab on grade. 

BASECALC requires entering a 2 m above grade wall height for slabs. So, a wall with a 0.01 W/m°C 

thermal conductivity, the minimum allowable value, is used. Including the inside and outside 

convective/radiative (7.95 in, 14.196 out) coefficients previously discussed, this wall has a very low 

equivalent U value of 0.04 W/m2°C. 

BASECALC requires entering the outside dimensions of the basement. So, for a 12 m × 12 m slab with a 

0.24 m thick wall, dimensions of 12.48 m × 12.48 m (12 + 2*0.24) are used. 

BASECALC also requires the construction type of the first storey. For the purpose of this work, the “Non 

brick veneer or thermally broken brick” option is selected. Furthermore, the software offers the possibility to 

describe thermal breaks around the edge of the slab and between the slab and footing. No thermal breaks are 

used in this work. 

Table 2E-1 presents the allowed inputs related to model geometry and thermal properties. 

Details for insulated slab on grade cases are presented in Figure 2E-3. In principle the horizontal insulation is 

taken to extend from the inner wall inwards. Vertical insulations is taken from the bottom of the slab 

downwards (skirt). A thermal break can be added around the edge of the wall (1), between the floor slab and 

the footer (2), or as part of the first storey construction (3). 
167 

Grade

Above Grade Wall

Above Grade 

Wall

BASECALC:

Soil

Slab IN Grade Detail

With Insulation

(no scale)

200 cm

5 cm

E

F

x

Floor Slab z

Not separately defined:

• Footer

• Sill Plate

Above ground wall bottom 

edge depth = slab top edge 

depth

Footer Footer only defined for indicating 

location of thermal breaks. Modeled 

in BASECALC as soil

1

Vertical

3

2 Horizontal

Grade

Above Grade Wall

Above Grade 

Wall

BASECALC:

Slab IN Grade Detail

Soil

With Insulation

(no scale)

200 cm

5 cm

E

F

x

Floor Slab

Not separately defined:

• Footer

• Sill Plate

Above ground wall bottom 

edge depth = slab top edge 

depth

z

Footer Footer only defined for indicating 

location of thermal breaks. Modeled 

in BASECALC as soil

3

1

Vertical

2 Horizontal

Figure 2E-3 BASECALC slab in grade details (insulated) 
168 

Table 2E-1. BASECALC Slab-on-Grade Model Geometry and Thermal Property Allowed Inputs 

Model and Version:

Horizontal Vertical Vertical

Foundation Above Grade Edge Interior Edge Exterior Edge

Slab Wall Footer Soil Sill Plate Wall Insulation Insulation Insulation

GEOMETRY*

Floor Slab In (below) Grade ("yes" or "no") yes n/a n/a n/a n/a n/a n/a n/a n/a

Floor Slab On (above) Grade ("yes" or "no") no n/a n/a n/a n/a n/a n/a n/a n/a

Floor Slab Minimum Thickness (cm) 5 n/a n/a n/a n/a n/a n/a n/a n/a

Floor Slab Maximum Thickness (cm) 50 n/a n/a n/a n/a n/a n/a n/a n/a

Minimum x- Thickness or Width (cm) n/a 0 0n/a0 5 0 0 0

Maximum x -Thickness or Width (cm) n/a 0 0 n/a 0 50 full width 0 0

Minimum z -Thickness (cm) n/a n/a 0 n/a 0 n/a 0 n/a n/a

Maximum z -Thickness (cm) n/a n/a 0 n/a 0 n/a p(7.6) or u n/a n/a

Minimum Bottom-Edge Depth Below Grade (z , cm) 10 0 0 n/a n/a 10 n/a 0 0

Maximum Bottom-Edge Depth Below Grade (z , cm) 55 0 0 n/a n/a 55 n/a 0 0

Minimum Top-Edge Height Above Grade (z , cm) 0 0 n/a n/a n/a 200 n/a 0 0

Maximum Top-Edge Height Above Grade (z , cm) 0 0 n/a n/a n/a 200 n/a 0 0

Minimum Water Table (slab + soil) Depth (E, m) n/a n/a n/a 5 n/a n/a n/a n/a n/a

Maximum Water Table (slab + soil) Depth (E, m) n/a n/a n/a 20 n/a n/a n/a n/a n/a

Minimum Soil Far-Field Distance (F, m) n/a n/a n/a 8 n/a n/a n/a n/a n/a

Maximum Soil Far-Field Distance (F, m) n/a n/a n/a 8 n/a n/a n/a n/a n/a

THERMAL PROPERTIES*

Minimum Conductivity (W/(mK)) 0.1 0 0 0.25 0 0.1 0 0 0

Maximum Conductivity (W/(mK)) 2 0 0 10 0 2 0 0 0

Minimum R-Value (m2

K/W)) **   **  0 ** 0 0 0

Maximum R-Value (m2

K/W))   **  ** 0 ** 20 (u) 0 0

Minimum Density (kg/m3

) p p 0p0 p p 0 0

Maximum Density (kg/m3

) p p 0p0 p p 0 0

Minimum Specific Heat (kJ/(kgK)) p p 0 p 0 p p 0 0

Maximum Specific Heat (kJ/(kgK)) p p 0 p 0 p p 0 0

COMMENTS

Uninsulated detail (Figure A-1) ok? ("yes" or "no") no

Insulated detail (Figure A-2) ok? ("yes" or "no") no

If no, include additional assumptions of your model In BASECALC a slab-on-grade is defined as a slab of 5 - 50 cm thickness with top of slab at 5 cm below

not covered here (add rows as needed) grade (fixed value). The wall height is fixed with the top at 200 cm above grade.

Slab-on-grade can have insulation skirts:

 - horizontal (0 - 5 m) from wall, at 20 cm depth

 - vertical (0 - 2.5 m from bottom of slab)

 - insulation skirts are characterizes by R-value only (0 - 20 m2K/W)

Slab-on-grade can also have thermal breaks:

 - around corner

 - between wall and footer

 - thermal breaks are charachterizes by R-value only (0 - 20 m2K/W)

The 'Water Table Depth' is defined as the depth at which the soil temperature is constant through the year.

Include other clarfications and/or comments here p = predefined structure components to choose from

(add rows as needed) u = user defined by using R(SI) values instead of dimensions

BASECALC version 1.0e Insulation Components 

Below-Grade High-Mass Components Low-Mass Components
169 

1.3. Modeling Adjustments 

1.3.1 Corrections for length in test GC45C 

BASECALC inputs are limited to 20 m × 20 m basements. But, since only the width is accounted for in the 

finite element runs, while the length is taken into account by the corner correction method, it is possible to 

correct results for lengths that exceed those limits. So, for case GC45 (36 m × 4 m), the corner correction 

technique is used to correct for the influence of the length as described in the following example. 

A BASECALC simulation using a 20 m × 4.48 m slab results in: 

• Sag = 1.145 W/°C 

• Sbg,avg = 77.574 W/°C 

• Sbg,var = 44.910 W/°C 

• Phase = 2.880 radians 

The corner correction method is applied as shown in Equations 1 to 3: 

S = S2dFE * [2(L-W) + 4W*Fc] (8) 

Evaluation of the corner correction correlations for this configuration yields: 

• Fc,avg = 0.705, the average (steady state) corner correction factor 

• Fc,var = 0.740, the variable corner correction factor 

Reversing equation 8 and using this reversed equation on the results for L=20 and W=4.48, we get: 

• S2dFE ,ag = Sag / [2(L+W)] = 0.0234 W/m°C 

• S2dFE ,bg,avg = Sbg,avg / [2(L-W) + 4W*Fc,avg] = 1.7764 W/m°C 

• S2dFE ,bg,var = Sbg,var / [2(L-W) + 4W*Fc,var] = 1.0136 W/m°C 

Reusing equations 1-3 directly with L=36.48 and W=4.48 and these values of S2dFE, we get the heat loss 

factors adjusted for length: 

• Sag,cor = S2dFE ,ag* [2(L+W)] = 1.915 W/°C 

• Sbg,avg,cor = S2dFE,avg * [2(L-W) + 4W*Fc,avg] = 136.125 W/°C 

• Sbg,var,cor = S2dFE,var * [2(L-W) + 4W*Fc,var] = 78.317 W/°C 

1.4. Modeling Difficulties

No difficulties were encountered when modeling these tests. 

1.5. Demonstration of Appropriate Level of Modeling Detail

Since BASECALC offers no control over the level of modeling details, there are no direct ways to perform 

these demonstrations. 

 
170 

2. BASESIMP/ESP-r 

Results file: GC-InDepth-Out-0107_Basesimp-ESP-r.xls 

2.1. Introduction

BASESIMP is a regression based algorithm developed by NRCAN from over 100,000 BASECALC runs. 

The correlations evaluate basement heat losses for different basements and slabs with various insulation 

configurations, 140 basements and slabs systems are available. 

The method has been implanted in different software like ESP-r and HOT2000. The present section 

evaluates results using NRCan’s implementation of the method in ESP-r. 

The BASESIMP correlations approximate the results of the 2-D finite element runs from BASECALC. The 

corner correction method described in Section 1.1 and used in Section 1.3.1 of this report is applied to 

calculate the heat loss factors described in Equations 1, 2 and 3. 

The correlations are described in Reference 2. Reproducing them and the related coefficients here would not 

serve any use but would make the text considerably heavier. 

2.2. Modeling Assumptions 

BASESIMP is based upon results from BASECALC. The principal model configuration and slab details for 

BASESIMP are therefore identical to those for BASECALC (see Figure 2E-1, 2E-2, 2E-3). However, as the 

BASESIMP correlations only cover part of the total envelope of parameter variation of BASECALC, some 

inputs may differ (see Table 2E-2). An overview of BASESIMP slab on grade configurations is presented in 

Table 2E-3. 

Like BASECALC, BASESIMP requires the construction type of the first storey. For the purpose of this 

work, the “Non brick veneer or thermally broken brick” with uninsulated walls option (case SCN_1 in 

BASESIMP terminology), is selected. 

The method also offers the possibility to describe thermal breaks around the edge of the slab. No thermal 

breaks are used in this work. 

ESP-r requires the definition of at least one zone. For this purpose, the 2.7 m high zone described in the 

specifications for tests GC30C ... GC80C was used for all cases. Since ESP-r does not allow definition of 

zero coefficients, the walls and ceiling of that zone are described as having: 

- thermal conductivity: 0.001 W/m°C 

- solar absorbtivity: 0.01 

- solar emissivity: 0.01.

All four walls and the ceiling of that zone are defined as having adiabatic boundary conditions. So, there are 

no heat losses from them in steady state. 

Finally, ESP-r runs demand the definition of a start up period. Since ESP-r uses a lumped method to evolve 

zone temperatures to the controller set points in the beginning of the simulation, use of a startup period is 

recommended for result precision. Tests demonstrated that it takes about 3 days for the zone temperature to 
171 

reach its set point of 30°C for the studied cases. A 365 day period was used for all cases. 

Table 2E-2 presents the allowed inputs related to the BASESIMP model geometry and thermal properties. 

Table 2E-2. BASESIMP Slab-on-Grade Model Geometry and Thermal Property Allowed Inputs 

Model and Version:

Horizontal Vertical Vertical

Foundation Above Grade Edge Interior Edge Exterior Edge

Slab Wall Footer Soil Sill Plate Wall Insulation Insulation Insulation

GEOMETRY*

Floor Slab In (below) Grade ("yes" or "no") yes n/a n/a n/a n/a n/a n/a n/a n/a

Floor Slab On (above) Grade ("yes" or "no") no n/a n/a n/a n/a n/a n/a n/a n/a

Floor Slab Minimum Thickness (cm) 5 n/a n/a n/a n/a n/a n/a n/a n/a

Floor Slab Maximum Thickness (cm) 50 n/a n/a n/a n/a n/a n/a n/a n/a

Minimum x- Thickness or Width (cm) n/a 0 0n/a0 5 0 0 0

Maximum x -Thickness or Width (cm) n/a 0 0 n/a 0 50 full width 0 0

Minimum z -Thickness (cm) n/a n/a 0 n/a 0 n/a 0 n/a n/a

Maximum z -Thickness (cm) n/a n/a 0 n/a 0 n/a p(7.6) or u n/a n/a

Minimum Bottom-Edge Depth Below Grade (z , cm) 10 0 0 n/a n/a 10 n/a 0 0

Maximum Bottom-Edge Depth Below Grade (z , cm) 55 0 0 n/a n/a 55 n/a 0 0

Minimum Top-Edge Height Above Grade (z , cm) 0 0 n/a n/a n/a 95 n/a 0 0

Maximum Top-Edge Height Above Grade (z , cm) 0 0 n/a n/a n/a 245 n/a 0 0

Minimum Water Table (slab + soil) Depth (E, m) n/a n/a n/a 5 n/a n/a n/a n/a n/a

Maximum Water Table (slab + soil) Depth (E, m) n/a n/a n/a 15 n/a n/a n/a n/a n/a

Minimum Soil Far-Field Distance (F, m) n/a n/a n/a 8 n/a n/a n/a n/a n/a

Maximum Soil Far-Field Distance (F, m) n/a n/a n/a 8 n/a n/a n/a n/a n/a

THERMAL PROPERTIES*

Minimum Conductivity (W/(mK)) 0.1 0 0 0.85 0 0.1 0 0 0

Maximum Conductivity (W/(mK)) 2 0 0 1.9 0 2 0 0 0

Minimum R-Value (m2

K/W)) **   **  0 ** 0 0 0

Maximum R-Value (m2

K/W))   **  ** 0 ** 9 0 0

Minimum Density (kg/m3

) p p 0p0 p p 0 0

Maximum Density (kg/m3

) p p 0p0 p p 0 0

Minimum Specific Heat (kJ/(kgK)) p p 0 p 0 p p 0 0

Maximum Specific Heat (kJ/(kgK)) p p 0 p 0 p p 0 0

COMMENTS

Uninsulated detail (Figure A-1) ok? ("yes" or "no") no

Insulated detail (Figure A-2) ok? ("yes" or "no") no

If no, include additional assumptions of your model In BASESIMP a slab-on-grade is defined as a slab of 5 - 50 cm thickness with top of slab at 5 cm below

not covered here (add rows as needed) grade (fixed value). 

Slab-on-grade can have insulation skirts:

 - horizontal (0 - 5 m) from wall, at 20 cm depth

 - vertical (0 - 2.5 m from bottom of slab)

 - insulation skirts are characterizes by R-value only (0 - 9 m2K/W)

Slab-on-grade can also have thermal breaks:

 - around corner

 - between wall and footer

 - thermal breaks are charachterizes by R-value only (0 - 9 m2K/W)

The 'Water Table Depth' is defined as the depth at which the soil temperature is constant through the year.

Include other clarfications and/or comments here p = predefined structure components to choose from

(add rows as needed) u = user defined by using R(SI) values instead of dimensions

ESP-r BASESIMP Insulation Components 

Below-Grade High-Mass Components Low-Mass Components
172 

Table 2E-3. Overview of Slab-on-Grade Cases, BASESIMP 

connection file formatconfiguration nameinstulated wallbrick veneer directly on slabthermal break around edgethermal break footervertical skirt (0.60 m)horizontal skirt (0.60 m)0.35 m0.60 m0.75 m1.0 mfull width0.6 m1.0 mfull width

28 SCN_1 x

29 SCN_2 x

30 SCN_3 x x

31 SCN_4 x x

32 SCN_7 x x x

33 SCN_8 x x x

34 SCB_1 x x

35 SCB_2 x x

36 SCB_3 x x x

37 SCB_4 x x x

38 SCB_5 x x x

39 SCB_6 x x x

40 SCB_9 xxx x

41 SCB_10 x x x x

42 SCB_11 x x x

43 SCB_12 x x x

44 SCB_13 x x

45 SCB_14 x x

46 SCB_17 x x x

47 SCB_18 x x x

48 SCB_21 x x x x

49 SCB_22 x x x x

50 SCB_23 x x x

51 SCB_24 x x x

52 SCB_25 x x

53 SCB_26 x x

54 SCB_29 x x x

55 SCB_30 x x x

56 SCB_33 x x x x

57 SCB_34 x x x x

58 SCB_35 x x x

59 SCB_36 x x x

60 SCA_17 x x

61 SCA_18 x x

62 SCA_19 x x x

63 SCA_20 x x x

64 SCA_21 x x x x

65 SCA_22 x x x x

66 SCA_23 x x x

67 SCA_24 x x x

81 SCB_31 x x x x

82 SCB_32 x x x x

83 SCB_37 x x x x

84 SCB_38 x x x x

85 SCB_39 x x x x

86 SCB_40 x x x x

104 SCA_1 x x

105 SCA_2 x x

106 SCA_9 x x

107 SCA_10 x x

First story wall Insulation below slab Insulation above slab
173 

2.3. Modeling Adjustments 

2.3.1 Corrections for dimensions 

BASESIMP requires entering the outside dimensions of the basement. So, for a 12 m × 12 m slab with a 

0.24 m thick wall, dimensions of 12.48 m × 12.48 m (12 + 2*0.24) should be used. 

The BASESIMP correlations were developed for basements with maximum dimensions of 100 m × 12 m. 

Therefore, using a 12.48 m width would mean working outside of the correlation ranges. To compensate, a 

12.98 m × 12 m slab is used instead in order to obtain the same area (155.75 m2). Reproducing test GC30C 

using BASECALC yields Qbg = 1971 W and Qag = 32 W for these dimensions. Since these are very close 

to the results obtained using a 12.48 m × 12.48 m slab (1973 W and 30 W), it can be assumed that using 

these dimensions provides the same results as using the required dimensions. 

Also, BASESIMP requires all dimensions to be above 5 m. Therefore, modeling test GC45C using all 

required dimensions is not possible. The 4.48 m × 36.48 m (163.43 m2) slab was replaced by a 5 m × 32.69 

m slab, which should give similar results. An additional BASECALC run was made for exact the same 

dimensions (5 m × 32.69 m) to check whether this assumption is valid; results are shown in Section 2.7.1. 

2.3.2 Basic configuration for correlations 

The BASESIMP correlations for slab heat losses are based upon BASECALC runs for a realistic 

configuration. For a concrete slab on grade this configuration is characterized by: 

BASECALC 

GC30C/40C/45C/55C – 

GC80C 

BASESIMP 

GC30C/40C/45C/55C – 

GC80C 

Wall thickness m 0.24 0.20 

Wall conductivity W/mK 0.01 1.73 

Slab thickness m 0.05 0.10 

Slab conductivity W/mK 1.9 – 0.85 1.73 

Soil conductivity above slab W/mK 1.9 – 0.85 1.8 – 0.8 

Soil conductivity below slab W/mK 1.9 – 0.85 2.0 – 0.9 

These BASESIMP parameter values are fixed in all simulations and result in a slab-on-grade configuration 

that is slightly different than the one prescribed for the c-series of GC-cases and implemented in 

BASECALC. BASESIMP results could therefore differ from BASECALC results. 

2.4. Modeling Difficulties

No modeling difficulties were encountered when performing the “c”-series test cases, see Part I. 

2.5. Demonstration of Appropriate Level of Modeling Detail

Since BASESIMP offers no control over the level of modeling details, there are no direct ways to perform 

these demonstrations. 
174 

2.6. Improvements to Tested Programs 

The current “c”-series of configurations are much better fitted to the specific limitations of BASECALC 

and BASESIMP (see Table 2E-6 in Section 3 of this modeler report). However, correctional calculations 

are still needed for both BASECALC and BASESIMP to meet the dimensions of GC45C. Besides, the 

BASESIMP results for GC80C differ significantly from the BASECALC results due to the limitations of 

the chosen standard configuration (see § 2.3.2) for developing the BASESIMP correlations. It should be 

noted here, however, that the BASESIMP case represents a much more realistic configuration than the 

more theoretical configuration prescribed for GC80C. The GC80c configuration is a consequence of 

using realistic low-range conductivity value for soil, and then applying that same relatively low value to 

the slab and foundation wall. The differences between the BASESIMP floor conduction results for case 

GC80C and those produced by BASECALC have been analyzed. Below an overview is given of the 

differences in modeling assumptions of BASESIMP [on left] and BASECALC [(in parenthesis)] and the 

contribution these differences in assumptions have in the total difference in floor conduction for the 

GC80C configuration [% on the right]: 

Slab cond. [W/mK] 1.73 (0.85) 34% 

Soil cond. [W/mK] 0.8/0.9 (0.85) 28% 

Wall cond. [W/mK] 1.73 (0.01) 19% 

Slab thickness [m] 0.10 (0.05) 16% 

Wall thickness [m] 0.20 (0.24) 3% 

For realistic buildings, the BASESIMP results will therefore be much closer to the BASECALC results as 

shown in Table 2E-4 below. 

The standard BASESIMP correlations cover only part of the operating envelope of BASECALC. In order 

to allow the user to use BASESIMP within the same limits as BASECALC, a new standard configuration 

type (type 999) has been developed for BASESIMP that allows the user to input the specific heat loss 

coefficients calculated by BASECALC for configurations that would normally fall outside of the 

envelope of parameter variations covered by the current heat loss correlations. The BASESIMP heat loss 

results for type 999 configurations identical to those of the BASECALC runs were used to supply the heat 

loss coefficients, as is shown in § 2.7.2. 

2.7. Results 

2.7.1. Results using standard BASESIMP correlations 

Comparisons of BASESIMP results (using standard BASESIMP correlations) with BASECALC results 

are shown in Table 2E-4. 

At first glance, the BASESIMP and BASECALC results for cases GC30C, GC40C, and GC55C look to be 

in good agreement, whereas the cases GC45C and especially GC80C display substantial differences. Further 

analysis of the results revealed that for all cases the BASESIMP results differ in two ways from the 

BASECALC results: 

• The differences in configuration described in §2.3.2 result generally in a 2%–5% higher heat loss for 

BASESIMP compared to the BASECALC result for the c-series cases. For case GC80c this difference is 

even 15%, because in the BASESIMP calculations the slab conductivity has a constant value (1.73 

W/mK) that is much higher than the value used by BASECALC (0.85 W/mK) for this specific case. 
175 

• The heat loss correlations used by BASESIMP are not a perfect fit to the original BASECALC data, but 

show a reasonable and expected spread of approximately 5% around the BASECALC results. 

Sometimes the BASESIMP value is lower than the BASECALC result, sometimes higher. 

Table 2E-4. Comparison of BASECALC and BASESIMP/ESP-r results for series c tests 

Test Below Grade Heat Losses (kWh/y) 

BASECALC BASESIMP/ESP-r 

GC30C 17285 17094 

GC40C 17285 17094 

GC45C 23849 (4.48 m × 36.48 m) 

 22610 (5.00 m × 32.69 m) 24584 (5.00 m × 32.69 m) 

GC55C 20850 19941 

GC80C 8635 10427 

For cases GC30C, GC40C, and GC55C the heat losses calculated using the BASESIMP fit are roughly 5% 

lower than when the original BASECALC results would be used, overcompensating the higher heat losses due 

to the configuration difference, and resulting in fairly similar numbers for both programs. The BASESIMP 

correlations used for cases GC45C and GC80C have a 5% higher value than the BASECALC values, 

amplifying the differences already caused by the differences in configuration, and resulting in a total 9% 

higher heat loss for case GC45C (5.00 m × 32.69 m slab) and a 21% higher heat loss for case GC80C. 

The results for the two different BASECALC simulations for GC45C, using a 4.48 m × 36.48 m slab and a 

5.00 m × 32.69 m slab, differ by 5%. 

2.7.2. Results using BASESIMP type 999 

Comparisons of BASESIMP results (using type 999) with BASECALC results are shown in Table 2E-5. 

Table 2E-5. Comparison of BASECALC and BASESIMP/ESP-r Results for Series c Tests 

using BASESIMP type 999 (Calculations are not based on correlations but on heat loss factors 

calculated by BASECALC)

Test Below Grade Heat Losses (kWh/y) 

BASECALC BASESIMP/ESP-r 

GC30C 17285 17285 

GC40C 17285 17285 

GC45C 23849 (4.48 x 36.48 m) 23849 (4.48 x 36.48 m) 

GC55C 20850 20850 

GC80C 8635 8635 

The annually totaled results for the cases GC30C to GC80C using BASESIMP with input of heat loss factors 

calculated by BASECALC exactly equaled the BASECALC results. This should not be a surprise, because 

the calculation of heat losses using the heat loss coefficients is identical in both programs. Only small 

differences in the maximum heat losses for floor and zone were detected (see detailed results in 

accompanying excel file), due to the difference in time basis for both programs (BASECALC uses monthly 

averages, while BASESIMP performs hourly simulations). 
176 

3. Conclusions and Recommendations

The current c series of configurations are much better fitted to the specific limitations of BASECALC and 

BASESIMP (see Table 2E-6). However, correctional calculations are still needed for both BASECALC and 

BASESIMP to meet the dimensions of GC45C. Besides, the BASESIMP results (using correlations for heat 

loss coefficients) for GC80C differ significantly from the BASECALC results due to the limitations of the 

chosen standard configuration (see § 2.3.2) for developing the BASESIMP correlations. It should be noted 

here, however, that the BASESIMP case represents a much more realistic configuration than the more 

theoretical configuration prescribed for GC80C. For realistic buildings, the BASESIMP results will therefore 

be much closer to the BASECALC results. 

A new standard configuration type (999) has successfully been implemented in BASESIMP. This type 

allows the user to input the specific heat loss coefficients calculated by BASECALC for configurations that 

would normally fall outside of the envelope of parameter variations covered by the current heat loss 

correlations. The BASESIMP type 999 results show perfect agreement to the BASECALC results for annual 

total heat losses. Peak heat losses differ slightly due to a difference in time basis between the two programs. 

After updating the BASESIMP program, both BASECALC and BASESIMP are able to model the c series 

test cases sufficiently close to the specs. No further revision of the specs for the c series test cases is 

necessary. 

Table 2E-6 Limitations of BASECALC and BASESIMP 

Method Comments 

BASECALC hi,BASECALC = 7.95 (required correction, see section 1.3.1) 

hout,BASECALC = infinite for all cases (not correctable) 

Water table depth 5-20 m 

Far field distance = 8 m 

20 m × 20 m maximum floor dimensions 

Temperatures as a function of position not available 

First 3 years of simulation not available 

BASESIMP 

(Correlations) 

hi,BASESIMP = 7.95 (required correction, see section 2.3.1) 

hout,BASESIMP = infinite for all cases (not correctable) 

ksoil ≤ 1.9 W/m°C BASESIMP limit 

Water table depth 5-15 m 

Far field distance = 8 m 

100 m × 12 m maximum floor dimensions 

Temperatures as a function of position not available 

First 3 years of simulation not available 

BASESIMP 

(Type 999) 

Same limitations as BASECALC 
177 

4. References 

1- Beausoleil-Morrison I., BASESIMP ESP-r implantation (Fortran code) 

2- Beausoleil-Morrison I. and Mitalas G. (1997), ‘BASESIMP: A Residential-Foundation Heat-Loss 

Algorithm for Incorporating into Whole-Building Energy-Analysis Programs’, Proc. Building Simulation 

’97, (2) 1-8, Int Building Performance Simulation Association, Prague Czech Republic. 

3- Beausoleil-Morrison, I. and Krarti, M. 1997. "Predicting Foundation Heat Losses: Neural 

Networks Versus the BASESIMP Correlations." Proc. Building Simulation ’97, (1) 251-258, Int Building 

Performance Simulation Association, Prague Czech Republic. 

4- NRCAN (1993), BASECALC Help. 

5- Beausoleil-Morrison, I., Mitalas, G., and Chin, H. 1995b. "Estimating Three-Dimensional 

Below-Grade Heat Losses from Houses Using Two-Dimensional Calculations." Thermal 

Performance of the Exterior Envelopes of Buildings VI. Clearwater Beach FL. pp.95-99. 

6- Beausoleil-Morrison, I. 1996. "BASECALC : A Software Tool for Modelling Residential- TM 

Foundation Heat Losses." Third Canadian Conference on Computing in Civil and Building 

Engineering. Montreal. pp.117-126. 
178 

Appendix II-F 

Modeler Report for BESTEST Cases GC10a-GC80c 

VA114 Version 2.20 using ISO-13370 ground heat transfer calculation method 

by 

Aad Wijsman 

VABI Software BV 

The Netherlands 

 

September 2007 

September 9, 2002 (first draft) 

November 7, 2002 (second draft) 

July 18, 2005 (third draft) 

September 9, 2005 (fourth draft) 

December 23, 2005 (fifth draft) 

May 9, 2006 (sixth draft) 

February 5, 2007 (draft 7) 

Remark:

This report is draft 7. With respect to draft 6 some more clarification was added based on comments of subtask leader 

Joel Neymark. 

A description of the model and its assumptions are given. The simulation program passed the BESTEST [1],[2],[3]. In 

the summer of 2005 the simulation program was subjected to the IEA-34/43 Ground Coupling tests (Slab cases only) 

[4]. In December 2005 the other defined tests and b-series of the In-Depth Diagnostic Cases for Slab-On-Grade [9] 

were done. Now the In-Depth Diagnostic Cases for Slab-On-Grade[11] were completed (some of the b-series cases 

were re-done; the c-series are done) . 
179 

1. Introduction

The Building simulation program VA114 is developed and distributed by VABI Software bv. The current 

version is 2.20. 

The program calculates the Demand, the Supply, the Distribution and the Generation of heat and cold for a 

building with its energy supply system. Moreover the internal comfort temperature and overheating are 

calculated. 

VA114 is a multi-zone program (up to 30 zones). The time step applied in VA114 is 1 hour. 

The boundary conditions, that are possible in VA114 are: 

- bounded to ambient 

- bounded to a neighbour zone 

- bounded to a mirror zone 

- bounded to the underground. 

The current program VA114 models: 

- heat exchange within a zone 

- heat exchange between zones by conduction 

- heat exchange between zones by airflow (ventilation) 

- solar gain and solar exchange between zones 

- solar shading 

- and other processes. 

The simulation program VA114 passed the BESTEST [1],[2],[3]. Moreover in 2002 the simulation program 

was subjected to the IEA SHC Task 22 ground-coupling tests [4]: GC100, GC120, GC125, GC160, GC180, 

GC190, GC125FF were carried out. Ground heat transfer was modelled with VA114 by describing the 

underground by one or more ‘zones’. Results are given in [5]. Comparison with the results of the other 

programs showed that this approach with VA114 gave low heat losses to the underground. 

In 2002 it was proposed to follow the approach of ISO 13370 [6]. The ground heat flow rate according to 

ISO 13370 (see Annex E) is treated as consisting of two components: 

- a fixed component representing the average heat flow rate through the ground 

- a varying component representing the variations in the ground heat flow rate about the average 

value 

The fixed component is obtained using the methods in standard ISO 13370. The varying component is a 

dynamic term obtained by solution of the heat diffusion equation. 

Because of manpower, budget, and priority, the implementation of the approach was delayed. 

In July 2005 a start was made with the implementation. In the third draft of this report [7] the new approach 

was described and results of first calculations were given for Task-22 tests GC100, GC120, GC125 and 

GC125FF. Based on these results it was decided to continue with the implementation of ISO 13370 in 

VA114. 

In September 2005, the work was continued: 

- a spreadsheet was developed that calculates the fixed heat loss component based on ISO 13370 

for the given configuration (for the slab-on-grade cases) 
180 

- this fixed component was put into the source of VA114 

- the Task-22 Ground Coupling tests (Slab-on-grade cases GC100, GC120, GC125, GC125FF, 

GC160 and GC180) were carried out 

Draft 4 of the report [8] describes the new model and gives the results. Very encouraging. 

In December 2005, the following work was done: 

- The IEA Task-22 Ground Coupling tests for Slab-on-Grade were redone. 

- The IEA 34/43 In-Depth Diagnostic Cases for the slab-on-grade (b-series) were done. 

- Spreadsheets were developed for the other configurations: suspended floor, heated basement 

and unheated basement. 

Remark about suspended floor and basements: Output of ISO 13370 is an overall heat loss value in W per 

m2

 of floor area; implementation of suspended floor and basement in VA114 requires a separation of this 

heat loss in two parts: heat loss through ground coupled floor and heat loss through ground coupled 

sidewalls. Both this separation in the spread sheet program and the implementation in VA114 are not yet 

done. 

 

Draft 5 of the report [10] gives the results. 

In ISO 13370 the Deep Ground Boundary Depth (E) is assumed to be infinite. In the In-Depth Diagnostic 

Cases this is not always the case. Now it was studied to take the Deep Ground Boundary Depth (E) into 

account by ground water table depth and by an infinite ground water flow. 

The In-Depth Diagnostic Cases were carried out: some of the b-series were redone, the c-series are done. 

The results are very promising. 

 

In this report (draft 6 and 7) the results of this work are given. 

2. Model description

The previous version of VA114 modeled ground heat transfer in a very simple way: 

- One-dimensional heat transfer through a ‘construction’ with at maximum 10 layers. 

- At the top this ‘construction’ is bounded to the building zone, at the bottom it is bounded to 

a constant temperature. 

- At the top of this ‘construction’ heat transfer takes place by convection, radiation, 

absorption of solar radiation; at the bottom of this construction heat transfer is modeled by a 

user given heat transfer coefficient to a constant, user given, temperature. 

Because of the IEA-Task-22 tests the ground heat transfer was modeled in more detail with VA114 by 

describing the underground by one or more ‘zones’. By this way in 2002 the Ground Coupling test cases 

were carried out. 

The results showed, that the VA114 approach gave low heat losses to the underground. 

In 2002 it was proposed to follow the approach of ISO 13370. The ground heat flow rate according to ISO 

13370 is treated as consisting of two components (see Annex E): 

- A fixed component representing the average heat flow rate through the ground 

- A varying component representing the variations in the ground heat flow rate about the average 

value. 
181 

The fixed component is obtained using the methods in standard ISO 13370. This component is calculated 

including any insulation of the floor in the determination of the heat transfer coefficients. Calculated is the 

total heat flow over the whole floor area. The heat flux density varies over the area of the floor, but an 

average value is used in the equations written. 

The varying component is obtained using the following assumptions and boundary conditions: 

- The dynamic heat flow in the ground is assumed to be 1-D. 

- The floor construction together with the ground is modelled as a single component consisting 

of each layer in the floor construction plus 0,50*) m depth of ground. 

- An adiabatic boundary is taken in the ground at a depth of 0,50*) m. 

*) ISO 13370 prescribes 1 m, but in later discussions 0,50 m was proposed.

The varying component is modelled in VA114 in the same way as other constructions (wall, roof, ...) are 

modelled, so no specific treatment. 

In CEN/TC 89 WG6 a modification on this approach was proposed and is under development now. When 

crystallized out this modification can be taken over. 

Before starting the development of a module to calculated the fixed component according to ISO 13370 an 

exploratory study was done with VA114: 

- The fixed component was user given. 

- The varying component was modelled as mentioned above. 

Results of this exploratory study were presented in third draft of this report - paragraph 7 [7]. Based on this 

results it was decided to continue with the implementation of ISO 13370 in VA114. 

In September 2005 the work was continued: 

ÎA spreadsheet was developed that calculates the fixed heat loss component based on ISO 13370 for the 

given configuration (for slab-on-grade). The fixed heat loss is expressed in three terms: 

 Q”(M) = Q”Average – Q”Ti*Cos(argTi(time of the year)) + Q”Te*Cos(argTe(time of the year)) 

- Q” (M) is the average rate of heat flow in month M 

- The first term contains the annual average indoor (internal) temperature and the annual average 

ambient (external) temperature. 

- The second term takes into account the amplitude of the variation of the internal temperature 

(the monthly average) about the average value 

- The third term does the same for the external temperature 

- Arg Ti and Arg Te contain the month number M and a delay in time (Tau-Alfa) and (Tau+Beta). 

ArgTi (time of the year) = 2*π*(M-Tau+Alfa)/12 

ArgTe (time of the year) = 2*π*(M-Tau-Beta)/12 

M = number of month of the year (M = 1 = January) 

So the Q”(M) changes per month, so every change of month a step change in this fixed component occurs. 
182 

VABI replaced in above equation the Month number of the year (M) by the Day number of the year (Iday) 

to get a smooth transition between this ISO-method (spreadsheet with monthly results) and the dynamic 

simulation program VA114. 

ArgTi (time of the year) = 2*π*(Iday-Ndaygci)/365 

ArgTe (time of the year) = 2*π*(Iday-Ndaygce)/365 

Iday = number of day of the year (Iday = 1 = January 1) 

Ndaygci and Ndaygce contain information about the delay in time. 

The spread sheet program has the constants Q”Average , Q”Ti , Q”Te, Ndaygci and Ndaygce as output 

Î the above shown formula (with given constants) was put into the source of VA114; the constants Q”Average

 , Q”Ti , Q”Te, Ndaygci and Ndaygce are input parameters for VA114 (later on a separate module, as part of 

VA114, will be developed that deliver these constants) 

Î the IEATask-22 Ground Coupling tests for Slab-on-Grade (GC100, GC120, GC125, GC125FF, GC160 

and GC180) were carried out. Each test has its specific constants. 

For the September 2005 results see draft 4 of this report [8] 

In December 2005, the following work was done: 

- The IEA Task-22 Ground Coupling tests for Slab-on-Grade were redone (because of an error in 

the spreadsheet for slab-on-grade). 

- The IEA-34/43 In-Depth Diagnostic Cases for the slab-on-grade (b-series) were done. 

- Spreadsheets were developed for the other configurations: suspended floor, heated basement 

and unheated basement. ISO-13370 heat loss is per m2

 of floor area; implementation in VA114 

requires a separation between heat loss through ground coupled floor and heat loss through 

ground coupled side-walls. This separation in the spread sheet and the implementation in 

VA114 is not yet done. 

 

The belonging results are given in draft 5 of this report [10]. 

In ISO 13370 the Deep Ground Boundary Depth (E) is assumed to be infinite. In the In-Depth Diagnostic 

Cases this is not always the case. Now it was studied to take the Deep Ground Boundary Depth (E) into 

account by ground water table depth and by an infinite ground water flow. 

In appendix H of ISO 13370 it is noticed, the effect of flowing ground water can be assessed by multiplying 

the steady-state heat flow rate by a factor Gw. This factor Gw is depending on 3 dimensionless ratios: 

- Zw/B’ 

- L/B’ 

- Dt/B’ 
183 

With 

- B’ = characteristic dimension of the floor 

- Zw = the depth of the water table 

- L = proportional to 1/ground water velocity 

- Dt = total equivalent thickness of the floor 

Appendix H of ISO 13370 gives values for the factor Gw as function of these 3 dimensionless ratios. 

However, the tables are far from user friendly. By interpolation and extrapolation of the values in these 

tables VABI made new, more user friendly tables. In Figure 2F-1 these tables are given. Yellow (shaded) 

cells contain the values from the ISO 13370, the other values were obtained by interpolation and 

extrapolation. 

The IEA-34/43 In-Depth Diagnostic Cases were carried out: some of the b-series were re-done (GC50b and 

GC55b), the c-series are done. The results are very promising. 

The belonging test results are given in Section 7 of this report 

Figure 2F-1: Factor Gw for ground water flow 
184 

3. Modeling Assumptions 

The IEA BESTEST Ground-Coupled Cases [4] and the IEA BESTEST In-Depth Diagnostic Cases for 

Ground-Coupled Heat Transfer related to Slab-on-Grade Construction [9,11] were both implemented. In this 

chapter information about the modeling assumptions are given. 

3.1 Weather 

The TMY2-weather files were made ready. No problems occurred. 

3.2 Soil 

Input as described. 

3.3 Boundary Conditions 

The floor construction together with the ground is modelled as a single component consisting of each layer 

in the floor construction plus 0,50 m depth of ground; an adiabatic boundary is taken in the ground at a depth 

of 0,50 m. 

The fixed component Q” describing the average heat loss to the underground was put at the bottom of the 

above described construction (as a kind of heat sink). 

Remark: putting this fixed component at the top of the construction doesn’t have a big influence 

 Zone 

------------------------------------------- 

 Floor 

------------------------------------------- 

 ^ 

 Soil | 0,50 m 

 | 

 Q” v 

------*-------------------.---------------- 

 | 

 | | hground = 0,0 W/(m2

.K) 

 | 

 . 

 Tground = 10,0 oC 

Figure 2F-2: Boundary condition to the ground 

The varying component is modelled in VA114 as a construction: bounded at the top to the zone (with all its 

processes) and at the bottom to Tground (in this specific case hground = 0,0 W/(m2

.K) ).

 

For the IEA-test cases the floor has the same properties as the soil. Floor thickness is assumed to be very 

small (0,001 m), so negligible with respect to the 0,50 m of soil. 

3.4 Initial conditions 

Initialization period is standard 42 days. The calculation need no longer initialization period than this 42 

days because only the capacity of the 0,5 m soil below the floor is taken into account. 
185 

3.5 Windows 

Input as described (Task 22 cases only). 

3.6 Solar Absorptivity 

Input as described. 

Remark: In case the prescribed internal solar absorptivity = 0,0, a minimum value of 0,01 was taken. For 

external solar absorptivity = 0,0 is no problem. 

3.7 Infrared Emissivity 

Input as described. 

Remark: In case the prescribed internal infrared emissivity = 0,0, a minimum value of 0,01 was taken.(0,06 

W/m2

K). For external infrared emissivity 0,0 is no problem. 

3.8 Exterior Radiative and Convective Surface Coefficients 

Separate coefficients are used. The radiative surface coefficient is calculated, the convective surface 

coefficient is constant. See Table 2F-1. 

3.9 Interior Radiative and Convective Surface Coefficients 

Separate coefficients are used. The radiative surface coefficient is calculated, the convective surface 

coefficient is constant. See Table 2F-1. For horizontal surfaces the convective surface coefficient is the 

same as for vertical surfaces. 

Table 2F-1: Surface Coefficients 

IEA-Bestest Cases IR Convective Total 

W/m2K W/m2K W/m2K 

IEA-22 GC-Cases Exterior for wall 5,00 24,3 29,3 

Exterior for window 5,00 16,0 21,0 

Interior for wall and window 5,00 3,16 8,16 

IEA-34/43 “b”-series cases Exterior for soil surface 0,00 100,0 100,0 

 0,00 11,95 11,95 

Interior for slab surface 0,06 99,94 100,0 

 0,06 7,89 7,95 

IEA-34/43 “c”-series cases Exterior for soil surface 0,00 5000,0 5000,0 

Interior for slab surface 0,06 7,89 7,95 

3.10 Interior Solar Distribution (Task-22 cases only) 

The interior solar distribution is calculated. Short wave absorptivity is as prescribed. Separate treatment for 

direct solar radiation and for diffuse/reflected solar radiation. 

3.11 Mechanical System 

The mechanical supply of fresh air is 0,0 m3/h. The heating and cooling to the zone is provided by local 

devices. These local devices have a capacity of 100 kW. For the IEA-22 cases, the set points are 23°C for 

heating and 25°C for cooling; for the IEA-34/43 cases, the heating set point is 30°C and there is no cooling. 
186 

3.12 Infiltration 

The infiltration is 0,0. 

3.13 Internal Loads 

The internal loads is 0,0 W. 

3.14 Above Grade Construction 

Input as described. 

3.15 Slab-on-Grade Cases 

The ISO 13370 approach was followed. 

Remark: the Deep Ground Boundary Depth (E) was simulated by ground water table depth and by an 

infinite ground water flow rate. 

3.16 Basement Cases (IEA-22 cases only) 

ISO 13370 approach was followed. 

Remark: Output of ISO 13370 is heat loss per m2

 of floor area. A distinction should be made between 

heat loss through ground coupled floor and heat loss through ground coupled side-walls. This separation 

is not yet made in the spread sheet program and is not yet implemented in VA114. 

3.17 Walkout Basement Case (IEA-22 cases only) 

ISO 13370 approach was followed. See remark under Basement Cases 

4. Modeling Options

For this IEA-34/43 work there is the option to have the fixed component attack in two places at the varying 

component (= floor construction together with 0,5 m of ground): 

- at the top of that construction 

- at the bottom of that construction 

It was decided to have it attack at the bottom. The influence is very small (see draft 3 of this report - 7). 

At the moment only Slab-on-Grade cases are possible; in future cases with suspended floor and cases with 

basement will be possible. The ISO 13370 spread sheet for these cases are available, but for simulation by 

VA114 it is necessary to make a separation between the floor to ground part and the sidewalls to ground 

part. Both parts are modeled as separate constructions in VA114. The output of the spreadsheet will concern 

the relevant constants both for the floor to ground part and the sidewalls to ground part. This double number 

of constants have to be put as input to VA114. 

5. Modeling Difficulties

See the remark about suspended floor and basements under section 1. 

6. Software Errors Discovered and/or Comparison between Different Versions of the Same 

Software 

In preliminary work during IEA SHC Task 22 [4], results for the Task 22 cases using VA114’s 1-D 

conduction model indicated low heating loads compared with other programs; see Figure 2F-3a. Based on 

these results, VABI decided to explore implementing the ISO-13370 ground heat transfer model into 

VA114. Figure 2F-3b shows VA114 annual heating load results versus results of other models before and 
187 

after initial implementation of ISO 13370 [13,14], which indicates improved agreement (see results 

labeled “VA114-ISO13370 (2005)” versus results labeled “VA114/VABI (2002)”). 

IEA BESTEST Ground Coupling

Heating Loads

0

2

4

6

8

10

12

14

16

18

GC100: Pure Slab

GC180: Pure Slab, 12x16

GC180-100: Slab Area

GC200: Pure Bsmt.

GC100: Pure Slab

GC180: Pure Slab, 12x16

GC180-100: Slab Area

GC200: Pure Bsmt.

HOT3000

Annual Heating Load (MWh) Peak Heating Load * 5 (kW)

SUNREL VA114 EnergyPlus

Figure 2F-3a. Task 22 heating loads, from September 2003 IEA-34/43 Zurich meeting presentation 

IEA BESTEST: Task 22 Preliminary Ground Coupling 

Annual Heating Loads

0

2

4

6

8

10

12

14

16

18

GC100: Pure Slab GC180: Pure Slab, 12x16 GC180-100: Slab Area

Sensitivity

Annual Load (MWh)

HOT3000-BASESIMP/NRCan (2002) SUNREL-GC/NREL (2002)

EnergyPlus/GARD (2003) VA114/VABI (2002)

VA114-ISO13370/VABI (2005)

Figure 2F-3b. IEA SHC Task-22 test results for VA114 versus other models, before (“VA114/VABI 

(2002)”) and after (“VA114-ISO13370/VABI (2005)”) preliminary adaptation of the ISO-13370 

European standard ground heat transfer calculation method with VA114. 
188 

The initial implementation of ISO-13370 with VA114 was also tested using the IEA-34/43 test cases (see 

Figure 2F-4). Except for cases GC50b and GC55b, good agreement is indicated for VA114/ISO 13370 

versus the TRNSYS and SUNREL-GC detailed 3-D numerical-methods models. The largest disagreement 

is for Case GC55b, which has shallow water table depth; Case GC50b is for large slab with no change in 

modeled soil depth versus GC40b, so in GC50b water-table depth also becomes somewhat shallow 

relative to the slab surface area. The initial implementation of ISO 13370 in VA114 did not include ISO 

13370’s model for water table depth sensitivity. Based on these results, the ISO-13370 shallow water 

table depth model was implemented; improved agreement resulting from this implementation is shown in 

Figure 2F-5. 

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Floor Conduction

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

GC40a,

ideal films

GC40b,

h=100

GC45b,

AR=36x4

GC50b,

large

slab/10

GC55b, 

2m depth

GC70b,

hint=7.95,

hext=11.95

GC80b,

k=0.5

GC40c,

hint=7.95,

hext=ideal

GC45c,

AR=36x4

GC55c, 

5m depth

GC80c,

k=0.85

Floor Heat Flow (kWh)

TRNSYS-ind/TESS

VA114/ISO13370 disagreeing 

for GC50b and GC55b 

GHT/NREL SUNREL/NREL

FLUENT/Nakhi Eplus/GARD VA114-ISO13370/VABI

ESP-r/NRCan BASECALC/NRCan

Figure 2F-4. Steady-Periodic Annual Floor Conduction, from April 2006 Iowa Meeting Presentation
189 

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Floor Conduction

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

GC40a,

ideal films

GC40b,

h=100

GC45b,

AR=36x4

GC50b,

large

slab/10

GC55b, 

2m depth

GC70b,

hint=7.95,

hext=11.95

GC80b,

k=0.5

GC40c,

hint=7.95,

hext=ideal

GC45c,

AR=36x4

GC55c, 

5m depth

GC80c,

k=0.85

Floor Heat Flow (kWh)

TRNSYS-ind/TESS

VA114/ISO13370, water table 

depth sensitivity model included 

GHT/NREL SUNREL/NREL

FLUENT/PAAET Eplus/GARD VA114-ISO13370/VABI

ESP-r/NRCan BASECALC/NRCan

Figure 2F-5. Steady-Periodic Annual Floor Conduction, from October 24, 2006 

7. Results

Results of earlier steps can be found in draft 3 [7] and draft 4 [8] of this report. Now results of the December 

2005 and May 2006 work are presented. 

For each configuration (slab on grade, suspended floor, heated basement and unheated basement) a separate 

spreadsheet was developed that calculates the fixed heat loss component based on ISO 13370. 

The heat loss is expressed in 3 terms (see section 2): 

 Q” = Q”Average – Q”Ti*Cos(argTi (time of the year)) + Q”Te*Cos(arg Te (time of the year)) 

With 

ArgTi (time of the year) = 2*π*(Iday-Ndaygci)/365 

ArgTe (time of the year) = 2*π*(Iday-Ndaygce)/365 

Iday = number of day of the year (Iday = 1 = January 1) 

Each spreadsheet program has the constants Q”Average , Q”Ti , Q”Te, Ndaygci, and Ndaygce as output 

The above shown formula (with given constants) is present in the source of VA114; the constants are input 

values for VA114. 
190 

A. IEA BESTEST GC Cases (test GC100-GC235) 

Table 2F-2 gives the constants for the several test cases 

Table 2F-2: Constants for the IEA BESTEST GC Cases

Test case Q”Average Q”Ti Q”Te Nday,gci Nday,gce

GC100 11,16 0,0 7,61 -20 54 

GC120 11,16 0,0 7,61 -20 54 

GC125-1 12,01 0,71 7,61 -20 54 

GC125-2 12,01 0,0 7,61 -20 54 

GC125FF-1 12,01 0,71 7,61 -20 54 

GC125FF-2 12,01 6,0* 7,61 -20 54 

GC160 7,98 0,71 5,21 -20 54 

GC180 7,12 0,0 3,81 -20 54 

GC190 7,12 0,0 3,81 -20 54 

GC200 29,46 0,0 11,46 -18 55 

GC260 17,17 0,0 6,04 0 68 

Remarks: 

- GC100, GC120 and GC180 have only a heating demand, so internal temperature is always the heating set point (= 23o

C). 

So term Q”Ti = 0,0; term Q”Average is based on average internal temperature of 23o

C 

- GC125 and GC160 have both a heating demand and a cooling demand, so internal temperature swings between both set 

points (23o

C in winter and 25oC in summer); term Q”Ti is based on an amplitude of 1 K; term Q”Ais based on average 

internal temperature of 24o

C. GC125-1 has in winter time 23oC and in summer time 25oC; GC125-2 has both in winter and 

summer time temperatures between 23o

C and 25oC 

- GC125FF has an unknown internal temperature. First calculations with the above constants (GC125FF-1) gave the order in 

which the internal temperature (monthly average) swings: the annual average was in the same order as the other cases 

(24°C), the annual swing in monthly averages was much larger than 1 K (order 6-10 KÎ Q”Ti = 6,0 is a better number – 

GC125FF-2), the minimum temperature was not in month 1 (January) but in month 4 (April). 

- GC200 and GC260 (Basement Cases) are in W/m2 of floor area; a separation should be made between heat loss through 

floor and heat loss through sidewalls. Implementation in VA114 was not yet done. So no annual results for these cases.

The results are given in GCResults-IEA22-20051223.XLS (see appendix B1 of this modeler report). 

Imported in spreadsheet GCResults-IEA22-0403plotted20051223.XLS it can be seen the results of VA114 

are much more close to the other programs. In appendix B1 some figures are given too. 

Remark: 

The results for GC125FF are for the constants given in Table 2F-2 (first estimate Q”Ti = 0,71): actual internal temperature is 6°-55 o

C. With a better estimate based on the first run results of the internal temperature the temperature range becomes 3°–53oC. So there 

is a strong interaction between internal temperature and ground heat loss; an iterative calculation procedure seems to be necessary. 
191 

B. IEA BESTEST GC Diagnostic Cases for slab-on-grade (B-series) 

Table 2F-3 gives the constants for the several test cases: 

Table 2F-3: Constants for the IEA BESTEST GC Diagnostic Cases for Slab On Grade 

Test case Q”Average Q”Ti Q”Te Nday,gci Nday,gce

GC30b 16,81 0,00 0,00 -25 51 

GC40b 16,81 0,00 3,32 -25 51 

GC45b 24,46 0,00 5,53 -25 51 

GC50b 5,17 0,00 0,50 -25 51 

GC55b 25,05 0,00 3,32 -25 51 

GC60b 14,37 0,00 0,00 -22 53 

GC65b 13,33 0,00 0,00 -20 54 

GC70b 13,33 0,00 2,31 -20 54 

GC80b 4,54 0,00 0,69 -22 59 

Remarks: 

- The ISO 13370 works with infinite “Deep Ground Boundary Depth (E)” and infinite “Far Field Boundary Distance (F)”; a 

“Deep Ground Temperature (TDG)” is not required. So different from the required input. 

- The Deep Ground Boundary Depth (E) was simulated by ground water table depth and an infinite ground water flow rate. 

For most cases the influence of that boundary was very small (factor Gw < 1,01) and neglected (Gw = 1,00); only for 

GC50b (Gw = 1,40) and GC55b (Gw = 1,49) the influence of that boundary is present and rather big (40%-49% extra 

losses). 

The results are given in GC-InDepth-Out-0505-20060509.XLS (see appendix B2 of this modeler report). 

C. IEA BESTEST GC Diagnostic Cases for slab on grade (C-series) 
192 

Table 2F-4 gives the constants for the several test cases: 

Table 2F-4: Constants for the IEA BESTEST GC Diagnostic Cases for Slab On Grade 

Test case Q”Average Q”Ti Q”Te Nday,gci Nday,gce

GC30c 14,53 0,00 0,00 -22 53 

GC40c 14,53 0,00 2,64 -22 53 

GC45c 20,64 0,00 4,41 -22 53 

GC55c 15,99 0,00 2,64 -22 53 

GC80c 7,11 0,00 1,14 -21 57 

Remarks: 

- The ISO 13370 works with infinite “Deep Ground Boundary Depth (E)” and infinite “Far Field Boundary Distance 

(F)”; a “Deep Ground Temperature (TDG)” is not required. So different from the required input. 

- The Deep Ground Boundary Depth (E) was simulated by ground water table depth and an infinite ground water flow 

rate. For most cases the influence of that boundary was a very small (factor Gw < 1,01) and neglected (Gw = 1,00); 

only for GC55c (Gw = 1,10). The influence of that boundary is present and gives about 10% extra losses . 

The results are given in GC-InDepth-Out-0505-20060509.XLS (see appendix B2 of this modeler report). 

8. Other (optional) 

 

[Editor’s note: no comments were provided here by VABI.] 

9. Conclusions and Recommendations 

VA114 uses ISO 13370 to describe the heat losses to the ground. At the moment the calculation is still 

decoupled: 

- Spreadsheet programs calculate the characteristic heat losses for a specific GC-configuration 

- These characteristic heat losses are fed to VA114 as input. 

In this way reasonable agreement is obtained with the results of other programs. 

Spreadsheets are available for slab, suspended floor, heated and unheated basement. The above mentioned 

decoupled procedure works for slab. For suspended floor and basements a split have to be made between 

heat loss through ground coupled floor and heat loss through ground coupled side walls. This step is not 

made yet both in the ISO 13370 spread sheet program; also the implementation in VA114 is not yet done. 

The final step will be the development of a module, that can be coupled to VA114. In that way the 

calculation can be done fully integrated. 

10. References

 

[1] Judkoff, R and Neymark, J 

 “International Energy Agency Building Energy Simulation Test (BESTEST) and Diagnostic 

Method”, IEA: SHC Task 12/ECBCS Annex 21, February 1995. 

[2] Soethout, L. L. 

“BESTEST Kwalificatietesten uitgevoerd aan het gebouwsimulatieprogramma VA114, 

versienummer 1.35”. TNO-rapport 98-BBI-R0830, mei 1998. 
193 

[3] Wijsman, A.J.Th.M.; Plokker, W. 

“Eerste thermische gebouwsimulatieprogramma’s ondergingen de keurmerktest”. 

TVVL Magazine, augustus 1999. 

[4] Deru, M., Judkoff, R. and Neymark, J. 

“Proposed IEA BESTEST Ground-Coupled Cases”, IEA: SHC Task 22, July 22, 2002. 

[5] Wijsman, A. and Maassen, W. 

“Ground Coupling Modeler Report – TNO – Draft 2”, IEA: SHC Task 22, November 2002. 

[6] ISO 13370:1998(E) 

“Thermal performance of buildings – Heat transfer via the ground – Calculation methods” 

[7] Wijsman, A. 

“Ground Coupling Modeler Report –VABI – Draft 3”, IEA: SHC Task 34/ECBCS Annex 43, 

July 18 2005. 

[8] Wijsman, A. 

“Ground Coupling Modeler Report –VABI – Draft 4”, IEA: SHC Task 34/ECBCS Annex 43, 

September 9, 2005. 

[9] Neymark, J. and Judkoff, R. 

“Proposed IEA BESTEST In-Depth Diagnostic Cases for Ground-Coupled Heat Transfer Related 

to Slab-on-Grade Construction”, IEA: SHC Task 34/ECBCS Annex 43, June 2005. 

[10] Wijsman, A. 

“Ground Coupling Modeler Report –VABI – Draft 5”, IEA: SHC Task 34/ECBCS Annex 43, 

December 23, 2005. 

[11] Neymark, J. and Judkoff, R. 

“Proposed IEA BESTEST In-Depth Diagnostic Cases for Ground-Coupled Heat Transfer Related to 

Slab-on-Grade Construction”, IEA: SHC Task 34/ECBCS Annex 43, March 2006. 

[12] Wijsman, A. 

“Ground Coupling Modeler Report –VABI – Draft 6”, IEA: SHC Task 34/ECBCS Annex 43, May 9, 

2006. 

[13] Neymark, J. 

“IEA BESTEST Ground Coupling Project Plan Review”. Presented at IEA SHC Task 34 

Meeting, Duebendorf, Switzerland, September 29, 2003. See “GC-Task22-Results091903-

revVABI090607.XLS”. 

[14] Wijsman, A. 

“VA114 Ground Coupling”. Presented at IEA Meeting of IEA SHC Task 34/ECBCS Annex 43, 

Aalborg, Denmark, October 2005. See “Aalborg-Ground Coupling October 2005.ppt”. 
194 

Appendix A: Model Geometry and Thermal Property Allowed Inputs – VA114 
195 

Appendix B1: Results of VA114 for IEA BESTEST Task-22 Cases 

 – 23 December 2005 

See output spreadsheet for Ground Coupling cases: GCResults-IEA22-20051223.XLS. 

Remark: 

Imported in spreadsheet GCResults-IEA22-0403plotted20051223.XLS a comparison with results of other 

programs can be made; an example plot is included below. 

IEA BESTEST Ground Coupling

Heating Loads

0

2

4

6

8

10

12

14

16

18

GC100: Pure Slab

GC180: Pure Slab, 12x16

GC180-100: Slab Area

GC200: Pure Bsmt.

GC100: Pure Slab

GC180: Pure Slab, 12x16

GC180-100: Slab Area

GC200: Pure Bsmt.

HOT3000

Annual Heating Load (MWh) Peak Heating Load * 5 (kW)

SUNREL VA114 EPlus, hc=8.29, e=0
196 

Appendix B2: Results of VA114 for IEA BESTEST In-Depth Diagnostic Cases 

 – 09 May 2006 

Output spreadsheet for Ground Coupling InDepth Diagnostic cases: GC-InDepth-Out-0505-20060509.XLS. 

Remark: 

Imported in spreadsheet GC-Results040806+PeerRev-20060509.XLS a comparison with results of other 

programs can be made; an example plot is included below. 

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Floor Conduction

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

GC40a,

ideal films

GC40b,

h=100

GC45b,

AR=36x4

GC50b,

large

slab/10

GC55b, 

2m depth

GC70b,

hint=7.95,

hext=11.95

GC80b,

k=0.5

GC40c,

hint=7.95,

hext=ideal

GC45c,

AR=36x4

GC55c, 

5m depth

GC80c,

k=0.85

Floor Heat Flow (kWh)

TRNSYS-ind/TESS GHT/NREL SUNREL/NREL

FLUENT/Nakhi Eplus/GARD VA114-ISO13370/VABI

ESP-r/NRCan BASECALC/NRCan

[Editors note: updated final results comparisons are included in Part III of this report.]
197 

Appendix II-G 

Modeler Report for BESTEST Cases GC10a-GC80c 

SUNREL-GC Version 1.14.01 

by 

Michael Deru 

National Renewable Energy Laboratory 

United States 

 

January 2006

1. Introduction

This report documents the use of the SUNREL-GC version 1.14.01 building energy simulation program 

to perform detailed modeling of the new ground-coupling cases for IEA BESTEST. This is a special 

version of SUNREL coupled with a ground-coupled heat transfer program called GHT. GHT can be run 

independently or integrated with SUNREL. The work was completed at NREL, Golden, Colorado, US. 

GHT was created specifically for ground heat transfer and uses finite element analysis to model 2-D or 3-

D heat-conduction problems (Deru 2003). All analyses completed for this report used 3-D linear 

hexahedron elements. GHT uses an explicit solution method for the 3-D calculations, which reduces the 

storage requirements and avoids matrix inversions required for an implicit solution. The time step used in 

the explicit solution can be fixed at a even divisions or fixed at a set of variable divisions. For example, 

when the program is run with hourly data, the hour can be divided into even divisions of [editor’s note: 

remainder of sentence missing]. 

GHT allows many options for boundary conditions, including detailed atmospheric boundary conditions 

with convection, evapotranspiration, short-wave radiation, and long-wave radiation exchange with the 

environment; simple atmospheric boundary conditions with convection and short-wave radiation; mixed 

convection and heat flux, or defined temperature. A special boundary condition for GC10 was created to 

simulate the linear temperature variation across the wall. The convection and evapotranspiration models 

include the effects of the surface cover. The rate of evapotranspiration is taken as a user defined fraction 

of the potential value since the moisture at the ground surface is not known. The long-wave radiation 

model accounts for cloud cover as read from the weather file. The model does not account for shading or 

snow cover. 

In SUNREL-GC, GHT models the 3-D heat transfer in the ground and in the concrete floors in contact 

with the ground. Each hour SUNREL calls GHT with the new weather parameters, interior solar gains, 

and zone air temperature inputs. GHT uses this information to calculate the new surface temperatures for 

the hour, which are passed back to SUNREL. SUNREL then performs the energy balance on the zone air 

node on sub hourly time steps. 

2. Modeling Assumptions

In GC10, GHT cannot model a semi-infinite solid. A lower boundary must be chosen and a boundary 

condition applied to it. The temperature of the lower boundary was maintained at 10°C to match the 
198 

surface temperature, and the depth of the lower boundary was varied from 10 m to 25 m. The results of 

the varying the depth are presented in Section 5. Other modeling assumptions that differ from the case 

specifications are noted in the Sections 3 and 4. 

3. Modeling Options

 

All cases were modeled to the specifications execpt the walls and as noted in Section 4. The walls were 

modeled as massless with a thermal reistence of 10,000 m2

·K/W. This provides effectively adiabatic 

walls and roof. This was verified in the SUNREL output by zero heat flows through the walls. 

4. Modeling Difficulties

The most notable difficulty in modeling the cases was the inability to use extremely high convection heat 

transfer coefficients. High convection coefficients made the solution unstable and resulted in incorrect 

answers. The convection coefficients were limited to less than 120 W/m2

·K. The reason for this is 

unclear and requires further investigation. The interior convection heat transfer coefficient was set to 100 

W/m2

·K for cases GC30-GC55. The exterior convection heat transfer coefficient was calculated from the 

wind speed, ground roughness, and terrain. The ground roughness was adjusted to get a value of 117 

W/m2

·K for cases GC30-GC60. Previous experience with a 2-D finite element code suggests that using h 

= 100 W/m2

·K instead of h = 5000 W/m2·K can introduce an error of up to 3%. The interior coefficient 

was set to 1 W/m2

·K for GC60-GC70 and the outside coefficient was set to 17 for GC65-GC70. 

Cases GC45 and GC50 were not modeled due to insufficient time to generate the mesh and run the cases. 

GC50 will require a very large mesh and long simulation times. 

GHT does not allow for the calculation of temperatures that are not at nodal points; therefore, the surface 

temperature output requirements. Modifications to the program to calculate these temperatures were 

initiated but there was not enough time to complete the modifications. The work should be completed for 

any future rounds of simulations. 

5. Demonstration of Appropriate Level of Modeling Detail

Four meshes were created to explore the effects of the deep ground and the far-field boundaries. The 

meshes were labeled A-D. All the meshes only modeled one-fourth of the slab and soil. The meshes are 

summarized in Table 2G-1. The element sizes varied throughout the mesh with small elements at the 

surface and near the exterior walls. The size of the elements was based on previous experience. The 

depth of the first element at the surface was 3.5 cm and then expanded with depth. The dimensions of the 

elements in the X and Y directions varied similarly near the exterior walls. 

Table 2G-1 Mesh Dimensions used for GC10 

Mesh Deep Ground 

(m) 

Far-field 

(m) 

Nodes Elements 

A 10 10 19,456 17,298 

B 15 15 26,950 24,276 

C 20 15 30,625 27,744 

D 25 20 40,432 36,963 
199 

The total floor heat loss for each of the meshes is shown in Figure 2G-1 for case GC10. The figure also 

shows the difference in the annual heat loss compared to mesh D. The difference between meshes C and 

D is less than 0.1% through year 6, but it continues to rise slowly and would exceed 0.1% in year 7. The 

other comparison to make is from year to year with the same mesh. Looking at the heat transfer for the 

last hour of one year to the last hour of the previous year, both meshes C and D are less than 0.1% in year 

5. From these results mesh C was selected to use with the remaining runs. The simulations times for all 

the runs was approximately one hour per year of simulation on a 3 GHz personal computer. 

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Year 1 Year 2 Year 3 Year 4 Year 5 Year 6

Year of Simulation

Floor Heat Loss (GJ)

0.0%

0.1%

0.2%

0.3%

0.4%

0.5%

0.6%

0.7%

0.8%

0.9%

1.0%

Percent Difference From D

A

B

C

D

D-A

D-B

D-C

Figure 2G-1 Total floor heat loss for GC10 and comparison with mesh D 

6. Software Errors Discovered, and/or Comparison Between Different Versions of the Same 

Software, and/or Lessons Learned Regarding Use of Detailed Models

7. Results

8. Other (optional) 

9. Conclusions and Recommendations

10. References

Deru, M. (2003). A Model for Ground-Coupled Heat and Moisture Transfer From Buildings. NREL/TP550-33954. Golden, CO: National Renewable Energy Laboratory. 

Deru, M., R. Judkoff, and J. Neymark. (2003). “Whole-Building Energy Simulation with a ThreeDimensional Ground-Coupled Heat Transfer Model,” NREL/CP-550-32690. presented at the ASHRAE 

Winter Meeting January 25-29, 2003.
200 

Appendix A: Model Geometry and Thermal Property Allowed Inputs 

Model Geometry and Thermal Property Allowed Inputs (pro forma)

Model and Version:

Horizontal Vertical Vertical

Foundation Above Grade Edge Interior Edge Exterior Edge

Slab Wall Footer Soil Sill Plate Wall Insulation Insulation Insulation

GEOMETRY*

Floor Slab In (below) Grade ("yes" or "no") Yes n/a n/a n/a n/a n/a n/a n/a n/a

Floor Slab On (above) Grade ("yes" or "no") Yes n/a n/a n/a n/a n/a n/a n/a n/a

Floor Slab Minimum Thickness (cm) See note 1 n/a n/a n/a n/a n/a n/a n/a n/a

Floor Slab Maximum Thickness (cm) unlimited n/a n/a n/a n/a n/a n/a n/a n/a

Minimum x- Thickness or Width (cm) n/a See note 1 See note 1 n/a See note 2 See note 2 unlimited unlimited unlimited

Maximum x -Thickness or Width (cm) n/a unlimited unlimited n/a See note 2 See note 2 unlimited unlimited unlimited

Minimum z -Thickness (cm) n/a n/a unlimited n/a See note 2 n/a unlimited n/a n/a

Maximum z -Thickness (cm) n/a n/a unlimited n/a See note 2 n/a unlimited n/a n/a

Minimum Bottom-Edge Depth Below Grade (z , cm) unlimited unlimited unlimited n/a n/a n/a n/a unlimited unlimited

Maximum Bottom-Edge Depth Below Grade (z , cm) unlimited unlimited unlimited n/a n/a n/a n/a unlimited unlimited

Minimum Top-Edge Height Above Grade (z , cm) unlimited unlimited n/a n/a n/a n/a n/a unlimited unlimited

Maximum Top-Edge Height Above Grade (z , cm) unlimited unlimited n/a n/a n/a n/a n/a unlimited unlimited

Minimum Soil Depth (E, m) n/a n/a n/a unlimited n/a n/a n/a n/a n/a

Maximum Soil Depth (E, m) n/a n/a n/a unlimited n/a n/a n/a n/a n/a

Minimum Soil Far-Field Distance (F, m) n/a n/a n/a unlimited n/a n/a n/a n/a n/a

Maximum Soil Far-Field Distance (F, m) n/a n/a n/a unlimited n/a n/a n/a n/a n/a

THERMAL PROPERTIES*

Minimum Conductivity (W/(mK)) See note 3 See note 3 See note 3 See note 3 See note 3 See note 3 See note 3 See note 3 See note 3

Maximum Conductivity (W/(mK)) See note 3 See note 3 See note 3 See note 3 See note 3 See note 3 See note 3 See note 3 See note 3

Minimum R-Value (m2

K/W)) **   **  See note 3 See note 3 See note 3 See note 3 See note 3

Maximum R-Value (m2

K/W)) **   **  See note 3 See note 3 See note 3 See note 3 See note 3

Minimum Density (kg/m3

) See note 3 See note 3 See note 3 See note 3 See note 3 See note 3 See note 3 See note 3 See note 3

Maximum Density (kg/m3

) See note 3 See note 3 See note 3 See note 3 See note 3 See note 3 See note 3 See note 3 See note 3

Minimum Specific Heat (kJ/(kgK)) See note 3 See note 3 See note 3 See note 3 See note 3 See note 3 See note 3 See note 3 See note 3

Maximum Specific Heat (kJ/(kgK)) See note 3 See note 3 See note 3 See note 3 See note 3 See note 3 See note 3 See note 3 See note 3

COMMENTS

Uninsulated detail (Figure A-1) ok? ("yes" or "no") no

Insulated detail (Figure A-2) ok? ("yes" or "no") no

If no, include additional assumptions of your model The slab may or may not have half its thickness above grade and half below grade.

not covered here (add rows as needed)

Include other clarfications and/or comments here

(add rows as needed)

NOTES

"n/a": not applicable

* If a listed input does not apply to your model, enter "0" in the relevant cells.

** For below grade high-mass components, only list R-value input limits if there is some difference versus what would be calculated based on listed 

 conductivity and thickness limits

SUNREL-GC 1.14-02 Insulation Components 

Below-Grade High-Mass Components Low-Mass Components

1 - There is no "minimum" thickness; however, thin highly conductive materials may introduce 

instabilities in the solution. Modeling thin layers depends on the thickness and thermal diffusivity of the 

material.

2 - The low mass components are modeled with a 1-D FDM model that does not have hard limits on 

thickness; however, the same restrictions apply as in note 1 for thin layers.

3 - The 3-D and the 1-D models in SUNREL-GC do not have any hard limits on thermal properties or 

thicknesses; however, values that are extreme can introduce instabilities in the solution or cause very 

long solution times.
3.0 Part III: Simulation Field Trial Results 

3.1 Introduction 

Here we present the simulation results for the field trials of cases GC10a-GC80c; see Section 3.4 for 

graphs and tables. These are results after numerous iterations to incorporate clarifications to the test 

specification, simulation input deck corrections, and simulation software improvements. Where 

improvements to simulation programs or simulation inputs were made as a result of running the 

tests, such improvements must have mathematical and physical bases and must be applied 

consistently across tests. Also, all improvements were required to be documented in modeler 

reports. Arbitrary modification of a simulation program’s input or internal code just for the 

purpose of more closely matching a given set of results is not allowed. The diagnostic process of 

trapping bugs discussed in Section 2.4 of Part II also isolated input errors that were corrected, as 

noted there and in the modeler reports (Part II, Section 2.9). 

Table 3-1 summarizes the following information for the nine models and the Case GC10a 

analytical solution that were implemented by the nine organizations that participated in this 

project: model-authoring organization, model testing organization (“Implemented by”), and 

abbreviation labels used in the results graphs and tables. 

3.2 Zone Heating Load versus Floor Conduction Results 

Heat conducted through the floor slab should be equal to the zone-heating load because the test 

cases specify adiabatic above-grade walls and ceiling such that heating zone air to maintain the 

thermostat set point drives all heat losses through the floor. The verified numerical models (quasianalytical solutions) were run independently of whole-building energy simulation models, where 

for the “b”-series and “c”-series cases the zone air temperature is input to those models as an 

inside boundary condition for an interior convective surface coefficient (thermal resistance 

between the zone air and floor slab surface). Therefore, verified numerical-model results are 

included with the floor conduction results only. However, for whole-building simulation 

programs that do not disaggregate floor conduction in their output, the zone heating load results 

are directly comparable to the floor conduction results. Minor differences in zone heating load 

versus floor conduction may occur if a simulation program cannot model strictly adiabatic abovegrade walls and ceilings, but rather is applying the lowest thermal conductance the simulation 

allows. 

3.3 Multi-Year Versus Single-Year Simulation Runs 

Because of the large thermal mass of the ground adjacent to the floor slab, ground-coupled heat 

transfer calculations have a large time constant. The modeler reports for the detailed numerical 

models used as a secondary mathematical truth standard (see Part II, Section 2.9, Appendices IIA, II-B, and II-C) indicate 2%–17% reduction of heat transfer for the second versus first year of 

simulation, 0.7%–1.1% reduction for the third versus second year, 0.4% reduction for the fourth 

versus third year, and so forth. Differences in definition of initial conditions within the ground by 

the modelers may be the primary cause of variation in the first years of simulation. A groundcoupled heat transfer modeling method that applies a single-year simulation run is likely to 

produce results more quickly (with less computer processing time), and may be more easily 

adaptable to a whole-building energy simulation program. However, such a model may be less 

accurate than a multi-year simulation if multi-year thermal capacitance effects or appropriate 

initial conditions within the ground are not considered. As required by the test specification, 

201 
results are given only for the final year simulated by a given model. Number of years simulated 

by the software tools for each test case is included within the following data tables. 

Table 3-1. Participating Organizations and Models 

Analytical Solution, 

Case GC10a Authoring Organization Implemented by Abbreviation 

Delsante, Stokes, and 

Walsh (1983) CSIRO,a

 Australia NREL/JNA, b,c United 

States 

Analytical 

Solution/CSIRO 

Verified Numerical 

Model Authoring Organization Implemented by Abbreviation 

FLUENT 6.0.20 Fluent, Incorporated, United 

States PAAET,d

 Kuwait FLUENT/PAAET 

MATLAB 7.0.4.365 

(R14) 

The Math Works, Inc., United 

States 

Dublin Institute of 

Technology, Ireland MATLAB/DIT 

TRNSYS 16.1 University of Wisconsin/TESS,e

United States TESS,e

 United States TRNSYS/TESS 

Simulation Program Authoring Organization Implemented by Abbreviation 

BASECALC V1.0e CETC,f

 Canada CETC,f Canada BASECALC/NRCan 

EnergyPlus 2.0.0.025 LBNL/UIUC/DOE-BT,g,h,i United 

States 

GARD Analytics, Inc., 

United States EnergyPlus/GARD 

ESP-r/BASESIMP CETC/ESRU,f,j Canada/United 

Kingdom CETC,f

 Canada ESP-rBASESIMP/NRCan 

GHT NREL,b

 United States NREL,b United States GHT/NREL 

SUNREL-GC 1.14.01 NREL,b

 United States NREL,b United States SUNREL-GC/NREL 

VA114 2.20/ISO-13370 VABI Software BV, The 

Netherlands; CEN/ISOk,l 

VABI Software BV, 

The Netherlands 

VA114/ISO13370/VABI 

a

CSIRO: Commonwealth Scientific and Industrial Research Organisation, Australia 

b

NREL: National Renewable Energy Laboratory, United States 

c

JNA: J. Neymark & Associates, United States 

d

PAAET: Public Authority for Applied Education and Training, Kuwait 

e

TESS: Thermal Energy Systems Specialists, United States 

f

CETC: CANMET Energy Technology Centre, Natural Resources Canada, Canada 

g

LBNL: Lawrence Berkeley National Laboratory, United States 

h

UIUC: University of Illinois Urbana/Champaign, United States i

DOE-BT: U.S. Department of Energy, Office of Building Technologies, Energy Efficiency and Renewable Energy, United 

States 

j

ESRU: Energy Systems Research Unit, University of Strathclyde, United Kingdom 

k

CEN: European Committee for Standardization, Belgium 

l

ISO: International Organization for Standardization, Switzerland 

202 
3.4 Results Graphs and Tables 

This section presents graphs of the results first, followed by tables of the results. Verified 

numerical-model results are shown in the bar charts with blue shaded background bars, and the 

analytical solution result (Case GC10a) is shown with a magenta background bar. The x-axis 

labels of the accompanying graphs include abbreviated descriptions of the test cases. See Section 

2.7 of Part II for definitions of the abbreviations and acronyms. Case descriptions are summarized 

in Tables 1-1 and 1-2 in Part I. The results tables include dates and hours of occurrences for 

hourly maxima and minima; times of occurrence are not indicated in the graphs depicting hourly 

maxima and minima. 

An electronic version of these results is included with the accompanying files in the file GCInDepth-Results.xls, with its navigation instructions included in GC-InDepth-Results.doc. 

203 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-State Floor Conduction

0

500

1000

1500

2000

2500

3000

GC10a 

linear dT

GC30a 

adiab. wall, 

ideal films

GC30b 

adiab. wall, 

h = 100 

GC30c 

h,int = 7.95; 

h,ext = ideal

GC60b 

h,int = 7.95; 

h,ext = 100

GC65b 

h,int = 7.95; 

h,ext = 11.95

Floor Heat Flow (W or Wh/h)

Analytical Solution/CSIRO TRNSYS/TESS FLUENT/PAAET

MATLAB/DIT GHT/NREL SUNREL-GC/NREL

EnergyPlus/GARD VA114-ISO13370/VABI ESP-r-BASESIMP/NRCan

BASECALC/NRCan

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-State Floor Conduction Sensitivity

-200

0

200

400

600

800

1000

1200

GC30aGC10a,

adiab v lin

dT

GC40a*-

GC30a, 

sp v. ss

GC40b*-

GC30b, 

sp v. ss

GC40c*-

GC30c, 

sp v. ss

GC30aGC30b,

h=inf. v

h=100

GC30aGC30c,

h,int=inf v

h,int=7.95

GC30bGC60b,

hint=7.95

GC60bGC65b,

hext=11.95

GC30bGC65b,

hint=7.95

hext=11.95

GC70b*-

GC65b, 

sp v. ss,

low h

Floor Heat Flow (W or Wh/h)

TRNSYS/TESS FLUENT/PAAET MATLAB/DIT

GHT/NREL SUNREL-GC/NREL EnergyPlus/GARD

VA114-ISO13370/VABI ESP-r-BASESIMP/NRCan BASECALC/NRCan

 * Values for GC40a, GC40b, GC40c and GC70b are: annual total × 1000 (W/kW) / 8760 (h/y) 

204 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-State Zone Heating Load

0

500

1000

1500

2000

2500

3000

GC30b: h = 100 GC30c: h,int = 7.95; 

h,ext = ideal

 GC60b: h,int = 7.95; 

h,ext = 100

 GC65b: h,int = 7.95; 

h,ext = 11.95

Heating Load (W or Wh/h)

SUNREL-GC/NREL EnergyPlus/GARD VA114-ISO13370/VABI

ESP-r-BASESIMP/NRCan BASECALC/NRCan

* Values for GC40b, GC40c and GC70b are: annual total × 1000 (W/kW) / 8760 (h/y)

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-State Zone Heating Load Sensitivity

-200

0

200

400

600

800

1000

1200

GC40b*-GC30b 

sp v. ss

GC40c*-GC30c 

sp v. ss

GC30b-GC60b 

hint=7.95

GC60b-GC65b 

hext=11.95

GC30b-GC65b 

hint=7.95

hext=11.95

GC70b*-GC65b 

sp v. ss, low h

Heating Load (W or Wh/h)

SUNREL-GC/NREL EnergyPlus/GARD VA114-ISO13370/VABI

ESP-r-BASESIMP/NRCan BASECALC/NRCan

205 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-State (Zone Heating Load) - (Floor Conduction)

0

200

400

600

800

1000

1200

GC30b: h = 100 GC30c: h,int = 7.95; 

h,ext = ideal

 GC60b: h,int = 7.95; 

h,ext = 100

 GC65b: h,int = 7.95; 

h,ext = 11.95

Heat Flow (W or Wh/h)

SUNREL-GC/NREL EnergyPlus/GARD VA114-ISO13370/VABI

ESP-r-BASESIMP/NRCan BASECALC/NRCan

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Case GC10a Modeling Parameters

0

50

100

150

200

250

300

350

E (depth, m) F (far-field, m)

Distance (m)

TRNSYS/TESS

The GC10a analytical 

solution assumes a semiinfinite solid (E = ∞, F = ∞) 

FLUENT/PAAET MATLAB/DIT GHT/NREL

206 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-State Zone Temperature

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

GC30b: h = 100 GC30c: h,int = 7.95; 

h,ext = ideal

 GC60b: h,int = 7.95; 

h,ext = 100

 GC65b: h,int = 7.95; 

h,ext = 11.95

Temperature (°C)

SUNREL-GC/NREL EnergyPlus/GARD VA114-ISO13370/VABI

ESP-r-BASESIMP/NRCan BASECALC/NRCan

207 
IEA BESTEST Ground Coupling: In-Depth Floor Slab, GC10a 

Steady-State Surface Temperatures (Y=0, thru edge center)

5.0

10.0

15.0

20.0

25.0

30.0

35.0

552 576 600 624 648 672

Distance from Slab Center (cm)

Temperature (°C)

TRNSYS-GC10a MATLAB-GC10a

IEA BESTEST Ground Coupling: In-Depth Floor Slab, GC10a 

Steady-State Surface Temperatures (Y=X, thru corner)

5.0

10.0

15.0

20.0

25.0

30.0

35.0

552 576 600 624 648 672

Distance from Slab Center (cm)

Temperature (°C)

TRNSYS-GC10a MATLAB-GC10a

208 
IEA BESTEST Ground Coupling: In-Depth Floor Slab, GC10a, GC30a 

Steady-State Near-Surface Temperatures (Y=0, thru center of edge)

5.0

10.0

15.0

20.0

25.0

30.0

35.0

552 576 600 624 648 672

Distance from Slab Center (cm)

Temperature (°C)

TRNSYS-GC10a FLUENT-GC10a MATLAB-GC10a

TRNSYS-GC30a FLUENT-GC30a MATLAB-GC30a

IEA BESTEST Ground Coupling: In-Depth Floor Slab, GC10a, GC30a 

Steady-State Near-Surface Temperatures (Y=X, thru corner)

5.0

10.0

15.0

20.0

25.0

30.0

35.0

552 576 600 624 648 672

Distance from Slab Center (cm)

Temperature (°C)

TRNSYS-GC10a FLUENT-GC10a MATLAB-GC10a

TRNSYS-GC30a FLUENT-GC30a MATLAB-GC30a

209 
IEA BESTEST: In-Depth Floor Slab, GC30b, GC60b, GC65b 

Steady-State Near-Surface Temperatures (Y=0, thru center of edge)

5.0

10.0

15.0

20.0

25.0

30.0

35.0

552 576 600 624 648 672

Distance from Slab Center (cm)

Temperature (°C)

TRNSYS-GC30b FLUENT-GC30b MATLAB-GC30b

TRNSYS-GC60b FLUENT-GC60b MATLAB-GC60b

TRNSYS-GC65b FLUENT-GC65b MATLAB-GC65b

IEA BESTEST: In-Depth Floor Slab, GC30b, GC60b, GC65b 

Steady-State Near-Surface Temperatures (Y=X, thru corner)

5.0

10.0

15.0

20.0

25.0

30.0

35.0

552 576 600 624 648 672

Distance from Slab Center (cm)

Temperature (°C)

TRNSYS-GC30b FLUENT-GC30b MATLAB-GC30b

TRNSYS-GC60b FLUENT-GC60b MATLAB-GC60b

TRNSYS-GC65b FLUENT-GC65b MATLAB-GC65b

210 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Floor Conduction

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

GC40a

ideal films

GC40b

h=100

GC45b

AR=36x4

GC50b

large

slab/10

GC55b 

2m depth

GC70b

hint=7.95,

hext=11.95

GC80b 

k=0.5

GC40c

hint=7.95,

hext=ideal

GC45c

AR=36x4

GC55c 

5m depth

GC80c

k=0.85

Floor Heat Flow (kWh)

TRNSYS/TESS FLUENT/PAAET MATLAB/DIT

GHT/NREL SUNREL-GC/NREL EnergyPlus/GARD

VA114-ISO13370/VABI ESP-r-BASESIMP/NRCan BASECALC/NRCan

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Floor Conduction Sensitivity

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

GC40a-GC40b

h=inf. v h=100

GC45b-GC40b

Aspect Ratio

GC40b-GC50b

Large Slab,

normalized

GC55b-GC40b

Depth = 2m

GC40b-GC70b

hint=7.95

hext=11.95 

GC40b-GC80b

k=0.5

GC45c-GC40c

Basesimp,

Aspect Ratio

GC55c-GC40c

Basesimp,

Depth=5m

GC40c-GC80c

Basesimp,

k=0.85

Floor Heat Flow (kWh)

TRNSYS/TESS FLUENT/PAAET MATLAB/DIT

GHT/NREL SUNREL-GC/NREL EnergyPlus/GARD

VA114-ISO13370/VABI ESP-r-BASESIMP/NRCan BASECALC/NRCan

211 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Zone Heating Load

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

GC40b

h=100

GC45b

AR=36x4

GC50b large

slab/10

 GC55b 

2m depth

GC70b

hint=7.95,

hext=11.95

GC80b 

k=0.5

GC40c

hint=7.95,

hext=ideal

GC45c

AR=36x4

 GC55c 

5m depth

GC80c

k=0.85

Heating Load (kWh)

SUNREL-GC/NREL EnergyPlus/GARD VA114-ISO13370/VABI

ESP-r-BASESIMP/NRCan BASECALC/NRCan

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Zone Heating Load Sensitivity

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

GC45b-GC40b 

Aspect Ratio

GC40b-GC50b 

Large Slab,

normalized

GC55b-GC40b 

Depth = 2m

GC40b-GC70b 

hint=7.95

hext=11.95 

GC40b-GC80b 

k=0.5

GC45c-GC40c 

Basesimp,

Aspect Ratio

GC55c-GC40c 

Basesimp,

Depth=5m

GC40c-GC80c 

Basesimp,

k=0.85

Heating Load (kWh)

SUNREL-GC/NREL EnergyPlus/GARD VA114-ISO13370/VABI

ESP-r-BASESIMP/NRCan BASECALC/NRCan

212 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic (Zone Heating Load) - (Floor Conduction)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

GC40b

h=100

GC45b

AR=36x4

GC50b large

slab/10

 GC55b 

2m depth

GC70b

hint=7.95,

hext=11.95

GC80b k=0.5 GC40c

hint=7.95,

hext=ideal

GC45c

AR=36x4

 GC55c 

5m depth

GC80c

k=0.85

Heating Load (kWh)

SUNREL-GC/NREL EnergyPlus/GARD VA114-ISO13370/VABI

ESP-r-BASESIMP/NRCan BASECALC/NRCan

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Hourly Floor Conduction, GC40a

1500

1700

1900

2100

2300

2500

2700

2900

3100

3300

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Hour

Floor Conduction (W or Wh/h)

TRNSYS FLUENT MATLAB GHT

TRNSYS 

MATLAB 

FLUENT 

GHT 

213 
EnergyPlus MATLAB 

TRNSYS & 

FLUENT 

GHT VA114 

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Hourly Floor Conduction, GC40b

1500

1700

1900

2100

2300

2500

2700

2900

3100

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Hour

Floor Conduction (W or 

Wh/h)

0

2

4

6

8

10

12

14

16

18

20

Temperature (°C)

TRNSYS FLUENT MATLAB GHT VA114 EnergyPlus ODB Temperature

VA114 

GHT 

TRNSYS and 

FLUENT 

EnergyPlus MATLAB 

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Hourly Floor Conduction, GC40c

1500

1700

1900

2100

2300

2500

2700

2900

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Hour

Floor Conduction (W or Wh/h)

TRNSYS FLUENT MATLAB VA114

EnergyPlus ESP-r-BASESIMP BASECALC

VA114 

ESP-r-BASESIMP 

BASECALC 

TRNSYS and 

FLUENT 

MATLAB 

EnergyPlus 

214 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Phase Shift, Coldest ODB to Peak Floor Conduction

0

200

400

600

800

1000

1200

1400

GC40a

ideal films

GC40b

h=100

GC45b

AR=36x4

GC50b

large slab

GC55b 

2m depth

GC70b

hint=7.95,

hext=11.95

GC80b

k=0.5

GC40c

hint=7.95,

hext=ideal

GC45c

AR=36x4

GC55c 

5m depth

GC80c

k=0.85

Hours

BASECALC and EnergyPlus are not included in 

the phase shift bar-chart plots because they 

calculate floor conduction monthly (see preceding 

hourly results). 

TRNSYS/TESS FLUENT/PAAET MATLAB/DIT

GHT/NREL SUNREL-GC/NREL VA114-ISO13370/VABI

ESP-r-BASESIMP/NRCan

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Phase Shift Sensitivity, Floor Conduction v. ODB

-350

-300

-250

-200

-150

-100

-50

0

50

GC40a-GC40b 

h=inf. v h=100

GC45b-GC40b 

Aspect Ratio

GC40b-GC50b 

Large Slab,

normalized

GC55b-GC40b 

Depth = 2m

GC40b-GC70b 

hint=7.95

hext=11.95 

GC40b-GC80b 

k=0.5

GC45c-GC40c 

Basesimp,

Aspect Ratio

GC55c-GC40c 

Basesimp,

Depth=5m

GC40c-GC80c 

Basesimp,

k=0.85

Hours

TRNSYS/TESS FLUENT/PAAET MATLAB/DIT

GHT/NREL SUNREL-GC/NREL VA114-ISO13370/VABI

ESP-r-BASESIMP/NRCan

215 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Phase Shift, Coldest ODB to Zone Load

0

200

400

600

800

1000

1200

1400

GC40b

h=100

GC45b

AR=36x4

GC50b 

large slab

 GC55b 

2m depth

GC70b

hint=7.95,

hext=11.95

GC80b k=0.5 GC40c

hint=7.95,

hext=ideal

GC45c

AR=36x4

 GC55c 

5m depth

GC80c

k=0.85

Hours

SUNREL-GC/NREL VA114-ISO13370/VABI ESP-r-BASESIMP/NRCan

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Delta Steady-Periodic Phase Shift Sensitivity, Zone Load v. ODB

-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

GC45b-GC40b 

Aspect Ratio

GC40b-GC50b 

Large Slab,

normalized

GC55b-GC40b 

Depth = 2m

GC40b-GC70b 

hint=7.95

hext=11.95 

GC40b-GC80b 

k=0.5

GC45c-GC40c 

Basesimp,

Aspect Ratio

GC55c-GC40c 

Basesimp,

Depth=5m

GC40c-GC80c 

Basesimp,

k=0.85

Hours

SUNREL-GC/NREL VA114-ISO13370/VABI ESP-r-BASESIMP/NRCan

216 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Peak-Hour Floor Conduction

0

1000

2000

3000

4000

5000

6000

GC40a

ideal films

GC40b

h=100

GC45b

AR=36x4

GC50b

large

slab/10

GC55b 

2m depth

GC70b

hint=7.95,

hext=11.95

GC80b

k=0.5

GC40c

hint=7.95,

hext=ideal

GC45c

AR=36x4

GC55c 

5m depth

GC80c

k=0.85

Floor Heat Flow (W or Wh/h)

TRNSYS/TESS FLUENT/PAAET MATLAB/DIT

GHT/NREL SUNREL-GC/NREL EnergyPlus/GARD

VA114-ISO13370/VABI ESP-r-BASESIMP/NRCan BASECALC/NRCan

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Peak-Hour Floor Conduction Sensitivity

0

500

1000

1500

2000

2500

GC40a-GC40b 

h=inf. v h=100

GC45b-GC40b 

Aspect Ratio

GC40b-GC50b 

Large Slab,

normalized

GC55b-GC40b 

Depth = 2m

GC40b-GC70b 

hint=7.95

hext=11.95 

GC40b-GC80b 

k=0.5

GC45c-GC40c 

Basesimp,

Aspect Ratio

GC55c-GC40c 

Basesimp,

Depth=5m

GC40c-GC80c 

Basesimp,

k=0.85

Floor Heat Flow (W)

TRNSYS/TESS FLUENT/PAAET MATLAB/DIT

GHT/NREL SUNREL-GC/NREL EnergyPlus/GARD

VA114-ISO13370/VABI ESP-r-BASESIMP/NRCan BASECALC/NRCan

217 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Peak-Hour Zone Heating Load

0

1000

2000

3000

4000

5000

6000

GC40b

h=100

GC45b

AR=36x4

GC50b large

slab/10

 GC55b 

2m depth

GC70b

hint=7.95,

hext=11.95

GC80b 

k=0.5

GC40c

hint=7.95,

hext=ideal

GC45c

AR=36x4

 GC55c 

5m depth

GC80c

k=0.85

Zone Heating Load (W or Wh/h)

SUNREL-GC/NREL EnergyPlus/GARD VA114-ISO13370/VABI

ESP-r-BASESIMP/NRCan BASECALC/NRCan

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Annual Peak-Hour Zone Heating Load Sensitivity

0

500

1000

1500

2000

2500

GC45b-GC40b 

Aspect Ratio

GC40b-GC50b 

Large Slab,

normalized

GC55b-GC40b 

Depth = 2m

GC40b-GC70b 

hint=7.95

hext=11.95 

GC40b-GC80b 

k=0.5

GC45c-GC40c 

Basesimp,

Aspect Ratio

GC55c-GC40c 

Basesimp,

Depth=5m

GC40c-GC80c 

Basesimp,

k=0.85

Zone Heating Load (W or Wh/h)

SUNREL-GC/NREL EnergyPlus/GARD VA114-ISO13370/VABI

ESP-r-BASESIMP/NRCan BASECALC/NRCan

218 
IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic (Peak Zone Heating Load) - (Peak Floor Conduction)

0

500

1000

1500

2000

2500

GC40b

h=100

GC45b

AR=36x4

GC50b: large

slab/10

 GC55b 

2m depth

GC70b

hint=7.95,

hext=11.95

GC80b k=0.5 GC40c

hint=7.95,

hext=ideal

GC45c

AR=36x4

 GC55c 

5m depth

GC80c

k=0.85

Heating Load (W or Wh/h)

SUNREL-GC/NREL EnergyPlus/GARD VA114-ISO13370/VABI

ESP-r-BASESIMP/NRCan BASECALC/NRCan

219 
220 

IEA BESTEST Ground Coupling: In-Depth

Steady-Periodic Minimum ODB

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

GC40a

ideal films

GC40b

h=100

GC45b

AR=36x4

GC50b

large slab

GC55b 

2m depth

GC70b

hint=7.95,

hext=11.95

GC80b

k=0.5

GC

hint=

hext=

Temperature (°C)

IEA BESTEST Ground Coupling: In-Depth Floor Slab 

Steady-Periodic Zone Temperature

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

GC40b

h=100

GC45b

AR=36x4

GC50b large

slab

 GC55b 

2m depth

GC70b

hint=7.95,

hext=11.95

GC80b k=0.5 GC40c

hint=7.95,

hext=ideal

GC45c

AR=36x4

 GC55c 

5m depth

GC80c

k=0.85

Temperature (°C)

 Floor Slab 

40c

7.95,

ideal

GC45c

AR=36x4

GC55c 

5m depth

GC80c

k=0.85

TRNSYS/TESS MATLAB/DIT GHT/NREL

SUNREL-GC/NREL EnergyPlus/GARD VA114-ISO13370/VABI

ESP-r-BASESIMP/NRCan BASECALC/NRCan

SUNREL-GC/NREL EnergyPlus/GARD VA114-ISO13370/VABI

ESP-r-BASESIMP/NRCan BASECALC/NRCan

BASECALC does not consider diurnal 

temperature variation in its model. 
221 

"a"-Series Case Summary, Quasi-Analytical Solution Verification 

Analytical Verified Numerical Models Statistics GHT/

Solution TRNSYS FLUENT MATLAB (Max-Min) GHT Q.A.Meana

CSIRO TESS PAAET DIT Min Max /Mean NREL -1

Floor Conduction GC10a (W or Wh/h) 2433 2427 2425 2432 2425 2432 0.3% 2415 -0.5%

GC30a (W or Wh/h) 2642 2585 2695 2585 2695 4.2% 2457 -7.0%

GC40a (kWh) 23033 22761 23609 22761 23609 3.7% 20812 -10.0%Phase Shift for Floor Conduction Peak (hours)GC40a 416 416 416 416 416 0.0% 487 17.1%GC10a Modeling Parameters

E (depth, m) infinite 40 40 300 40 300 30

F (far-field, m) infinite 40 40 150 40 150 20Time Simulated (Years)GC10a s.s. soln. 8.0 s.s. model s.s. model 6.0GC30a 7.0 s.s. model s.s. model 6.0GC40a 6.0 5.0 10.0 5.0 10.0 6.0

a "Q.A.Mean" is average of verified numerical-model results; for zone results the average of the floor results is used.

Steady-State Conduction 

 Verified Numerical Models VA114/ ESP-r/ Statistics, Other Simulation Models

TRNSYS FLUENT MATLAB (Max-Min) GHT SUNREL-GC EnergyPlus ISO-13370 BASESIMP BASECALC (Max-Min)/

TESS PAAET DIT /Mean NREL NREL GARD VABI NRCan NRCan Min Max (Q.A.Mean)a

Floor Conduction (W or Wh/h)GC30b 2533 2504 2570 2.6% 2341 2341 2652 2421 2341 2652 12.3%GC30c 2137 2123 2154 1.5% 2308 2092 1973 1973 1973 2308 15.7%

GC60b 2113 2104 2128 1.1% 1999 2219 2069 1999 2219 10.4%

GC65b 1994 1991 2004 0.7% 1895 1616 1920 1616 1920 15.3%Zone Heating Load (W or Wh/h)GC30b 2341 2652 2427 2341 2652 12.3%

GC30c 2308 2098 2003 2003 2003 2308 14.3%GC60b 1999 2219 2075 1999 2219 10.4%

GC65b 1895 1616 1925 1616 1925 15.5%

(Zone Heating Load) - (Floor Conduction), [W or Wh/h]GC30b 006 0 6GC30c 0 6 30 30 0 30

GC60b 006 0 6

GC65b 005 0 5

a "Q.A.Mean" is average of verified numerical-model results; for zone results the average of the floor results is used.

Steady-State Supporting Information

 Verified Numerical Models VA114/ ESP-r/ Statistics, All Results

TRNSYS FLUENT MATLAB GHT SUNREL-GC EnergyPlus ISO-13370 BASESIMP BASECALC (Max-Min)

TESS PAAET DIT NREL NREL GARD VABI NRCan NRCan Min Max /Mean

Zone Air Temperature (°C)GC30b 30.0 30.0 30.0 30.0 30.0 0.0%

GC30c 30.0 30.0 30.0 30.0 30.0 30.0 0.0%GC60b 30.0 30.0 30.0 30.0 30.0 0.0%

GC65b 30.0 30.0 30.0 30.0 30.0 0.0%

Simulation Duration (Years)

GC30b 6.0 s.s. model s.s. model 5.0 5.0 7.0 1.0 0.0 7.0GC30c 6.0 s.s. model s.s. model 6.0 1.0 2.0 3.0 0.0 6.0GC60b 6.0 s.s. model s.s. model 5.0 7.0 1.0 0.0 7.0GC65b 6.0 s.s. model s.s. model 5.0 8.0 1.0 0.0 8.0
222 

Steady-Periodic Last-Simulation-Year Conduction 

 Verified Numerical Models VA114/ ESP-r/ Statist

TRNSYS FLUENT MATLAB (Max-Min) GHT SUNREL-GC EnergyPlus ISO-13370 BASESIMP BASECALC 

TESS PAAET DIT /Mean NREL NREL GARD VABI NRCan NRCan Mi

Floor Conduction (kWh)GC40b 22099 21932 22513 2.6% 20513 20513 23204 21206 20GC45b 32758 32456 33483 3.1% 33415 30856 30

GC50b 277923 277988 281418 1.3% 324257 289925 289GC55b 35075 34879 35491 1.7% 33211 39932 31601 31GC70b 17396 17434 17552 0.9% 16607 15553 16817 15GC80b 6029 5939 6151 3.5% 5661 6059 5728 5

GC40c 18649 18598 18873 1.5% 20255 18330 17285 17285 17

GC45c 27004 26906 27392 1.8% 28707 26038 23849 23849 23

GC55c 20760 20714 20986 1.3% 22570 20172 20850 20850 20

GC80c 9192 9137 9314 1.9% 10073 8966 8635 8635 8

Zone Heating Load (kWh)GC40b n/a n/a 20513 23204 21260 20

GC45b n/a n/a 33415 30924 30

GC50b n/a n/a 324257 291502 291GC55b n/a n/a 33211 39932 31654 31

GC70b n/a n/a 16607 15553 16865 15

GC80b n/a n/a 5661 6059 5778 5

GC40c n/a n/a 20255 18379 17545 17545 17GC45c n/a n/a 28707 26101 24185 24185 24GC55c n/a n/a 22570 20221 21111 21111 20GC80c n/a n/a 10073 9013 8848 8848 8(Zone Heating Load) - (Floor Conduction) [kWh]GC40b 0 054 

GC45b 0 68 

GC50b 0 1577 

GC55b 0 053 

GC70b 0 048 

GC80b 0 050 

GC40c 0 49 260 260 GC45c 0 63 336 336 GC55c 0 49 261 261 GC80c 0 47 213 213 

a "Q.A.Mean" is average of verified numerical-model results; for zone results the average of the floor results is used.
223 

Steady-Periodic Last-Simulation-Year Peak-Hour Conduction 

 Verified Numerical-Model Results

TRNSYS FLUENT MATLAB (Max-Min)

TESS Date Hour PAAET Date Hour DIT Date Hour /Mean

Floor Conduction (W or Wh/h)GC40a 3087 1-Feb 12 3042 1-Feb 12 3174 1-Feb 12 4.2%GC40b 2941 1-Feb 13 2914 3-Feb 13 3002 2-Feb 13 3.0%GC45b 4444 1-Feb 13 4396 2-Feb 13 4551 2-Feb 13 3.5%GC50b 34531 4-Feb 13 34510 3-Feb 13 35033 3-Feb 13 1.5%GC55b 4366 22-Jan 13 4336 21-Jan 13 4427 21-Jan 13 2.1%GC70b 2254 11-Feb 16 2259 11-Feb 15 2276 11-Feb 16 1.0%GC80b 776 7-Feb 20 763 8-Feb 19 794 7-Feb 19 4.0%GC40c 2454 7-Feb 14 2444 7-Feb 14 2487 6-Feb 14 1.7%GC45c 3634 4-Feb 14 3618 6-Feb 14 3691 6-Feb 14 2.0%GC55c 2710 4-Feb 14 2703 6-Feb 14 2744 6-Feb 14 1.5%GC80c 1190 9-Feb 17 1181 9-Feb 17 1207 8-Feb 17 2.2%

O t h e r S I m u l a t I o n R e s u l t s Statistics, Other Sim. Mode

GHT SUNREL-GC EnergyPlus VA114/ISO-13370 ESP-r/BASESIMP BASECALC (Max-Min

NREL Date Hour NREL Date Hour GARD Date Hour VABI Date Hour NRCan Date Hour NRCan Date Hour Min Max (Q.A.Mea

Floor Conduction (W or Wh/h)GC40a 2758 4-Feb 11GC40b 2710 4-Feb 13 2710 4-Feb 13 3005 02/02 03:00 2899 21-Feb 2 2710 3005 10

GC45b 4415 02/02 04:00 4318 20-Feb 20 4318 4415 2

GC50b 39570 01/01 01:00 36304 20-Feb 7 36304 39570 9GC55b 4102 22-Jan 14 4860 01/01 01:00 4085 20-Feb 24 4085 4860 17GC70b 2144 11-Feb 18 1906 02/03 08:00 2252 24-Feb 2 1906 2252 15GC80b 722 9-Feb 22 766 02/04 02:00 753 5-Mar 2 722 766 5

GC40c 2650 02/03 11:00 2472 24-Feb 5 2231 31-Jan 8 2224 Feb 0 2224 2650 17GC45c 3827 02/03 07:00 3606 25-Feb 1 3192 31-Jan 6 3178 Jan 0 3178 3827 17GC55c 2926 02/03 11:00 2682 24-Feb 22 2666 29-Jan 23 2659 Jan 0 2659 2926 9GC80c 1300 02/05 05:00 1187 1-Mar 24 1094 2-Feb 5 1091 Feb 0 1091 1300 17

GHT SUNREL-GC EnergyPlus VA114/ISO-13370 ESP-r/BASESIMP BASECALC (Max-Mi

NREL Date Hour NREL Date Hour GARD Date Hour VABI Date Hour NRCan Date Hour NRCan Date Hour Min Max /Mean

Zone Heating Load (W or Wh/h)GC40b 2710 4-Feb 13 3005 02/02 03:00 2907 22-Feb 4 2710 3005 10GC45b 4415 02/02 04:00 4328 22-Feb 4 4328 4415 2

GC50b 39570 01/01 01:00 36021 21-Feb 3 36021 39570 9

GC55b 4102 22-Jan 14 4860 01/01 01:00 4093 22-Feb 3 4093 4860 17

GC70b 2144 11-Feb 18 1906 02/03 08:00 2259 27-Feb 3 1906 2259 16GC80b 722 9-Feb 22 766 02/04 02:00 760 8-Mar 4 722 766 5

GC40c 2650 02/03 11:00 2479 26-Feb 3 2273 1-Feb 20.0 2261 Feb 0 2261 2650 16GC45c 3827 02/03 07:00 3616 26-Feb 3 3246 31-Jan 4.0 3228 Jan 0 3228 3827 17GC55c 2926 02/03 11:00 2690 25-Feb 4 2708 28-Jan 4.0 2698 Jan 0 2690 2926 8GC80c 1300 02/05 05:00 1194 4-Mar 3 1128 31-Jan 4.0 1122 Feb 0 1122 1300 15(Zone Heating Load) - (Floor Conduction), [W or Wh/h, may not be for same hour]GC40b 00 8 0 8

GC45b 0 10 0 10GC50b 0 -283 -283 0

GC55b 00 8 0 8

GC70b 00 7 0 7GC80b 00 7 0 7GC40c 0 742 37 0 42

GC45c 0 10 54 50 0 54

GC55c 0 842 39 0 42

GC80c 0 734 31 0 34

a "Q.A.Mean" is average of verified numerical-model results; for zone results the average of the floor results is used.
224 

Time from Coldest Hour (Jan 15, Hour 4) to Peak Conduction Occurrence

 Verified Numerical Models VA114/ ESP-r/ Statistics, Other Simulation Models

TRNSYS FLUENT MATLAB (Max-Min) GHT SUNREL-GC EnergyPlus ISO-13370 BASESIMP BASECALC (Max-Min)/

TESS PAAET DIT /Mean NREL NREL GARD VABI NRCan NRCan Min Max (Q.A.Mean)a

Phase Shift for Floor Conduction Peak (hours)GC40b 417 465 441 10.9% 489 489 886 489 886 90.0%GC45b 417 441 441 5.5% 880 880 880 0.0%

GC50b 489 465 465 5.1% 867 867 867 0.0%

GC55b 177 153 153 14.9% 178 884 178 884 438.5%

GC70b 660 659 660 0.2% 662 958 662 958 44.9%

GC80b 568 591 567 4.2% 618 1174 618 1174 96.6%

GC40c 562 562 538 4.3% 961 388 388 961 103.4%GC45c 490 538 538 9.2% 981 386 386 981 114.0%GC55c 490 538 538 9.2% 978 355 355 978 119.3%GC80c 613 613 589 4.0% 1100 433 433 1100 110.2%Phase Shift for Zone Load Peak (hours)GC40b 489 912 489 912 95.9%

GC45b 912 912 912 0.0%GC50b 887 887 887 0.0%GC55b 178 911 178 911 455.3%

GC70b 662 1031 662 1031 55.9%

GC80b 618 1248 618 1248 109.5%

GC40c 1007 424 424 1007 105.2%

GC45c 1007 384 384 1007 119.3%

GC55c 984 312 312 984 128.7%

GC80c 1151 384 384 1151 126.8%

a "Q.A.Mean" is average of verified numerical-model results; for zone results the average of the floor results is used.

Steady-Periodic Supporting Information

 Verified Numerical Models VA114/ ESP-r/ Statistics, All Results

TRNSYS FLUENT MATLAB GHT SUNREL-GC EnergyPlus ISO-13370 BASESIMP BASECALC (Max-Min)

TESS PAAET DIT NREL NREL GARD VABI NRCan NRCan Min Max /Mean

Mean Annual Zone Air Temperature (°C)GC40b 30.0 30.0 30.0 30.0 30.0 0.0%

GC45b 30.0 30.0 30.0 30.0 0.0%

GC50b 30.0 30.0 30.0 30.0 0.0%

GC55b 30.0 30.0 30.0 30.0 30.0 0.0%

GC70b 30.0 30.0 30.0 30.0 30.0 0.0%

GC80b 30.0 30.0 30.0 30.0 30.0 0.0%

GC40c 30.0 30.0 30.0 30.0 30.0 30.0 0.0%GC45c 30.0 30.0 30.0 30.0 30.0 30.0 0.0%GC55c 30.0 30.0 30.0 30.0 30.0 30.0 0.0%GC80c 30.0 30.0 30.0 30.0 30.0 30.0 0.0%Simulation Duration (Years)GC40b 5.0 6.0 10.0 5.0 5.0 7.0 1.0 1.0 10.0

GC45b 5.0 3.0 10.0 7.0 1.0 1.0 10.0

GC50b 8.0 8.0 10.0 8.0 1.0 1.0 10.0

GC55b 3.0 3.0 10.0 2.0 3.0 1.0 1.0 10.0GC70b 6.0 3.0 10.0 5.0 7.0 1.0 1.0 10.0GC80b 10.0 3.0 10.0 5.0 16.0 1.0 1.0 16.0

GC40c 5.0 3.0 10.0 6.0 1.0 2.0 3.0 1.0 10.0

GC45c 5.0 3.0 10.0 6.0 1.0 2.0 3.0 1.0 10.0

GC55c 3.0 3.0 10.0 3.0 1.0 2.0 3.0 1.0 10.0

GC80c 8.0 4.0 10.0 10.0 1.0 2.0 3.0 1.0 10.0
225 

Steady-Periodic Minimum ODB and Time of Occurrence

 Verified Numerical-Model Results

TRNSYS # hours at FLUENT # hours at MATLAB # hours at

TESS Date Hour ODBmin PAAET Date Hour ODBmin DIT Date Hour ODBmin

Outdoor Dry-Bulb Temperature (°C)GC40a 2.1 8-Jan 4.0 30.0 2.0 8-Jan 4.0 15.0GC40b 2.1 8-Jan 4.0 30.0 2.0 8-Jan 4.0 15.0GC45b 2.1 8-Jan 4.0 30.0 2.0 8-Jan 4.0 15.0GC50b 2.1 8-Jan 4.0 30.0 2.0 8-Jan 4.0 15.0GC55b 2.1 8-Jan 4.0 30.0 2.0 8-Jan 4.0 15.0GC70b 2.1 8-Jan 4.0 30.0 2.0 8-Jan 4.0 15.0GC80b 2.1 8-Jan 4.0 30.0 2.0 8-Jan 4.0 15.0GC40c 2.1 8-Jan 4.0 30.0 2.0 8-Jan 4.0 15.0GC45c 2.1 8-Jan 4.0 30.0 2.0 8-Jan 4.0 15.0GC55c 2.1 8-Jan 4.0 30.0 2.0 8-Jan 4.0 15.0GC80c 2.1 8-Jan 4.0 30.0 2.0 8-Jan 4.0 15.0

O t h e r S I m u l a t I o n R e s u l t s

GHT # hours at SUNREL-GC # hours at EnergyPlus # hours at VA114/ISO-13370 # hours at ESP-r/BASESIMP # hours at 

NREL Date Hour ODBmin NREL Date Hour ODBmin GARD Date Hour ODBmin VABI Date Hour ODBmin NRCan Date Hour ODBmin 

Outdoor Dry-Bulb Temperature (°C)GC40a 2.0 8-Jan 4.0 15.0GC40b 2.0 8-Jan 4.0 15.0 2.0 8-Jan 4.0 15.0 2.0 01/08 04:00 15.0 2.0 8-Jan 4.0 16.0GC45b 2.0 01/08 04:00 15.0 2.0 8-Jan 4.0 16.0GC50b 2.0 01/08 04:00 15.0 2.0 8-Jan 4.0 16.0GC55b 2.0 8-Jan 4.0 15.0 2.0 01/08 04:00 15.0 2.0 8-Jan 4.0 16.0GC70b 2.0 8-Jan 4.0 15.0 2.0 01/08 04:00 15.0 2.0 8-Jan 4.0 16.0GC80b 2.0 8-Jan 4.0 15.0 2.0 01/08 04:00 15.0 2.0 8-Jan 4.0 16.0GC40c 2.0 01/08 04:00 15.0 2.0 8-Jan 4.0 16.0 2.0 8-Jan 4.0 15.0 GC45c 2.0 01/08 04:00 15.0 2.0 8-Jan 4.0 16.0 2.0 8-Jan 4.0 15.0 GC55c 2.0 01/08 04:00 15.0 2.0 8-Jan 4.0 16.0 2.0 8-Jan 4.0 15.0 GC80c 2.0 01/08 04:00 15.0 2.0 8-Jan 4.0 16.0 2.0 8-Jan 4.0 15.0 
226 

Delta Steady-State Conduction 

 Verified Numerical Models VA114/ ESP-r/ Statistics, Other Simulation Models

TRNSYS FLUENT MATLAB (Max-Min) GHT SUNREL-GC EnergyPlus ISO-13370 BASESIMP BASECALC (Max-Min)/

TESS PAAET DIT /Mean NREL NREL GARD VABI NRCan NRCan Min Max (Q.A.Mean)a

Floor Conduction (W or Wh/h)GC30a-GC10a 214 160 263 48.5% 42 42 42 0.0%

GC40ab-GC30a -12 13 0.1 8227.4% -81 -81 -81 0.0%

GC40bb-GC30b -10 -0.1 0.0 -297.9% 0 0 -4 0 -4 0 -117.7%

GC40cb-GC30c -8 0.2 0.0 -314.3% 4 0 0 0 0 4 -166.8%

GC30a-GC30b 109 81 125 41.7% 116 116 116 0.0%GC30a-GC30c 505 462 541 15.6%GC30b-GC60b 420 400 442 10.0% 342 434 352 342 434 21.8%GC60b-GC65b 120 114 125 9.3% 104 603 149 104 603 418.5%

GC30b-GC65b 539 513 566 9.9% 446 1037 501 446 1037 109.5%

GC70bb-GC65b -8 -0.4 0.0 -284.9% 0.5 160 0 0 160 -5797.5%

Zone Load (W or Wh/h)GC40bb-GC30b 0 -4 0 -4 0 -117.7%GC40cb-GC30c 4 0 0 0 0 4 -172.4%

GC30b-GC60b 342 434 352 342 434 21.8%GC60b-GC65b 104 603 150 104 603 418.5%GC30b-GC65b 446 1037 502 446 1037 109.5%GC70bb-GC65b 0 160 0 0 160 -5780.2%

a "Q.A.Mean" is average of verified numerical-model results; for zone results the average of the floor results is used.b Values for GC40a, GC40b, GC40c and GC70 are: annual total × 1000 (W/kW) / 8760 (h/y)

Delta Steady-Periodic Annual Total Conduction

 Verified Numerical Models VA114/ ESP-r/ Statistics, Other Simulation Models

TRNSYS FLUENT MATLAB (Max-Min) GHT SUNREL-GC EnergyPlus ISO-13370 BASESIMP BASECALC (Max-Min)/

TESS PAAET DIT /Mean NREL NREL GARD VABI NRCan NRCan Min Max (Q.A.Mean)a

Floor Conduction (kWh)GC40a-GC40b 933 829 1096 28.1% 299 299 299 0.0%GC45b-GC40b 10659 10524 10971 4.2% 10211 9650 9650 10211 5.2%GC40b-GC50bc 15846 15677 16181 3.2% 15908 14683 14683 15908 7.7%

GC55b-GC40b 12976 12947 12978 0.2% 12698 16728 10395 10395 16728 48.8%

GC40b-GC70b 4704 4498 4961 9.8% 3906 7650 4389 3906 7650 79.3%

GC40b-GC80b 16071 15993 16362 2.3% 14852 17145 15478 14852 17145 14.2%

GC45c-GC40c 8355 8309 8519 2.5% 8452 7708 6564 6564 6564 8452 22.5%

GC55c-GC40c 2111 2117 2113 0.3% 2315 1842 3565 3565 1842 3565 81.5%

GC40c-GC80c 9457 9461 9559 1.1% 10182 9364 8650 8650 8650 10182 16.1%

Zone Conduction (kWh)GC45b-GC40b 10211 9664 9664 10211 5.1%

GC40b-GC50bc 15908 14701 14701 15908 7.6%

GC55b-GC40b 12698 16728 10394 10394 16728 48.8%

GC40b-GC70b 3906 7650 4395 3906 7650 79.3%

GC40b-GC80b 14852 17145 15482 14852 17145 14.2%

GC45c-GC40c 8452 7722 6640 6640 6640 8452 21.6%GC55c-GC40c 2315 1842 3566 3566 1842 3566 81.6%GC40c-GC80c 10182 9366 8697 8697 8697 10182 15.6%

a "Q.A.Mean" is average of verified numerical-model results; for zone results the average of the floor results is used.c GC50b with normalized floor area: GC50b / (80 x 80) x (12 x 12)
227 

Delta Steady-Periodic Last-Year Peak Hour Floor Conduction

 Verified Numerical Models VA114/ ESP-r/ Statistics, Other Simulation Models

TRNSYS FLUENT MATLAB (Max-Min) GHT SUNREL-GC EnergyPlus ISO-13370 BASESIMP BASECALC (Max-Min)/

TESS PAAET DIT /Mean NREL NREL GARD VABI NRCan NRCan Min Max (Q.A.Mean)a

Floor Conduction (W or Wh/h)GC40a-GC40b 145 128 171 29.1% 48 48 48 0.0%GC45b-GC40b 1503 1482 1549 4.4% 1410 1419 1410 1419 0.6%

GC40b-GC50bc 2164 2138 2214 3.5% 2115 2082 2082 2115 1.5%

GC55b-GC40b 1425 1422 1425 0.2% 1391 1855 1186 1186 1855 47.0%GC40b-GC70b 687 655 726 10.2% 566 1099 647 566 1099 77.3%

GC40b-GC80b 2166 2151 2208 2.6% 1988 2239 2146 1988 2239 11.5%GC45c-GC40c 1180 1173 1205 2.7% 1176 1134 961 954 954 1176 18.7%GC55c-GC40c 256 258 258 0.9% 275 210 435 435 210 435 87.4%GC40c-GC80c 1265 1264 1279 1.2% 1351 1285 1137 1133 1133 1351 17.1%Zone Conduction (W or Wh/h)GC45b-GC40b 1410 1421 1410 1421 0.7%

GC40b-GC50bc 2115 2097 2097 2115 0.8%

GC55b-GC40b 1391 1855 1186 1186 1855 47.0%

GC40b-GC70b 566 1099 648 566 1099 77.3%GC40b-GC80b 1988 2239 2147 1988 2239 11.5%

GC45c-GC40c 1176 1137 973 967 967 1176 17.6%GC55c-GC40c 275 211 435 437 211 437 87.8%GC40c-GC80c 1351 1285 1145 1139 1139 1351 16.7%

a "Q.A.Mean" is average of verified numerical-model results; for zone results the average of the floor results is used.c GC50b with normalized floor area: GC50b / (80 x 80) x (12 x 12)

Delta Steady-Periodic Conduction v Coldest Hour Phase Shift 

 Verified Numerical Models VA114/ ESP-r/ Statistics, Other Simulation Models

TRNSYS FLUENT MATLAB (Max-Min) GHT SUNREL-GC EnergyPlus ISO-13370 BASESIMP BASECALC (Max-Min)/

TESS PAAET DIT /Mean NREL NREL GARD VABI NRCan NRCan Min Max (Q.A.Mean)a

Floor (Hours)GC40a-GC40b -1 -49 -25 -192.0% -2 -2 -2 0.0%GC45b-GC40b 0 -24 0 -300.0% -6 -6 -6 0.0%

GC40b-GC50bc -72 0 -24 -225.0% 19 19 19 0.0%

GC55b-GC40b -240 -312 -288 -25.7% -311 -2 -311 -2 -110.4%

GC40b-GC70b -243 -194 -219 -22.4% -173 -72 -173 -72 -46.2%GC40b-GC80b -151 -126 -126 -18.6% -129 -288 -288 -129 -118.4%

GC45c-GC40c -72 -24 0 -225.0% 20 -2 -2 20 -68.8%

GC55c-GC40c -72 -24 0 -225.0% 17 -33 -33 17 -156.3%GC40c-GC80c -51 -51 -51 0.0% -139 -45 -139 -45 -184.3%

Zone (Hours)GC45b-GC40b 0 0 0 0.0%

GC40b-GC50bc 25 25 25 0.0%

GC55b-GC40b -311 -1 -311 -1 -110.7%

GC40b-GC70b -173 -119 -173 -119 -24.7%GC40b-GC80b -129 -336 -336 -129 -154.1%GC45c-GC40c 0 -40 -40 0 -125.0%

GC55c-GC40c -23 -112 -112 -23 -278.1%

GC40c-GC80c -144 40 -144 40 -360.8%

a "Q.A.Mean" is average of verified numerical-model results; for zone results the average of the floor results is used.c GC50b with normalized floor area: GC50b / (80 x 80) x (12 x 12)
F1147-E(09/2007) 

REPORT DOCUMENTATION PAGE Form Approved 

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1. REPORT DATE (DD-MM-YYYY)

September 2008 

2. REPORT TYPE

Technical Report 

3. DATES COVERED (From - To)

 

4. TITLE AND SUBTITLE

International Energy Agency Building Energy Simulation Test and 

Diagnostic Method (IEA BESTEST): In-Depth Diagnostic Cases for 

Ground Coupled Heat Transfer Related to Slab-on-Grade 

Construction 

5a. CONTRACT NUMBER

DE-AC36-99-GO10337 

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

J. Neymark and R. Judkoff 

Contributors: 

I. Beausoleil-Morrison, A. Ben-Nakhi, M. Crowley, M. Deru, 

R. Henninger, H. Ribberink, J. Thornton, A. Wijsman, and 

M. Witte 

5d. PROJECT NUMBER

NREL/TP-550-43388 

5e. TASK NUMBER

BEC7.6051 

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National Renewable Energy Laboratory 

1617 Cole Blvd. 

Golden, CO 80401-3393 

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REPORT NUMBER

NREL/TP-550-43388 

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14. ABSTRACT (Maximum 200 Words)

This report documents a set of idealized in-depth diagnostic test cases for use in validating ground-coupled floor slab 

heat transfer models. These test cases represent an extension to IEA BESTEST, which originally focused on testing 

and validation of building thermal fabric models, but addressed only cursorily the modeling of heat transfer between 

the building and the ground. 

15. SUBJECT TERMS

iea; international energy agency; bestest; building energy simulation test 

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