Reports of Research Institute for Applied Mechanics, Kyushu University No.150 (71–83) March 2016

Reproducibility of Complex Turbulent Flow
Using Commercially-Available CFD Software―Report 3: For the Case of a Three-dimensional Cube―
Takanori UCHIDA*1
E-mail of corresponding author: takanori@riam.kyushu-u.ac.jp(Received January 29, 2016)
Abstract
Choosing appropriate sites for wind turbines is extremely important in Japan because the spatial distribution of windspeed is highly complex over steep complex terrain, which is abundant in Japan. The author's research group has beendeveloping an unsteady CFD software package called RIAM-COMPACT®. This package is based on an LES
turbulence model. In this paper, to examine the accuracy of RIAM-COMPACT®, numerical simulations of uniform,
non-stratified airflow past a three-dimensional cube were performed. The analysis primarily focused on airflow
characteristics in the wake region. The results from the simulation with RIAM-COMPACT® were compared to thosefrom a commercially-available CFD software package (STAR-CCM+) and were found to be in good agreement.
Key words: Commercially-available CFD software, STAR-CCM+, RIAM-COMPACT®, Cube model

1. Introduction
The author's research group has developed the numerical

2. Summary of Commercially-Available
CFD Softwarewind diagnosis technique named RIAM-COMPACT® 1, 2).

Commercially-available computational fluid dynamics

The core technology of RIAM-COMPACT® is under(CFD) software packages have been developed and used

continuous development at the Research Institute for Applied

mainly as design tools primarily in the automobile andMechanics, Kyushu University, Japan. An exclusive license

aviation industries up to the present time. The following is aof the core technology has been granted by Kyushu TLO Co.,
Ltd. (Kyushu University TLO) to RIAM-COMPACT Co.,
Ltd. (http://www.riam-compact.com/), a venture corporation

list of the major CFD software packages available on themarket:which was founded by the author and originated at Kyushu
University in 2006. A trademark, RIAM-COMPACT®, and a

General-purpose CFD thermal fluid analysis software

utility model patent were granted to RIAM-COMPACT Co.,packages

Ltd. in the same year. In the meantime, a software package
has been developed based on the above-mentioned technique■STAR-CCM+

and is named the RIAM-COMPACT® natural terrain version

http://www.cd-adapco.co.jp/products/star_ccm_plus/index.

software. Efforts have been made to promote this software as

html

a standard software package in the wind power industry.
In the previous paper 1, 2), a numerical simulation was
performed for airflow around an isolated-hill with a steep■ANSYS(CFD, Fluent, CFX)
http://ansys.jp/solutions/analysis/fluid/index.html

slope angle using RIAM-COMPACT® natural terrain

version, and the results were compared to those fromnumerical simulations performed using anothercommercially-available CFD software package.
In the present paper, a similar study is conducted for
airflow around a three-dimensional cube, and theresults of the comparisons are discussed.

■SCRYU/Tetra
http://www.cradle.co.jp/products/scryutetra/■STREAM
http://www.cradle.co.jp/products/stream/index.html■CFD2000
http://www.cae-sc.jp/docs/cfd2000/index.htm*1 Research Institute for Applied Mechanics, Kyushu University

72

Uchida : Reproducibility of Complex Turbulent Flow Using Commercially-available CFD Software, Report 3■PHOENICS■MASCOT

http://www.phoenics.co.jp/

http://aquanet21.ddo.jp/mascot/■Autodesk Simulation CFD■WindSimhttp://www.cfdesign.com/

http://www.windsim.com/■CFD++■METEODYN

http://bakuhatsu.jp/software/cfd/

http://meteodyn.com/■CFD-ACE+
http://www.wavefront.co.jp/CAE/cfd-ace-plus/

In the present paper, the simulation results from
RIAM-COMPACT® natural terrain version are compared tothose from STAR-CCM+, one of the leading commercially-■AcuSolve

available CFD software packages. The results of the

http://acusolve.jsol.co.jp/index.html

comparison are discussed.

■FLOW-3D

3. Summary of STAR-CCM+ Software

http://www.terrabyte.co.jp/FLOW-3D/flow3d.htm■FloEFD
http://www.sbd.jp/product/netsu/floefd3cad.shtml■Flow Designer
http://www.akl.co.jp/■PowerFLOW
http://www.exajapan.jp/pages/products/pflow_main.html■KeyFlow
http://www.kagiken.co.jp/product/keyflow/index.shtml■OpenFOAM
http://www.cae-sc.jp/docs/FOAM/■FrontFlow
http://www.advancesoft.jp/product/advance_frontflow_red/
The wind power industry has independently developed anddistributed CFD software designed for selecting sites
appropriate for the installation of wind turbines (see the list
below). Recently, some of the above-listed general-purpose
thermal fluid analysis software packages have also started
being adopted in the wind power industry.
CFD software packages designed for the wind power industry(wind farm design tools)■RIAM-COMPACT®
http://www.riam-compact.com/

In this section, a summary of STAR-CCM+, ageneral-purpose thermal fluid analysis software package
distributed by CD-adapco is provided (see Table 1). The
version of the software package used in the present study is
8.02.008 (for 64-bit Windows).
STAR-CCM+ uses a single graphical user interface (GUI)for computational grid generation, execution of fluid
analyses, and data post-processing. The grid generation
method in STAR-CCM+ is distinctive. In STAR-CCM+,
both a polyhedral grid and a prism layer grid can be used(for example, see Fig.3). The polyhedral grid is a new typeof grid offered and promoted by CD-adapco and consists ofpolyhedral cells which possess 10 to 15 faces on average.
The use of this cell type makes it possible to dramaticallyreduce 1) the number of grid cells required to obtain
analysis results equivalent to those that can be obtainedusing a conventional tetrahedral grid and 2) the memory
required by the solver. With the use of this cell type, thecomputational stability improves significantly, and the timerequired to obtain convergent solutions also decreases. The
prism layer grid is a refined grid designed to capture thebehavior of the boundary layer that develops over thesurface of an object. In this type of grid, layers of thin gridcells are distributed regularly over the object. Since thethickness and number of layers in the normal direction withrespect to the object surface can be freely adjusted, thebehavior of the boundary layer in the vicinity of a wall canbe captured with high accuracy. However, when the numberof prism layer grid cells is very large, the computation timeincreases significantly.

Reports of Research Institute for Applied Mechanics, Kyushu University, No.150 March 2016
Numerical simulations are based on the finite-volume

Coefficient of viscosity μ73

1.0 × 10-5 [Pa•s]

method (FVM), and the Navier-Stokes equation is used as

Cube model height h

0.1 [m]the governing equation. Iterative calculations are performed

Inflow wind velocity U

1.0 [m/s]

for the velocity and pressure fields using an algebraic

Reynolds number

multi-grid (AMG) linear solver. For the time marching= U h (ρ / μ) = U h / νmethod, a first-order implicit method is used. STAR-CCM+

Non-dimensional time step

can be run either with a Reynolds-averaged Navier-Stokes∆ｔ = (∆t U) / h(RANS) turbulence model or a large-eddy simulation (LES)

Number of grid cells

1.0 × 10４
2.5 × 10-2
Approx. 1.06 million

turbulence model. For the convective term in the

Table 1 Overview of STAR-CCM+, for the case of the

RANS models, a second-order upwind scheme is adopted.

simulation using a steady RANS model in the present study

For the convective term in the LES models, a bounded
central differencing (BCD) scheme is employed. Table 1
shows an overview of the computational techniques,

4. Summary of RIAM-COMPACT® Softwareparameters, and simulation set-up used for one of the

In this section, a summary of RIAM-COMPACT® natural

simulations performed with STAR-CCM+ in the present

terrain version, developed by the author's research group, will

study, namely the simulation with a steady RANS

be described. In this software package, a collocated grid in aturbulence model, as an example.

general curvilinear coordinate system is adopted in order tonumerically predict local wind flow over complex terrain withhigh accuracy while avoiding numerical instability. In thisSimulation code
Governing equation

STAR-CCM+ v.8.02.008
Three-dimensional unsteady
Navier-Stokes equation
Steady RANS

Turbulence model(Spalart-Allmaras
one-equation eddy-viscosity
turbulence model)
1. First-order implicit
unsteady analysis

Time marching

2. Steady analysis(The steady-state solution is
obtained by specifying thenumber of time steps.)
1. Spin-up: 0 - 100s
in non-dimensional time
(Time averaging: 100 - 200s

Duration of simulationin non-dimensional time)
2. Spin-up: 0 - 2000
in time step number(Time averaging: 2000 4000 in time step number)
A second-order upwind
schemeDiscretization of the(No options available

convective termother than first-order andsecond-order upwind
schemes)

Gas

Constant density

Density ρ

1.0 [kg/m3]

collocated grid, the velocity components and pressure aredefined at the grid cell centers, and variables that result frommultiplying the contravariant velocity components by the
Jacobian are defined at the cell faces. The numerical technique
is based on the finite-difference method (FDM), and an LES
model is adopted for the turbulence model. In the LES model,
a spatial filter is applied to the flow field to separate eddies ofvarious scales into grid-scale (GS) components, which arelarger than the computational grid cells, and sub-grid scale(SGS) components, which are smaller than the computational
grid cells. Large-scale eddies, i.e., the GS components of
turbulence eddies, are directly numerically simulated without
the use of a physically simplified model. In contrast,
dissipation of energy, which is the main effect of small-scaleeddies, i.e., the SGS components, is modeled according to aphysics-based analysis of the SGS stress.
For the governing equations of the flow, a spatially-filteredcontinuity equation for incompressible fluid (Eq.(1)) and a
spatially-filtered Navier-Stokes equation (Eq.(2)) are used.

ui
0
x i

-(1)

ij
ui
ui
p
1 2 ui
 uj



t
x j
x i Re x jx j x j

ij  u 'i u 'j 

1 ' 'u k u k ij  2SGS Sij
3

-(3)

-(2)

74

Uchida : Reproducibility of Complex Turbulent Flow Using Commercially-available CFD Software, Report 3

Upper and lateral boundaries: free-slip condition

Inflow boundary:uniform inflow condition

Ground surface:no-slip condition

Outflow boundary:
convective outflow condition

Fig.1 Computational domain, coordinate system, boundary conditions, and other related information

SGS   Cs fs   S2

S  2SijSij

Sij 

1/ 2

  hx h yhz



1/3

function.

-(5)

1  u i u j 2  x j x i modeling, the standard Smagorinsky model is adopted with amodel coefficient of 0.1 in conjunction with a wall-dampingfs  1  exp  z  / 25



-(4)

-(6)

5. Flow Field and Simulation-setup
Considered in the Present StudyIn this section, the flow field, coordinate system, and



-(7)

simulation-setup considered for the present study aredescribed (Fig.1).

-(8)

For the computational algorithm, a method similar to a
fractional step (FS) method is used, and a time marching
method based on the Euler explicit method is adopted. The
Poisson’s equation for pressure is solved by the successive
over-relaxation (SOR) method. For discretization of all the
spatial terms except for the convective term in Eq.(2), a

For the boundary conditions, uniform inflow conditions,free-slip conditions, and convective outflow conditions areapplied at the inflow, lateral and upper, and outflow boundaries,
respectively. On the surfaces of the cube and the groundsurface, no-slip conditions are imposed. In the present study,
the Reynolds number is Re (=Uh / ν) = 104, where h is thelength of a side of the cube (height) and U is the wind speed atheight h at the inflow boundary. The time step is set to Δt = 2.0

second-order central difference scheme is applied. For theconvective term, a third-order upwind difference scheme isapplied. An interpolation technique based on four-pointhdifferencing and four-point interpolation by Kajishima is used
for the fourth-order central differencing that appears in thediscretized form of the convective term. For the weighting of
the numerical diffusion term in the convective termhdiscretized by third-order upwind differencing, α = 3.0 iscommonly applied in the Kawamura-Kuwahara scheme.
However, α = 0.5 is used in the present study to minimize theinfluence of numerical diffusion. For LES subgrid-scaleFig.2 Computational grid in the vicinity of the cubefrom the simulation with RIAM-COMPACT®, structured
grid, central plane (y = 0) normal to the spanwise (y) axis

Reports of Research Institute for Applied Mechanics, Kyushu University, No.150 March 2016

75(c) Top view (z = 0.5h), overall view(a) Side view (y = 0), overall viewhh(d) Top view (z = 0.5h), enlarged view(b) Side view (y = 0), enlarged viewFig.3 Computational grid used for the simulation with STAR-CCM+, unstructured gridmodels are referred to as Cases 1 to 5. The models
× 10-3 (h / U) for the simulation with RIAM-COMPACT®. In

considered in the present study are the same as those fromcontrast, the time step is set to Δt = 2.5 × 10-2 (h / U) for thethe previous study1, 2). A brief description of the WALE

simulation with STAR-CCM+.

model in Case 4 is as follows: the WALE model has been

Fig.2 shows the computational grid (structured grid) used forthe simulation with RIAM-COMPACT®. The number of grid

Spalart-Allmaras one-equation

points used for this simulation are 326 (x) × 226 (y) × 67 (z)Case 1eddy-viscosity turbulence model:

points (approximately 5 million points in total). The grid points

RANS

steady RANS

in the x- and y-directions are spaced at an even interval ofmodelsSST k-ω two-equation eddy

0.04h, and the grid points in the z-direction are spaced at

Case 2

uneven intervals ranging from 0.003h to 0.6h.

(URANS)For comparison, Fig.3 shows the computational grid
(unstructured grid) used for the simulation with STAR-CCM+.

LES

The total number of grid points is approximately 1.5 million

modelsCase 3
Case 4(1/3 of that used for the simulation with RIAM-COMPACT®).
The grid resolution in the vicinity of the cube in the simulation
with STAR-CCM+ is set to be nearly identical to that withmodels) considered in the present comparative study. For
convenience, simulations performed with the use of each of theStandard Smagorinsky model:
LES
WALE model: LES

Table 2 Turbulence models
used in the simulations with STAR-CCM+

RIAM-COMPACT®.
Tables 2 and 3 list the turbulence models (RANS and LES-viscosity model: unsteady RANSLES model

Case 5

Standard Smagorinsky model:
LES

Table 3 Turbulence model
used in the simulation with RIAM-COMPACT®

76

Uchida : Reproducibility of Complex Turbulent Flow Using Commercially-available CFD Software, Report 3

Flowfigures compare only the simulation results from Case 1(STAR-CCM+ with the steady RANS model; a steadysimulation in which the steady-state solution is obtained byusing the number of time steps specified in Table 1 for timemarching) and Case 5 (RIAM-COMPACT® with the LES
model) as an example. An examination of Figs.5 and 6
reveals the following result: although a complex turbulent
flow field is generated in the vicinity of the cube as was(a) Side view (y = 0)

described for Fig.4, no significant difference exists between
the results from the simulation which uses the RANS model(steady) and those from the simulation which uses the LES
model (the standard Smagorinsky model). That is, the overall
trends of the results are nearly the same between the twocases.
Figs.7 and 8 show comparisons of various turbulence
statistics acquired with the use of the turbulence models
considered for comparisons in the present study (RANS andLES models) (Tables 2 and 3). The turbulence statistics were(b) Top view (z = 0.5h), where h is the height of the cube
Fig.4 Wind tunnel experiment, flow visualizationby the smoke-wire method, instantaneous field
designed in such a way that 1) the eddy viscosity coefficient
becomes zero in the vicinity of the ground surface without
the use of a wall damping function and 2) the eddy viscosity
coefficient is not calculated for laminar shear flow.

6. Simulation Results and Discussions

evaluated at the positions x = -1h, 0h, +1h, and +3h. The
figures also include the turbulence statistics acquired from awind tunnel experiment previously conducted by the author.
Comparisons of the profiles of the mean streamwise (x)velocity (Fig.7) reveal that the profiles vary at x = +3h inassociation with the use of different turbulence models,
however, they generally resemble one another at the otherpositions (x = -1h, 0h, and +1h), independent of the
turbulence model used. Comparisons of the standard
deviation of the streamwise (x) velocity (Fig.8) show that no
significant non-zero values were output at any of theFirst, flow patterns generated in the vicinity of the cube

positions when using the RANS models, as was the case inconsidered in the present study are described based on

the previous study 1, 2). In contrast, the simulations with thephotographs acquired during a wind tunnel experiment

LES models reveal similar trends for the standard deviation(smoke-wire method) (Fig.4). Both the vertical and horizontalof the streamwise (x) velocity for both the simulations withcross-sections of the flow field (Figs.4(a) and 4(b),STAR- CCM+ (the standard Smagorinsky model and therespectively) show that the shear layer which separates from

WALE model) and with RIAM-COMPACT® (the standard

the upstream, upper corners of the cube rolls up into isolated

Smagorinsky model).

vortices. These isolated vortices then form into large-scale

Regarding the computational time, although the number ofvortices, which are periodically shed downstream of the cube

grid points used for the simulation with RIAM-COMPACT®

and then advance downstream. As a result, a three-(structured grid, approximately 5 million points) was

dimensional, complex turbulent flow field is generated in theapproximately three times as large as that used for thevicinity of the cube.

simulations

with

STAR-CCM+(unstructured

grid,

Figs.5 to 8 show comparisons of the simulation results.

approximately 1.5 million points), the simulation with

The time-averaged flow field and the turbulence statistics for

RIAM-COMPACT® completed much faster than those with

Case 5 in these figures (RIAM-COMPACT® with the LES

STAR-CCM+, as was the case in the previous study 1, 2).

model) were evaluated from the time period t = 100 - 200 (h /U), during which the flow field was fully developed.
Subsequently, comparisons of the visualized flow fields in
Figs.5 and 6 are discussed. Due to space limitations, theseReports of Research Institute for Applied Mechanics, Kyushu University, No.150 March 2016

Flow(a) Case 1, Simulation results from STAR-CCM+ with the use of the steady RANS model,
Spalart-Allmaras one-equation eddy-viscosity turbulence model

-1h

0h

+1h

+3h

height h(b) Case 5, Simulation results from RIAM-COMPACT® with the use of the LES model,
standard Smagorinsky model, time-averaged field
Fig.5 Comparison of the streamwise (x) velocity component distribution,
central plane (y = 0) normal to the spanwise (y) axis.
Here, the velocity component is normalized by the magnitude of the uniform inflow wind velocity.

77

78

Uchida : Reproducibility of Complex Turbulent Flow Using Commercially-available CFD Software, Report 3

Flow(a) Case 1, Simulation results from STAR-CCM+ with the use of the steady RANS model,
Spalart-Allmaras one-equation eddy-viscosity turbulence model

-1h

0h

+1h

+3h

height h(b) Case 5, Simulation results from RIAM-COMPACT® with the use of the LES model,
standard Smagorinsky model, time-averaged field
Fig.6 Comparison of velocity vectors, central plane (y = 0) normal to the spanwise (y) axis.
Here, the velocity component is normalized by the magnitude of the uniform inflow wind velocity.

Reports of Research Institute for Applied Mechanics, Kyushu University, No.150 March 2016

STAR-CCM+
RIAM-COMPACT®

x=-1h

x=0h
Local increase in velocity

Nearly the samevalues

x=+1h

x=+3h
Variations in profiles associatedwith the use of different
turbulence models

Similar trends between the
profiles from the simulations
with RANS and those with LES
Reverse flow region

Fig. 7 Comparison of the mean streamwise (x) velocity profiles.
Here, the velocity component is normalized by the upper-air wind velocity above the location of each profile evaluation.

79

80

Uchida : Reproducibility of Complex Turbulent Flow Using Commercially-available CFD Software, Report 3

STAR-CCM+
RIAM-COMPACT®

x=0h

x=-1h

Occurrence of maxima
Nearly the samevalues (zero)

x=+1h

Similar profile
trends among
the simulations
with LES models

x=+3hSimilar profile
trends among
the simulations
with LES models

Fig.8 Comparison of the standard deviation of the streamwise (x) velocity.
Here, the velocity component is normalized by the upper-air wind velocity above the location of each profile evaluation.

Reports of Research Institute for Applied Mechanics, Kyushu University, No.150 March 2016

7. Conclusion
In the previous paper 1, 2), the simulation results from
RIAM-COMPACT® natural terrain version of airflow
around an isolated-hill with a steep slope angle werecompared to those from another commercially available
CFD software.
In the present paper, in order to examine the prediction
accuracy of RIAM-COMPACT® (turbulence model: thestandard Smagorinsky LES model), developed by theauthor's research group, the simulation results from RIAMCOMPACT® of airflow around a three-dimensional cube
were compared to those from one of the leading software
packages, STAR-CCM+. For the simulations with STARCCM+, both RANS and LES turbulence models wereadopted. Specifically, for the RANS turbulence model, twosuch models were selected for use: the Spalart-Allmaras
one-equation eddy-viscosity model (steady RANS) and the
SST k-ω two-equation eddy-viscosity model (unsteady
RANS). Similarly, for the LES turbulence model, two suchmodels were selected for use: the standard Smagorinsky

the use of different turbulence models. However, at otherpositions (x = -1h, 0h, and +1h), the velocity profiles
generally resembled one another, independent of the
turbulence model used in each simulation. As for the standard
deviation of the streamwise (x) velocity, no significant
non-zero values were output with the use of the RANS
models at any of the positions, as was the case in the previous
study 1, 2). The simulations with the LES models revealed thatthe trends of this variable were similar among the simulations
with STAR-CCM+ (the standard Smagorinsky model and the
WALE model) and RIAM-COMPACT® (the standard
Smagorinsky model).
Regarding the computational time, although the numberof grid points used for the simulation with RIAMCOMPACT® was approximately three times as large(structured grid, approximately 5 million grid points) as thatused for the simulations with STAR-CCM+ (unstructured
grid, approximately 1.5 million grid points), the simulation
with RIAM-COMPACT® completed much faster than thosewith STAR-CCM+, as was the case in the previous study
1,2 )

.

model and the WALE model.
The comparisons of the simulation results from the use ofReferences

the four turbulence models revealed the following findings.
Comparisons of the visualized large-scale flow fields
showed no significant differences between the simulation

1)

Software –Report 1: For the Case of a Three-steady and unsteady RANS models) and those from the use

Dimensional Isolated-Hill With Steep Slopes–, Reportsof the LES models (i.e., the standard Smagorinsky model
turbulent flow field in the vicinity of the cube. The overall
trends of the visualized flow field were nearly the sameamong all the simulations.
Comparisons of the mean streamwise (x) velocity profiles
revealed variations in the velocity at x = +3h, associated with

Takanori UCHIDA, Reproducibility of Complex
Turbulent Flow Using Commercially-Available CFD

results from the use of the RANS turbulence models (i.e.,

and the WALE model) despite the generation of a complex

81

of RIAM, Kyushu University, No.150, in press, 2016
2)

Takanori UCHIDA, Reproducibility of Complex
Turbulent Flow Using Commercially-Available CFD
Software –Report 2: For the Case of a TwoDimensional Ridge With Steep Slopes–, Reports of
RIAM, Kyushu University, No.150, in press, 2016

82

Uchida : Reproducibility of Complex Turbulent Flow Using Commercially-available CFD Software, Report 3

Appendix
In order to compare the results of the simulation with RIAM-COMPACT® (turbulence model: the standard Smagorinsky LES
model) and those from the wind tunnel experiment previously conducted by the author more closely, an additional simulation
was performed with RIAM-COMPACT®, in which the computational domain upstream of the cube was extended. Fig.9 shows
the computational domain used in this simulation. Figs.10 - 12 show the simulation results. Both Figs.11 and 12 indicate that
RIAM-COMPACT® (turbulence model: the standard Smagorinsky LES model), with the use of the extended computational
domain, successfully reproduced the flow field from the wind tunnel experiment..

10h

h
h
9h
Flow
(Uniform flow)

9h

free-slip condition

6h

no-slip condition

7.5h
7.5h

■Number of computational grid points
221×121×101 (approx. 2.7 million)■Computational grid cell width
x-direction: 0.025 - 0.5h
y-direction: 0.025 - 0.3h
z-direction: 0.025 - 0.6h

Fig.9 Computational domain geometrically similar to the set-up from the wind tunnel experiment,boundary conditions identical to those in Fig.1 except as shown for the ground surface.

Reports of Research Institute for Applied Mechanics, Kyushu University, No.150 March 2016

-1h

Flow

0h

+1h

+3h

height h
Fig.10 Case 5, simulation results from RIAM-COMPACT®
with the use of the LES model,
the standard Smagorinsky model, time-averaged field(a)x=-1h(b)x=0h(c)x=+1h(d)x=+3h

Fig.11 Comparison of the mean streamwise (x) velocity profiles,
filled circle: wind tunnel experiment, line: simulation with RIAM-COMPACT® (turbulence model: LES)(a)x=-1h(b)x=0h(c)x=+1h(d)x=+3h

Fig.12 Comparison of the standard deviation of the streamwise (x) velocity,
filled circle: wind tunnel experiment, line: simulation with RIAM-COMPACT® (turbulence model: LES)

83