bluuebunny/crossref_metadata_2025 huggingface dataset:
Micromechanical modeling of Common yew and Norway spruce
Authors: Bader Thomas K. , de Borst Karin , Eberhardsteiner Josef
Published: November 2013

In this contribution, a micromechanical modeling approach in the framework of poromechanics is adopted to study structure‐stiffness relations of two quite different species, namely spruce and yew, in detail. In particular, microstructural specialties of yew and spruce are assessed. A dominant influence of the cellulose content and its orientation on the stiffness of the cell wall is revealed, while on the macroscopic scale, density is found to be the governing microstructural characteristic for elastic properties. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A constitutive model for granular materials with microstructures using the concept of energy relaxation
Authors: Khan Muhammad Sabeel , Hackl Klaus
Published: November 2013

In this paper, we present a constitutive model for granular materials exhibiting microstructures using the concept of energy relaxation. Within the framework of Cosserat continuum theory the free energy of the material is enriched with an interaction energy potential taking into account the counter rotations of the particles. The enhanced energy potential fails to be quasiconvex. Energy relaxation theory is employed to compute the relaxed energy which yields all possible displacement and micro‐rotations field fluctuations as minimizers. Based on a two‐field variational principle the constitutive response of the material is derived. The developed constitutive model is then implemented in a finite element analysis program using the finite element method. Numerical simulations are presented to observe the localized deformation phenomenon in a granular medium. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Bacterial methane oxidation in landfill cover layers ‐ a coupled FE multiphase description
Authors: Sindern Andrea , Ricken Tim , Bluhm Joachim , Widmann Renatus , Denecke Martin
Published: November 2013

Landfill gas is composed of methane (CH4) and (CO2) at a ratio of about (60% – 40%), whereby the impact of methane on the greenhouse effect is about 25 times higher than that of carbon dioxide. Bacterial methane oxidation, taking place in the landfill cover layer, helps to reduce the climate active emissions from landfill sites. This contribution presents a theoretical and numerical approach to model the coupled processes of bacterial methane oxidation. An isothermal biphasic model based on the Theory of Porous Media (TPM) and Mixture Theory is introduced as well as the coupled finite element (FE) calculation concept. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On heat exchange and heat transport in a geothermal plant
Authors: Koch David , Ehlers Wolfgang
Published: November 2013

In the long term, the only way to address the challenging task of power supply, is to make renewable energy sources economically attractive and to use them efficiently. In particular, geothermal energy is promising to take over the base load of the power supply. Nevertheless, a lot of investigations needs to be made to use the almost inexhaustible source of thermal energy in the interior of the earth effectively.

Starting from the initially isothermal state, a cold fluid is injected through a borehole into a rock. By the rising pressure gradient, the fluid flows through the porous rock and escapes through another borehole. While the fluid passes the micro cracks in the hot rock, the water is heated by the rock due to the heat exchange between the constituents. This process is simulated based on the Theory of Porous Media (TPM). The presented modelling approach of the heat transport and the flow processes in a fully saturated subsurface includes two non‐isothermal constituents: an elastically deformable, materially incompressible solid skeleton where thermal expansion is neglected, and a viscous, materially incompressible fluid constituent.

To solve the initial‐boundary‐value problem, the governing primary variables of the coupled model are spatially approximated by mixed finite elements, and the time‐discretisation is carried out by an implicit Euler time‐integration scheme. The aim of the presented numerical simulations is to study the heat transport and to evaluate the efficiency by varying flow rates. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Linear and nonlinear Finite Element modeling of coupled electro‐magneto‐mechanical multifield problems
Authors: Avakian Artjom , Ricoeur Andreas
Published: November 2013

In this paper we present the theoretical background and application of Finite Element algorithms for linear and nonlinear problems of multiple field coupling. They enable the prediction of the electromagnetomechanical behavior of materials and structures and supply useful tools for the optimization of multifunctional composites. First, linear three‐field coupling is presented within the context of a Finite Element implementation. Then, a homogenization procedure is discussed. Finally, a micromechanical model for nonlinear ferroelectric constitutive behavior and its numerical realization are outlined. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
High‐order time‐integration applied to p‐version finite elements within finite strain thermo‐viscoelasticity
Authors: Hartmann Stefan , Netz Torben
Published: November 2013

In this essay a fully coupled, monolithic thermo‐mechanical coupled simulation using high‐order finite elements based on hierarchical shape‐functions in combination with a high‐order time‐integration scheme using diagonally‐implicit Runge‐Kutta schemes is presented. The constitutive model is based on a finite strain thermo‐viscoelasticity relation of overstress‐type. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Energy‐Conserving Data Transfer in the Partitioned Treatment of Thermo‐Viscoplastic Problems
Authors: Erbts Patrick , Rothe Steffen , Düster Alexander , Hartmann Stefan
Published: November 2013

Partitioned coupling approaches are a well‐established solution strategy for the numerical treatment of multi‐physical problems. The nature of the decoupled algorithm requires a repetitive data exchange to achieve a proper balance between the different fields concerned. In the case of non‐matching meshes, the data transfer becomes of particular importance when the values of interest are only available at the local integration points. In this case, an additional interpolation scheme has to be initialized in order to assure an energy‐conserving data transfer. This contribution looks at a thermo‐viscoplastic material that requires the interpolation of history‐dependent data onto the thermal mesh. We propose a technique employing a least‐square fit procedure and present a numerical example demonstrating the accurate data transfer. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Degree of cure‐dependent modelling for polymer curing processes at small strains
Authors: Hossain Mokarram , Saxena Prashant , Steinmann Paul
Published: November 2013

In this paper, a thermodynamically consistent small strain constitutive model is formulated that is directly based on the degree of cure, a key parameter in the curing (reaction) kinetics. The new formulation is also in line with the earlier proposed hypoelastic approach, cf. Hossain et al., 2010. The curing process of polymers is a complex phenomenon involving a series of chemical reactions which transform a viscoelastic fluid into a viscoelastic solid during which the temperature, the chemistry and the mechanics are coupled. Some representative numerical examples conclude the paper and show the capability of the newly proposed constitutive formulation to capture major phenomena observed during the curing processes of polymers. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
FE‐Analysis of concentration dependent healing processes in a polymer matrix
Authors: Specht Steffen , Bluhm Joachim , Schröder Jörg
Published: November 2013

In this contribution, a macroscopic four‐phase model, based on the Theory of Porous Media, is presented to simulate healing processes in a polymer matrix which depend on the amount (concentration) of catalysts. Therefore, the healing process is described by the phase transition from liquid like healing agents to solid like healed material. This phase transition is a function depending on the concentration. To show the applicability of the developed model, a numerical example will be presented. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Methodenentwicklung zur numerischen Strömungsanalyse von Schaufelwasserrädern
Authors: Schippke Hans‐Henning , Seidel Christian , Zilian Andreas , Dinkler Dieter
Published: November 2013

Es wird ein Berechnungsmodell vorgestellt, mit dem eine numerischen Analyse der Strömungsvorgänge innerhalb von Schaufelwasserrädern möglich ist. Der Arbeitsschwerpunkt liegt dabei auf der strömungsmechanischen Optimierung von Hochleistungswasserrädern der Weiterentwickelten Wasserradtechnologie. In dem Berechnungsmodell werden die inkompressiblen Navier‐Stokes‐Gleichungen in den unabhängigen Variablen Geschwindigkeiten und Druck mit Hilfe der zeit‐diskontinuierlichen Raum‐Zeit‐Finite‐Elemente‐Methode diskretisiert und die auftretende Gebietsveränderung infolge der sich drehenden Struktur mit der Shear‐Slip Mesh Update Methode als diskontinuierlichem Netzbewegungsverfahren erfasst. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Computational Modeling of Liquid Droplets Moving on Rough Surfaces
Authors: Rasool Raheel , Osman Muhammad , A. Sauer Roger
Published: November 2013

We present a de‐coupled approach for computational modeling of liquid droplets moving on rough substrate surfaces. The computational model comprises solving the membrane deformation problem and the fluid flow problem in a segregated manner. The droplet shape is first computed by solving the Young‐Laplace equation where contact constraints, due to the droplet‐substrate contact, are applied through the penalty method [1]. The resulting configuration constitutes the domain for the fluid flow problem, where the bulk fluid behavior is modeled by the unsteady Stokes' flow model expressed in Arbitrary Lagrangian‐Eulerian (ALE) framework. The entire analysis is performed in the framework of Finite Element Method (FEM). Application of the approach to the case of a droplet moving on a rough surface is presented as an example. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Coupled Multi‐field and Multi‐rate Problems – Numerical Solution and Stability Analysis
Authors: Zinatbakhsh Seyedmohammad , Markert Bernd , Ehlers Wolfgang
Published: November 2013

The numerical solution of coupled differential equation systems is usually done following a monolithic or a decoupled algorithm. In contrast to the holistic monolithic solvers, the decoupled solution strategies are based on breaking down the system into several subsystems. This results in different characteristics of these families of solvers, e. g., while the monolithic algorithms provide a relatively straight‐forward solution framework, unlike their decoupled counterparts, they hinder software re‐usability and customisation. This is a drawback for multi‐field and multi‐rate problems. The reason is that a multi‐field problem comprises several subproblems corresponding to interacting subsystems. This suggests exploiting an individual solver for each subproblem. Moreover, for the efficient solution of a multi‐rate problem, it makes sense to perform the temporal integration of each subproblem using a time‐step size relative to its evolution rate. Nevertheless, decoupled solvers introduce additional errors to the solution and, thus, they must always be accompanied by a thorough stability analysis.

Here, tailored solution schemes for the decoupled solution of multi‐field and multi‐rate problems are proposed. Moreover, the stability behaviour of the solutions obtained from these methods are studied. Numerical examples are solved and the reliability of the outcome of the stability analysis is investigated. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Estimation of large domain Al foam permeability by Finite Difference methods
Authors: Osorno Maria , Steeb Holger , Uribe David , Ruiz Oscar
Published: November 2013

Classical methods to calculate permeability of porous media have been proposed mainly for high density (e.g. granular) materials. These methods present shortcomings in high porosity, i.e. high permeability media (e.g. metallic foams). While for dense materials permeability seems to be a function of bulk properties and occupancy averaged over the volume, for highly porous materials these parameters fail to predict it. Several authors have attacked the problem by solving the Navier‐Stokes equations for the pressure and velocity of a liquid flowing through a small domain (Ωs) of aluminium foam and by comparing the numerical results with experimental values (prediction error approx. 9%). In this article, we present calculations for much larger domains (ΩL) using the Finite Difference (FD) method, solving also for the pressure and velocity of a viscous liquid flowing through the Packed Spheres scenario. The ratio Vol(ΩL)/Vol(Ωs) is around 103. The comparison of our results with the Packed Spheres example yields a prediction error of 5% for the intrinsic permeability. Additionally, numerical permeability calculations have been performed for Al foam samples. Our geometric modelling of the porous domain stems from 3D X‐ray tomography, yielding voxel information, which is particularly appropriate for FD. Ongoing work concerns the reduction in computing times of the FD method, consideration of other materials and fluids, and comparison with experimental data. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling reorientation phenomena in nonwoven materials with random fiber network microstructure
Authors: Raina Arun , Linder Christian
Published: November 2013

In this work, a micromechanically motivated affine full network model (AFNM) is used to simulate the load‐displacement response of nonwoven materials. These materials are made from synthetic advanced fibers by bonding or interlocking networks of randomly laid fibers through mechanical, chemical or thermal processes. This results into a random fibrous network microstructure and a highly inhomogeneous response to external loadings with a very high degree of anisotropy. The load‐displacement response under large strains is observed to be highly non‐linear with a stiffening behavior which is also accompanied by complex dissipative phenomena. The preliminary simulation results with the AFNM, after reducing to two‐dimensional setting, highlight its limitations and help identify the areas of improvement for a realistic material modeling. Reorientation of fibers are shown to play a critical role in the overall macroscale response of the materials. A new evolution law for reorientation is presented in the form of a first order ordinary differential equation where an exact analytical solution to the same is also computed. Improvements of the predicted load‐displacement response signify the microscopic origins of the non‐linear stiffening behavior as reorientation of fibers. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Generalized boundary conditions on representative volume elements and their use in determining the effective material properties
Authors: Glüge Rainer
Published: November 2013

We discuss generalized boundary conditions for representative volume elements (RVE), which include the classical boundary conditions as special cases. From the generalization, stochastic boundary conditions are derived. These allows to adjust the the stiffness of the boundary conditions smoothly between the extremal cases of homogeneous strain and homogeneous stress boundary conditions. We found that it needs to be distinguished between the resistance of the boundary conditions against homogeneous and inhomogeneous RVE deformation. The stochastic BC can combine the moderate stiffness of the well known periodic boundary conditions with the high resistance against localization of the homogeneous strain boundary conditions. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Non‐linear deformation properties of materials with stochastically distributed anisotropic inclusions
Authors: Nazarenko Lidiia , Bargmann Swantje , Khoroshun Leonid
Published: November 2013

In the present contribution, the problem of non‐linear deformation of materials with stochastically distributed anisotropic inclusions is considered on the basis of the methods of mechanics of stochastically non‐homogeneous media. The homogenization model of materials of stochastic structure with physically non‐linear components is developed for the case of a matrix which is strengthened by unidirectional ellipsoidal inclusions. It is assumed that the matrix is isotropic, deforms non‐linearly; inclusions are linear‐elastic and have transversally‐isotropic symmetry of physical and mechanical properties. Stochastic differential equations of physically non‐linear elasticity theory form the underlying equations. Transformation of these equations into integral equations by using the Green's function and application of the method of conditional moments allow us to reduce the problem to a system of non‐linear algebraic equations. This system of non‐linear algebraic equations is solved by the Newton‐Raphson method. On the analytical as well as the numerical basis, the algorithm for determination of the non‐linear effective characteristics of such a material is introduced. The non‐linear behavior of such a material is caused by the non‐linear matrix deformations. On the basis of the numerical solution, the dependences of homogenized Poisson's coefficients on macro‐strains and the non‐linear stress‐strain diagrams for a material with randomly distributed unidirectional ellipsoidal pores are predicted and discussed for different volume fractions of pores. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical analysis of two‐phase magneto‐electric composites
Authors: Labusch Matthias , Keip Marc‐André , Schröder Jörg , Lupascu Doru C.
Published: November 2013

The focus of this paper is on the simulation of two‐phase magneto‐electric (ME) composites, consisting of a piezoelectric matrix with piezomagnetic inclusions. In such composites, the coupling between electric and magnetic fields is strain‐induced and thus ME coupling arises as a product porperty. In order to compute the effective properties of the composite a computational homogenization scheme based on the Finite Element Method will be applied. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Homogenization of Elastic Properties of Short Fiber Reinforced Composites Based on Discrete Microstructure Data
Authors: Müller Viktor , Böhlke Thomas , Dillenberger Felix , Kolling Stefan
Published: November 2013

Since the microstructure of short fiber reinforced composites is inhomogeneous, the application of micromechanical models is useful, that take into account their characteristics like the fiber orientation and the aspect ratio of fibers. Two different methods are considered in this work: A two‐step approach is utilized to get approximately the upper and lower bounds of the elastic properties. Furthermore, an approximation for the elastic properties is calculated by the self‐consistence method. Both methods use discretely microstructural information including the length, the diameter and the orientation of each single fiber. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Linking Micro‐ and Macroscopic Aspects of a Dislocation Based Continuum Model by Investigating the Dislocation Double Pileup
Authors: Schmitt Severin , Schulz Katrin , Dickel Doyl , Gumbsch Peter
Published: November 2013

In this contribution we discuss the problem of a dislocation double pileup at impenetrable boundaries which serves as a benchmark test to examine the continuum dislocation dynamics (CDD). We enhance a formulation for a numerical implementation and the mean‐field theory to account for the ‘long‐range’ stress field due to inhomogeneous plastic deformations by a suitable correction term. This allows us to handle the motion of dislocation densities at impenetrable boundaries and study the influence of dislocation interactions on a scale much smaller than the scale of the proposed mean‐field stress. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Influence of pitching on performance of VAWTs
Authors: Bogateanu Radu , Dumitrache Alexandru , Cardos Vladimir , Dumitrescu Horia
Published: November 2013

Self‐ starting is the major obstacle to be overcome for successful design of a vertical axis wind turbine (VAWT). In the past has been suggested that pitching the turbine blades such that pitch angle is not 90 degrees allows for self‐starting. To understand the physics surrounding pitching, an analysis is carried out for a common airfoil profile, NACA 0012. The vortex model is used to predict aerodynamic performance of VAWT with pitched blades at various angles. As a result of the analysis carried out for the airfoil at various pitch angles, it was shown that the “dead band” phenomenon could be overcome, but only slightly. At the same time, to overcome the “dead band” with a level on confidence, torques in the tip speed ratio (TSR ) range of 0.75 to 2.75 must be increased to values further above zero. The paper aimed at giving an insight into the small wind turbine starting behavior and its influence parameters. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The boundary layer in the hub area of wind turbine blades at high wind speeds
Authors: Dumitrescu Horia , Cardos Vladimir , Frunzulica Florin
Published: November 2013

At low tip speed ratios, the strongest effect at the inboard half‐span, when a vortex like flow occurs, is produced. These 3‐D rotational effects contribute to a stall delay as well as higher lift and angles of attack at the inboard sections, as compared to 2‐D flow conditions. A greater understanding of the mechanisms and properties of the shear layer close to the upper side surface of blade is sought through the development of an analytic theory and then is completed by CFD computations. The results show that the secondary flow has a slip effect on the blade surface and its circumferential velocity is less than that of blade revolution, particularly important for TSR <3.0. While at the high tip speed ratios the flow around the blade is much as the 2‐D one, then at the low tip speed ratios, TSR < 3.0 the flow behaves rather like the impinging flow on a rotating disc. Therefore, the 3‐D rotational effects dominate the flow at high wind speeds and a special approach of such flows would be to assume. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Non‐linear Proper Orthogonal Decomposition Reduced Order Modeling: Bifurcation Study of a Natural Convection Circuit
Authors: Prill Dennis P. , Class Andreas G.
Published: November 2013

Boiling water reactors (BWRs) not only show growing power oscillations at high‐power low‐flow conditions but also amplitude limited oscillations with temporal flow reversal. Methodologies, applicable in the non‐linear regime, allow insight into the physical mechanisms behind BWR dynamics. The present paper aims at a general non‐linear methodology capable to achieve reliable and numerical stable reduced order models (ROMs). Model‐specific options and prediction capabilities are adressed and illustrated by means of two strongly non‐linear dynamical systems: Firstly, the tubular reactor (TR), treated as a generic “pathologic” test case for perturbation investigations violating the inlet conditions, and secondly, the natural convection in a closed circuit (NCC), considered due to dynamical similarities to BWRs. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A model for fluid flow in non‐fully filled tribological interfaces – Part 1: Basics and Numerics
Authors: Müller Michael , Bubser Florian , Ostermeyer G.‐P.
Published: November 2013

In literature, most contributions on starved lubrication focus on the occurring pressures in macroscopic devices. Hereby, usually the Reynolds equation is modified in different ways. In contrast to this proceeding, this paper's intention is the general investigation of this tribological regime to get a fundamental comprehension on the transition from boundary lubrication to mixed lubrication. The respective model describes the flow of the fluid through two rough surfaces moving relative to each other. The lack of fluid is regarded by the fact that elements may not be fully filled with the fluid. Only elements where the fluid fully fills the gap, generate a pressure. This effect is considered by a type of unilateral constraint in combination with a penalty function. The fluid flow is computed according to the Navier‐Stokes equation. In combination with the continuity equation, a set of implicit nonlinear equations has to be solved. Its potential and basic application fields are finally discussed. A further paper will show applications of the algorithm towards different scenarios. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical Simulation of Turbulent Swirling Flows
Authors: Ćoćić Aleksandar , Pritz Balazs , Gabi Martin , Lečić Milan
Published: November 2013

In this paper, turbulent swirling flow in circular pipe in the wake behind an axial fan is investigated by URANS and LES using two different CFD codes: SPARC, developed at Institute of Fluid Machinery, at Karlsruhe Institute of Technology and OpenFOAM. Results of simulations are compared with experimental results obtained with LDA measurement techniques in that flow field. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical and experimental investigation of the turbulent flow through a low‐pressure turbine cascade in the endwall region
Authors: Koschichow Denis , Fröhlich Jochen , Ciorciari Roberto , Kirik Ilker , Niehuis Reinhard
Published: November 2013

In the present work, direct numerical simulations (DNS) of the flow through a low‐pressure linear turbine cascade T106 with parallel endwalls were conducted to investigate the effects of unsteady passing wakes of the upstream blade row on the secondary flow in the endwall region of the passage. The impact of the wakes on the secondary flow is discussed by means of the time‐averaged values. Furthermore, the results of DNS are compared with experimental data. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Influence of Mass Loading on Particle‐Laden Turbulent Pipe Flow
Authors: Reinhardt Yvonne , Kleiser Leonhard
Published: November 2013

A CFD code in the framework of OpenFOAM was validated for simulations of particle‐laden pipe and channel flows at low to intermediate mass loadings. The code is based on an Eulerian two‐fluid approach with Reynolds‐averaged conservation equations, including turbulence modeling and four‐way coupling. Pipe flow simulations of particles in air against gravity were conducted at Reynolds numbers up to 50000. The particle mass loading was varied and its effect on the mean velocities and turbulent fluctuations of the two phases was studied. Special attention was paid to the influence of mass loading on the centerline velocity and the wall shear velocity of the fluid phase for various flow parameters and particle properties. Empirical correlations were established between these two quantities and the flow Reynolds number, particle Reynolds number, Stokes number and particle to fluid density ratio for a range of particle mass loadings. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Coarse‐Grid‐CFD for a Wire Wrapped Fuel Assembly
Authors: Viellieber Mathias , Dietrich Philipp , Class Andreas G.
Published: November 2013

Computational fluid dynamics (CFD) simulations of complete nuclear reactor core geometries requires exceedingly large computational resources. However, in most cases there are repetitive geometry‐ and flow patterns allowing the general approach of creating a parameterized model for one segment and composing many of these reduced models to obtain the entire reactor simulation. Traditionally, this approach lead to so‐called subchannel analysis codes that are relying heavily on transport models based on experimental and empirical correlations. With our method, the Coarse‐Grid‐CFD (CGCFD), we intend to replace the experimental or empirical input with CFD data. Our method is based on detailed and well‐resolved CFD simulations of representative segments. From these simulations we extract and tabulate volumetric source terms. Parameterized data is used to close an otherwise strongly under resolved, coarsely meshed model of a complete reactor setup. In the previous formulation only forces created internally in the fluid are accounted for. The Anisotropic Porosity (AP) formulation wich is subject of the present investigation adresses other influences, like obstruction and flow guidance through spacers and in particular geometric details which are under resolved or ignored by the coarse mesh. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
ALE‐FEM for Two‐Phase Flows
Authors: Hahn Andreas , Held Kristin , Tobiska Lutz
Published: November 2013

We present a finite element method for the flow of two immiscible incompressible fluids in two and three dimensions. Thereby the presence of surface active agents (surfactants) on the interface is allowed, which alter the surface tension. The model consists of the incompressible Navier‐Stokes equations for velocity and pressure and a convection‐diffusion equation on the interface for the distribution of the surfactant. A moving grid technique is applied to track the interface, on that account a Arbitrary‐Lagrangian‐Eulerian (ALE) formulation of the Navier‐Stokes equation is used. The surface tension force is incorporated directly by making use of the Laplace‐Beltrami operator technique [5]. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A hybrid level set / front tracking approach
Authors: Basting Steffen , Weismann Martin , Prignitz Rodolphe
Published: November 2013

In finite element simulations of fluid flows with free boundaries, the representation of boundaries and interfaces plays an essential role. Common approaches can be categorized into two groups, interface tracking and interface capturing methods, each with individual pros and cons. The proposed approach provides a hybrid description of the interface. The main ingredient is a mesh optimization technique that aligns a given triangulation to the geometry which is implicitly represented by a level set function. Resulting triangulations are of optimal quality while connectivity of the mesh is retained. Consequently, finite element spaces defined on the aligned triangulations can be efficiently modified to account for solution specific properties such as discontinuities across interfaces.

We outline an ALE‐based finite element method which can be used in various application scenarios. We briefly demonstrate the benefits of the method by applying it to two applications: The first application is concerned with a finite element method for particulate flows for which we provide an a priori error estimate. The estimate indicates that by using the proposed approach, h2 convergence can be obtained on aligned meshes, while a sharp h1/2 results holds for non‐aligned meshes. The second application is concerned with a fully coupled two‐phase flow benchmark problem. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical analysis of wave propagation in fluid‐filled deformable tubes
Authors: Uribe David , Steeb Holger , Saenger Erik H. , Kurzeja Patrick , Ruiz Oscar
Published: November 2013

The theory of Biot describing wave propagation in fluid saturated porous media is a good effective approximation of a wave induced in a fluid‐filled deformable tube. Nonetheless, it has been found that Biot's theory has shortcomings in predicting the fast P‐wave velocities and the amount of intrinsic attenuation. These problems arises when complex mechanical interactions of the solid phase and the fluid phase in the micro‐scale are not taken into account. In contrast, the approach proposed by Bernabe does take into account micro‐scopic interaction between phases and therefore poses an interesting alternative to Biot's theory. A Wave propagating in a deformable tube saturated with a viscous fluid is a simplified model of a porous material, and therefore the study of this geometry is of great interest. By using this geometry, the results of analytical and numerical results have an easier interpretation and therefore can be compared straightforward. Using a Finite Difference viscoelastic wave propagation code, the transient response was simulated. The wave source was modified with different characteristic frequencies in order to gain information of the dispersion relation. It was found that the P‐wave velocities of the simulations at sub‐critical frequencies closely match those of Bernabe's solution, but at over‐critical frequencies they come closer to Biot's solution. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Analysis of optimal metal flow in incremental sheet forming
Authors: Bambach Markus , Grzibovskis Richards
Published: November 2013

Sheet metal forming processes are manufacturing processes in which a piece of sheet metal is shaped to a specified geometry, e.g. a car door. A promising new forming process is incremental sheet metal forming, in which the deformation is imposed by a progressive, localised plastic deformation induced by a pin‐like forming tool that moves under numerical control along a pre‐defined trajectory. This process offers the possibility to control the metal flow by adjusting the trajectory of the forming tool. Mathematically, sheet metal forming processes can be considered as a mapping between the initial, undeformed sheet metal and the final, deformed state. In most applications the surface area of the sheet metal is enlarged during the deformation. In this case, an ideal mapping would produce a homogeneous stretching of the sheet metal such that the final sheet thickness is the same everywhere. In this work, we analyze the following question: for each point in the initial configuration, what must be its location on the final geometry such that the thickness is the same everywhere? We construct a special type of surface evolution that combines flow along the surface normal with appropriate tangential velocity corrections, and show that the flow yields a constant sheet thinning on a sheet metal. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Treatment Planning Optimization for Radiotherapy
Authors: Barnard Richard C. , Frank Martin , Herty Michael
Published: November 2013

We study the problem of treatment planning in radiotherapy. We use an energy‐dependent Boltzmann‐based particle transport model as a partial integro‐differential constraint for a convex optimization problem. We solve the resulting optimal control problem using a minimum entropy moment closure. Numerical results for problems on patient data are presented. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Variation of friction drag via spanwise transversal surface waves
Authors: Meysonnat Pascal , Klumpp Stephan , Meinke Matthias , Schröder Wolfgang
Published: November 2013

The turbulent wall shear stress can be influenced through the introduction of spanwise velocity components in the near‐wall flow field. The underlying physical mechanisms for the drag reduction still remains to be fully understood. Two distinct wave configurations are analyzed and compared to an unactuated turbulent boundary layer to obtain further inside of the drag reducing mechanism using the dynamic mode decomposition. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the dynamics of the vortex structures generated by plasma DBD actuator
Authors: Procházka Pavel , Uruba Václav , Antoš Pavel
Published: November 2013

The plasma actuator is used to generate pseudo‐periodical vortices moving almost parallel to the wall under various settings of high‐voltage high‐frequency power AC. Low‐frequency amplitude modulation is desired to generate vortices, otherwise wall‐jet‐like flow is present. It will be shown how the dynamics of generated coherent vortices alternates depending on generator setting, frequency spectrum will be introduced in dependency on frequency of amplitude modulation and duty cycle. Measurements will be performed using TR‐PIV technique or HW anemometry across wall‐jet flow. The generated flow patterns are to be applied for control of boundary layers. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The Armstrong‐Frederick Plasticity model with Cosserat effects
Authors: Chełmiński Krzysztof , Neff Patrizio , Owczarek Sebastian
Published: November 2013

We propose an extension of equations formulated by Armstrong and Frederick which includes micropolar effects. We study existence of solutions to the quasistatic Armstrong‐Frederick model with Cosserat effects which is still of non‐monotone type. It was shown that the limit in the Yosida approximation process satisfies the energy inequality. The limit functions have a better regularity than it could be found in the literature, where the original Armstrong‐Frederick model was studied. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Some Poincaré type inequalities for quadratic matrix fields
Authors: Bauer Sebastian , Neff Patrizio , Pauly Dirk , Starke Gerhard
Published: November 2013

We present some Poincaré type inequalities for quadratic matrix fields with applications e.g. in gradient plasticity or fluid dynamics. In particular, an application to the pseudostress‐velocity formulation of the stationary Stokes problem is discussed. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Cavitation and Singular Solutions in Nonlinear Elastodynamics
Authors: Giesselmann Jan
Published: November 2013

Based on works of Ball (1982) and Pericak‐Spector and Spector (1988), we investigate singular solutions to the compressible nonlinear elastodynamics equations. These solutions have discontinuous displacement fields and describe fracture or cavitation. We explore a definition of singular solution via approximating sequences of smooth functions. We employ these approximating sequences to investigate the energy of such solutions, taking into account the energy needed to open a crack or hole. We show that the existence of singular solutions and the finiteness of their energy is strongly related to the behavior of the stress response function for infinite stretching. We outline our findings in one space dimension. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Gamma‐convergence for Ginzburg‐Landau functional with degenerate 3‐well potential in one dimension
Authors: Raguž Andrija
Published: November 2013

We consider the Ginzburg‐Landau functional in one dimension, endowed with epsilon‐dependent 3‐well potential which degenerates as small parameter epsilon tends to zero. By using the approach in G. Alberti, S. Muller: A new approach to variational problems with multiple scales, Comm. Pure Appl. Math. 54, 761‐825 (2001), we obtain Gamma‐convergence as small parameter epsilon tends to zero. We also recover the underlying geometric properties shared by all minimizing sequences. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Evolutional contact with Coulomb's friction on a periodic microstructure
Authors: Orlik Julia , Shiryaev Vladimir
Published: November 2013

We consider the elasticity problem in a heterogeneous domain with an ε‐periodic micro‐structure, ε ≪ 1, including a multiple micro‐contact in a simply connected matrix domain with inclusions completely surrounded by cracks, which do not connect the boundary, or a textile‐like material. The contact is described by the Signorini and Coulomb‐friction contact conditions. In the case of the Coulomb friction, the dissipative functional is state dependent, like in [2]. A time discretization scheme from [2] reduces the contact problem to the Tresca one (with prescribed frictional traction or state independent dissipation) on each time‐increment. We further look for the spatial homogenization. The limiting energy and the dissipation term in the stability condition were obtained for the contact with Tresca's friction law in [4] for closed cracks and can be extended to textile‐like materials. Using these results and the concept of energetic solutions for evolutional quasi‐variational problems from [2], for a uniform time‐step partition, the existence can be proved for the solution of the continuous problem and a subsequence of incremental solutions weakly converging to the continuous one uniformly in time. Furthermore, the irreversible frictional displacements at micro‐level lead to a kind of an evolutional plastic behavior of the homogenized medium. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A PDE constraint formulation of Open Pit Mine Planning Problems
Authors: Strogies Nikolai , Griewank Andreas
Published: November 2013

The modeling of open pit mine schedules employing continuous functions [1] yields several difficulties regarding the optimization process. Besides the dynamic capacity constraint one of the most challenging problems is a proper way of ensuring the physical stability of the obtained profile functions of an excavation schedule. This paper shows, that under certain suitable assumptions the physically stable excavation path is the solution of a certain Hamilton Jacobi equation. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Parallel solvers for flow control based on domain decomposition
Authors: Ketelaer Eva , Heuveline Vincent , Heinkenschloss Mathias
Published: November 2013

We sketch a non‐overlapping domain decomposition method (DDM) for a linear quadratic optimal control problem governed by the Oseen equations. The DDM is applied to the system of necessary and sufficient optimality conditions. The approach extends balanced Neumann Neumann DDMs from single partial differential equations (PDEs) to the optimization control context, and it extends previous work on balanced Neumann Neumann DDMs for the optimal control of scalar elliptic PDEs to the optimal control of the Oseen equations. This extension requires a careful handling of the incompressibility constraint and resulting compatibility conditions, as well as a careful handling of the advection term. The DDM is used to parallelize the matrix‐vector operations for the optimality system, as well as to parallelize the preconditioner. We present two approaches. One tackles the global optimality system directly, the other forms the Schur complement corresponding to variables on the subdomain interfaces. We present numerical experiments which clearly show the potential of the approaches. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Iterative solution of inconsistent systems of linear inequalities
Authors: Carp Doina , Popa Constantin , Serban Cristina
Published: November 2013

In 1980 S.P. Han proposed a finitely terminating (in exact arithmetic) algorithm for solving an inconsistent system of linear inequalities in a least squares sense. This algorithm uses a singular value decomposition of a submatrix of the problem matrix on each iteration, making it impractical for all but only smaller problems. In this paper we show that a modification of Han's algorithm allows us to introduce an iterative approximation to the singular value decomposition solution. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Diagonal scaling in eigenvalue localization for the Schur complement
Authors: Cvetković Ljiljana , Nedović Maja
Published: November 2013

Geršgorin theorem is a well‐known result in eigenvalue localization area. In this paper, using diagonal scaling method, we obtain more Geršgorin‐type localizations for the eigenvalues of the Schur complement using the entries of the original matrix instead of the entries of the Schur complement. We deal with classes of matrices with some form of diagonal dominance. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Backward error analysis of an inexact Arnoldi method
Authors: Kandler Ute , Schröder Christian
Published: November 2013

We investigate the behavior of Arnoldi's method for Hermitian matrices in the case of inexact vector operations. A special purpose variant of Gram Schmidt orthogonalization is introduced which computes a nearly orthogonal Krylov subspace basis and additionally implicitly provides an exactly orthogonal basis. In the second part we perform a backward error analysis and show that the exactly orthogonal basis satisfies a Krylov relation for a perturbed system matrix. The norm of the backward error is shown to be on the level of the accuracy of the vector operations. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Convection‐diffusion‐reaction problems on a B‐type mesh
Authors: Brdar Mirjana , Zarin Helena
Published: November 2013

One‐dimensional singularly perturbed problems with two small parameters are considered. Numerical methods for such problems are discussed in several papers, but on a Shishkin‐type mesh. The first optimal result of convergence in an energy norm on a Bakhvalov‐type mesh for one‐dimensional convection‐diffusion problem was given by Roos in [9]. In this paper we analyze Galerkin finite element method on a Bakhvalov‐type mesh for two‐parameter convection‐diffusion‐reaction problems. In the interpolation error analysis, instead of the usual interpolation operator in the finite element space we use a quasi‐interpolant with improved stability properties. We prove that the finite element method for these problems is uniformly convergent in the energy norm. Numerical results confirm our theoretical analysis and show first‐order convergence rate. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Verification of Functional A Posteriori Error Estimates for Obstacle Problem in 1D
Authors: Harasim Petr , Valdman Jan
Published: November 2013

We verify functional a posteriori error estimates of numerical solutions of a obstacle problem proposed by S. Repin. The simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution can be derived and also an exact quadrature can be applied. Quality of a numerical solution obtained by the finite element method is compared with the exact solution to demonstrate the sharpness of the studied error estimated. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Making the semi‐implicit space‐time conservation‐element solution‐element method of Jerez et al. more explicit
Authors: Niessner Herbert
Published: November 2013

In the beginning of the nineties a NASA‐group around S. C. Chang started to work on a new method for unsteady flow computation with seemingly good results. Thereby elements are space‐time domains. Within solution‐elements state and flux variables are linearized satisfying the underlying differential equation, within conservation‐elements space‐time flux is conserved. Proceeding this way for one‐dimensional pipe flow Jerez et al. include source terms with all cross‐section dependencies making the method semi‐implicit. We show that by taking simple measures as

‐ accounting for cross‐sections in state and flux variables of mass and energy or

‐ subtracting spatially integrated source terms from the flux

the method may become more or completely explicit, particularly helpful when chemical species transport is involved. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Approximate solution of boundary integral equations for biharmonic problems in non‐smooth domains
Authors: Didenko Victor , Helsing Johan
Published: November 2013

This paper deals with approximate solutions to integral equations arising in boundary value problems for the biharmonic equation in simply connected piecewise smooth domains. The approximation method considered demonstrates excellent convergence even in the case of boundary conditions discontinuous at corner points. In an application we obtain very accurate approximations for some characteristics of two‐dimensional Stokes flow in non‐smooth domains. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)