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In Douglas Adams' book 'Hitchhiker's Guide to the Galaxy', hyper-intelligent beings reached a point in their existence where they wanted to understand the purpose of their own existence and the universe. They built a supercomputer, called Deep Thought, and upon completion, they asked it for the answer to the ultimate question of life, the universe and everything else. The computer worked for several millennia on the answers to all these questions. When the day arrived for hyper-intelligent beings the to receive the answer, they were stunned, shocked and disappointed to hear that the answer was simply 42. The still open questions to scientists and engineers are typically much sim­ pler and consequently the answers are more reasonable. Furthermore, because human beings are too impatient and not ready to wait for such a long pe­ riod, high-performance computing techniques have been developed, leading to much faster answers. Based on these developments in the last two decades, scientific and engineering computing has evolved to a key technology which plays an important role in determining, or at least shaping, future research and development activities in many branches of industry. Development work has been going on all over the world resulting in numerical methods that are now available for simulations that were not foreseeable some years ago. However, these days the availability of supercomputers with Teraflop perfor­ mance supports extensive computations with technical relevance. A new age of engineering has started.



Large-Scale Fluid-Structure Interaction Simulations Using Parallel Computers

A methodology to simulate large-scale fluid-structure interaction prob­lems on parallel machines has been developed. Particular emphasis was placed on shock-structure interaction problems. For the fluid, a high-resolution FEM-FCT solver based on unstructured, moving, body fitted grids is used. For the structure, a Lagrangean large-deformation finite element code is employed. The coupled system is solved using a loose coupling algorithm, with position and velocity interpolation and force projection. Several examples, run on parallel machines, demonstrate the range of applicability of the proposed methodology

R Löhner, J D Baum, Ch. Charman, D. Pelessone

MEGAFLOW - An Industrial Flow Simulation Tool for Aircraft Applications

Some years ago, the national CFD project MEGAFLOW was initiated in Germany which combines many of the CFD development activities from DLR, universities and aircraft industry. Its goal is the development and validation of a dependable and efficient numerical tool for the aerodynamic simulation of complete aircraft. Today, the MEGAFLOW software system has reached a high level of quality and efficiency. As a consequence, the MEGAFLOW system is being intensively used by the German aerospace industry in the design processes for new aircraft. This paper highlights recent enhancements of the software and it‘s capability to simulate viscous flows around complex industrial applications

N. Kroll

Development of a Parallel FVM Based Groundwater Flow Model

Although parallel computing is gaining in importance in environmental engineering, there has been a lack of graduate education in this field. There are not enough models using parallel algorithms, which are simple enough to be understood with only the educational background of a student. The authors want to close this gap by developing a parallel FVM based groundwater flow model

B. Witte, R. Hinkelmann, R. Helmig

Adaptive Hybrid Mixed Finite Element Discretization of Instationary Variably Saturated Flow in Porous Media

For the Richards equation, a nonlinear elliptic-parabolic partial differential equation modelling saturated-unsaturated flow in porous media, we present a hybrid mixed finite element discretization. The efficiency of the algorithm is improved by local time step and grid adaption. The adaption algorithms are based on rigorous error estimators, whose derivation is indicated. Examples elucidate the performance of the algorithm

P. Knabner, E. Schneid

Simulation of High Pressure Liquid Chromatography (HPLC) Columns with CFD

Steep concentration gradients of the chromatographical separation process lead to discretisation errors. Different approaches to reduce these inaccuracies are applied and compared. The following methods have been investigated: Local grid refinementApplication of different discretisation schemesMoving meshRelation of the discretisation with respect to time and spaceWeighting of the differential equation system

H Boysen, G. Wozny, M. Lisso, W. Arlt, T. Laiblin

CFD Calculations of Flow, Dispersion and Chemical Reactions in Fixed Bed Tubular Reactors Using the Lattice Boltzmann Method

Detailed 3-D simulations are required to correctly predict the coupled behaviour of flow and mass transport in chemical reactors with O-asymmetry. These simulations can be of great technical and economical interest as the reactor performance and safety during operation are significantly influenced by the local flow behaviour. One particular interesting example are randomly filled tubular fixed bed reactors with small tube-to-particle diameter ratios. New numerical methods such as the lattice Boltzmann approach together with the increasing computational power can provide detailed insight into the flow and transport processes in complex geometries. The present paper demonstrates the applicability of this approach by investigating complex flows and showing first results of the inhomogeneities in the 3-D flow of reacting species in a tubular fixed bed reactor

Th. Zeiser*’, H. Freund, J. Bernsdorf, G. Brenner, F. Durst

Computational Engineering for Wind-Exposed Thin-Walled Structures

In this paper a computer-aided simulation approach for fluid-structure interaction of wind-exposed structures is presented. In the center of our software architecture is the geometric model of the structure, from which a finite element mesh for the structure and a finite volume mesh for the fluid are derived. The attention is concentrated to thin-walled structures like membranes and thin shells composed of light and flexible materials. The interaction of fluid and structure is effected by wind-induced vibrations and causes large elastic deformations of the structure. A powerful simulation tool is provided by coupling two codes developed for flow simulation and structural dynamics by a fully implicit coupling algorithm. Results of three-dimensional simulations of fluid-structure interaction for several test cases as well as for a real-life example will be presented

A. Halfmann, E. Rank, M. Glück, M. Durst, F. Breuer, J. Bellmann, C. Katz

Numerical Simulation of Wind Loads on Antenna Structures

This contribution considers the modeling and simulation of the wind loads applied to a 35m deep space antenna. The performance of such large structures can be heavily affected by deformations due to wind effects. The aim of the investigation is the prediction of the deformation of the antenna structure caused by wind loads. The presented work constitutes an example for the use of numerical simulation techniques to complex practical multi—physics problems by suitably coupling the numerical methodologies available for the fluid mechanics and structural mechanics subtasks

R. Sieber, P. Droll, M. Schäfer

Numerical Calculation of Turbulent Premixed Flames with an Efficient Turbulent Flame Speed Closure Model

A numerical model for premixed gaseous turbulent combustion is investigated, where the combustion process is modelled in terms of a single transport equation for a reaction progress variablecThe reaction term of the progress variable is modelled with an efficient turbulent flame speed closure approach. The model is checked by comparing numerical results with experimental data from a turbulent premixed V-shaped flame, where the conditions of the approaching turbulent flow and of the chemical processes have been varied separately. Regarding the simple structure of this model, it is found to predict the flame shape and flame width well. Further extension of the model account for local variations of stoichiometry, allowing to consider the entrainment of additional air. With that, it was possible to calculate turbulent Bunsen flames of significantly different size (Reynolds number 7000 and 44000) and a free standing turbulent premixed low swirl stabilized flame for different flow conditions

F. Dinkelacker

Monte Carlo Simulations of Radiative Heat Transfer with Parallel Computer Architectures

This work presents a parallel Monte Carlo algorithm for the calculation of combined radiative and conductive heat transfer. The proposed formulation effectively separates the time-consuming ray-tracing part of the Monte Carlo method from the energy computations required in the iterative solution of the energy equation. The method is applied for a simple combined radiative and conductive heat transfer problem and excellent agreement with the benchmark results is found. The ray-tracing part of the algorithm is parallelised and applied in two configurations, which represent the opposite ends of the currently available parallel computer architectures; a PC cluster and the Hitachi SR8000-F1 supercomputer. For sufficiently large sampling sets, the computation experiments show an almost ideal speed-up

J. G. Marakis, J. Chamiço, G. Brenner, F. Durst

Direct Numerical Simulation of Bubble Swarms with a Parallel Front-Tracking Method

Direct numerical simulations are performed to study the behaviour of an important class of dispersed multiphase flows, namely gas bubbles rising in a liquid. The numerical method combines a finite difference scheme for solving the Navier-Stokes equations with a front tracking method for following the gas-liquid interfaces. The size of the problem as well as the simulation time requirements necessitate the use of large parallel computers. Sample simulation results are presented illustrating the evolution of such systems and the dependence of statistical quantities on the gas volume fraction. The goal of these numerical experiments is to gain insight into fundamental properties of bubbly flows and support the development of simplified models

M. F. Göz, B. Bunner, M. Sommerfeld, G. Tryggvason

Symmetry-Preserving Discretization of Turbulent Channel Flow

We propose to perform turbulent flow simulations in such manner that the difference operators do have the same symmetry properties as the underlying differential operators, i.e. the convective operator is represented by a skew-symmetric matrix and the diffusive operator is approximated by a symmetric, positive-definite matrix. Such a symmetry-preserving discretization of the NavierStokes equations is stable on any grid, and conserves the total mass, momentum and kinetic energy (when the physical dissipation is turned off). Its accuracy is tested for a turbulent channel flow at Re=5,600 (based on the channel width and the mean bulk velocity) by comparing the results to those of physical experiments and previous numerical studies. This comparison shows that with a fourth-order, symmetry-preserving method a 64 x 64 x 32 grid suffices to perform an accurate direct numerical simulation

R. W. C. P. Verstappen, A. E. P. Veldman

Parallelization Strategies and Efficiency of CFD Computations in Complex Geometries Using Lattice Boltzmann Methods on High-Performance Computers

A frequently stated property of the Lattice Boltzmann (LB) method is, that it is easy to implement and that the generation of computational grids is trivial even for three-dimensional problems. This is mainly due to the usually chosen approach of using full matrices to store the primary variables of the scheme. However this kind of implementation has severe disadvantages for simulations, where the volume of the bounding box of the flow domain is large compared to the actual volume of the flow domain. Thus the authors developed data structures which allow to discretize only the fluid volume including boundary conditions to minimize memory requirements, while retaining the excellent performance with respect to vectorization of standard LB-implementations on supercomputers. Due to extensive communication hiding using asynchronous non-blocking message transfer an almost linear parallel speedup is achieved

M. Schulz, M. Krafczyk, J. Tölke, E. Rank

Applications of the Lattice Boltzmann Method to Complex and Turbulent Flows

We briefly review the method of the lattice Boltzmann equation (LBE). We show the three-dimensional LBE simulation results for a non-spherical particle in Couette flow and 16 particles in sedimentation in fluid. We compare the LBE simulation of the three-dimensional homogeneous isotropic turbulence flow in a periodic cubic box of the size 1283with the pseudo-spectral simulation, and find that the two results agree well with each other but the LBE method is more dissipative than the pseudo-spectral method in small scales, as expected

L. S. Luo, D. Qi, L. P. Wang

Computation of Flows Around Space Configurations

Numerical investigations in the sub-and supersonic flowfield around space configurations are presented. The subsonic turbulent flow around the space plane configuration ELAC as well as the supersonic laminar flow around have been considered. The third configuration is a two-stage, i. e. EOS mounted on ELAC. system. The numerical results are obtained by solving the Navier-Stokes equations using a finite volume method based on node-centered blockstructured grids in curvilinear coordinates. The Baldwin-Lomax turbulence model was used for fully turbulent flow without transition. The results presented are compared with experimental findings and show satisfactory agreement

A. Henze, W. Schröder, M. Meinke

Flow Visualization on Hierarchical Cartesian Grids

Due to the limitations of the traditional finite volume CFD approach modern Lattice-Boltzmann methods are becoming more and more widespread. The results of developing an efficient visualization and exploration tool based on the Lattice-Boltzmann solver PowerFlow are summarized here to give the reader a basic insight into the pros and cons of such an approach. Also, the implementation of an automotive soiling simulation, which has been incorporated into the visualization tool, is presented here

St. Roettger, Th. Ertl, M. Schulz, W. Bartelheimer

The Finite Mass Method — A New Approach to the Solution of Flow Problems

The finite mass method, a new Lagrangian method for the numerical simulation of gas flows, is presented. In contrast to the finite volume and the finite element method, the finite mass method is founded on a discretization of mass, not of space. Mass is subdivided into small mass packets of finite extension each of which is equipped with finitely many internal degrees of freedom. These mass packets move under the influence of internal and external forces and the laws of thermodynamics and can undergo arbitrary linear deformations. The basic reference is Gauger, Leinen, and Yserentant, SIAM J. Numer. Anal. 37 (2000), pp. 1768-1799. In the present note, a short survey is given

H. Yserentant

An Octree-Based Approach for Fast Elliptic Solvers

We discuss an octree-based approach for the solution of elliptic partial differential equations, especially Poisson’s equation and the convection diffusion equation. The discretization is derived from a starting discretization on a very fine octree grid. For the actual computation a discretization on a much coarser grid is generated by an accumulation process based on hierarchical transformation and partial elimination of unknowns. We also describe an efficient multigrid solver which takes advantage of the underlying octree structure. It is based on recursive substructuring of the domain and is very similar to the accumulation process. By adding additional unknowns to the coarse grids the resulting solver is robust even for the convection diffusion equation

M. Bader, A. C. Frank, Ch. Zenger

A Variable Order Method of Lines: Accuracy, Conservation and Applications

The variable order method of lines is presented for the DNS of incompressible flows. The present method is constructed by the spatial discretization, i.e., the variable order proper convective scheme and modified differential quadrature method, and time integration. The accuracy and conservation property are validated in the 2D Taylor-Green solutions and 3D homogeneous isotropic turbulence. As applications, the flows around a circular cylinder and a sphere are simulated by using Cartesian grid approach with virtual boundary method. Consequently, the present method is very promising for the DNS of the incompressible flows

H Nishida, N. Satofuka

A Hybrid Direct/Iterative Algorithm for the Solution of Poisson’s Equation Based on the Schur Complement Method

An algorithm for efficient solution of large 3-D Poisson problems arising in the numerical simulation of the incompressible, unsteady Navier Stokes equations is presented. It is demonstrated that for a certain class of flows with onehomogeneouscoordinate direction an efficient load balancing on massively parallel machines can be achieved by simultaneous direct and iterative solution of 2-D Helmholtz problems. The use of the Schur complement method in conjunction with direct solution based on precomputed LU decomposition is capable to significantly reduce memory need and execution time

H. J. Kaltenbach, A. Jäkel

High-Performance Computing, Multi-Scale Models for Crystal Growth Systems

Large-scale numerical simulation carried out via high performance computing is proving to be an increasingly useful approach to understand crystal growth systems. However, increasing realism demands new approaches for describing phenomena important at several disparate length scales. Of special importance is the ability to represent three-dimensional and transient continuum transport (flows, heat and mass transfer), phase-change phenomena (thermodynamics and kinetics), and system design (such as furnace heat transfer during melt growth). A brief overview is presented of mathematical models and numerical algorithms employed to include such multi-scale effects. Sample results are presented for Bridgman crystal growth and solution crystal growth systems

J. J. Derby, P. Daoutidis, Y. Kwon, A. Pandy, P. Sonda, B. Vartak, A Yeckel, M. Hainke, G. Müller

Semi-Direct Numerical Simulation of a Czochralski Melt Flow on High-Performance Computers

Abstract. The three-dimensional and time-dependent turbulent flow field and heat transfer of the melt in a Czochralski crystal growth process were predicted using an efficient block-structured finite-volume Navier-Stokes solver. From semi-direct numerical simulations, detailed information of instantaneous and time-averaged quantities were obtained. Two different crucible rotation rates were considered,,f2c = —2 rpm and —5 rpm, whereas the crystal rotation was kept constant at,f29 = 20 rpm. Exact boundary conditions for the temperature were obtained from experiments. The time-averaged results are discussed and it is shown that, due to velocity and temperature fluctuations underneath the crystal, the growth conditions are superior at higher crucible rotation rates. The main reason for this is the stabilizing effect of the centrifugal forces. Furthermore, it is shown that the boundary layer below the crystal is very thin, so that the influence on the bulk flow is negligible. Rotation will mainly maintain the circular shape of the crystal and ensure the homogeneous distribution of dopants

S. Enger, F. Schäfer, M. Breuer, F. Durst

High-Order Numerical Solutions for Rotating Flows with Walls

The study of rotating viscous flows with walls has significant importance for many industrial devices. In this approach subsystems of simple geometry coming from realistic geometries are studied using accurate methods (spectral). The three-dimensional incompressible Navier-Stokes equations are solved using a projection scheme. Depending on the aspect ratio of the cavity and on the Reynolds number, annular and spiral patterns of the generic types I and II boundary layer instabilities as well as vortex breakdown phenomena are investigated. Taylor-Couette flows in a finite-length cavity with counter-rotating walls, are also studied. Two complex regimes of wavy vortex and spirals are emphasized for the first time via direct numerical simulation in this configuration

E. Serre, I. Raspo, O. Czarny, P. Bontoux, P. Droll, M. Schäfer

Parallel Coupled Simulation of Casting Processes on Cluster of PCs

This paper describes the parallelization of a thermo-mechanical software package that is used to simulate the solidification and cooling process in casting. Such problems require a substantial amount of computing power of high-end workstations which are typically not available in small and medium sized enterprises. In order to overcome this bottleneck this paper introduces clusters of PCs as a computing resource. To show the feasibility of the approach a casting code has been parallelized using a direct substructuring method first. Results show that this method is limited to small problems. Therefore, also an iterative method is presented. Results for realistic examples show a good speedup and give proof that clusters of PCs can make up for the lack of high-end computers in small and medium sized enterprises

P. A. Adamidis, M. M. Resch

Controlling Point Defects in Single Silicon Crystals Grown by the Czochralski Method

Silicon is the basic material which makes the functions of semiconductors possible. Most of the conveniences we take for granted would simply not have existed without this essential resource. The need for more and more complex devices increases the size of the device and the requirements on the quality of the material. Crystal quality will therefore be of utmost importance in the coming years as these trends continue to decrease the tolerance on wafer specifications. We present a mathematical model and numerical simulations which help to design the growth process in order to improve the crystal quality. A macroscopic model for heat transfer is therefore combined with a microscopic model for intrinsic point defect diffusion

A Voigt, J. Nitschkowski, Ch. Weichmann, K. H. Hoffmann

A Two—Scale Method for Liquid—Solid Phase Transitions with Dendritic Microstructure

A two—scale model for liquid—solid phase transitions with equiaxed dendritic microstructure for binary material with slow solute diffusion is presented. The model consists of a macroscopic energy transport equation, coupled with local cell problems describing the evolution of the microstructure and the microsegregation. It is derived by an asymptotic expansion of a sharp interface model with Gibbs—Thomson effect. A discretization of the model leading to a two—scale method for such problems is presented, and a numerical example is given

Ch Eck, P. Knabner

Application of Higher Order BDF Discretization of the Boussinesq Equation and the Heat Transport Equation

During the growth of crystals there were observed crystal defects under some conditions of the growth device. As a result of experiments a transition from the twodimensional flow regime of a crystal melt in axisymmetric zone melting devices to an unsteady threedimensional behavior of the velocity and temperature field was found. This behavior leads to striations as undesirable crystal defects. For the investigation of this symmetry break a mathematical model of the crystal melt was formulated fori) the theoretical description of the experimentally observed behavior andii) the identification of critical parameters of the growth device, i.e. the evaluation of bifurcation pointsTo describe and to avoid such a behavior it is necessary to solve the unsteady three-dimensional Boussinesq equation coupled with the heat transport equation efficientlyTo improve first and second Euler, leapfrog and Adams-Bashforth methods higher order explicit and BDF (Backward Differenciation Formulas) methods are applied and constructed for time dependend calculations and a Newton method is discussed for the resulting nonlinear equation systems for implicit integration methods and the steady state solution

G. Bärwolff

Spectral and Finite Volume Numerical Approximations for Solutal Convection in Melted Alloys

This work concerns a numerical study of steady and time-dependent flow patterns induced by solutal free convection appearing during the directional solidification of binary alloys in 2D and cylindrical 3D domains. Numerical approximations are based on the spectral chebychev collocation and finite volume methods

R. Guérin, M. El Ganaoui, P. Haldenwang

Numerical Simulation of Physical Vapour Transport Crystal Growth Processes by a Finite Volume Solution Algorithm

A mathematical model for the numerical simulation of physical vapour transport (PVT) crystal growth processes is presented in this paper. The model is based on the two-dimensional conservation equations for mass, momentum, energy and chemical species. Radiative heat transfer and species generation/consumption by heterogeneous chemical reactions are taken into account. The equations are solved by a finite volume algorithm on block-structured grids using the multi-grid technique to speed up convergence. The efficiency of the method is demonstrated. Results on the simulation of the SiC bulk growth process are given, and physical phenomena involved in the growth process are discussed

M. Selder, L. Kadinski, F. Durst

3D Block-Structured Grid Algorithms for the Numerical Simulation of Chemical Vapor Deposition in Horizontal Reactors

In this paper an advanced numerical approach for the simulation of epitaxial growth in metalorganic chemical vapor deposition (MOCVD) reactors is presented. The mathematical model is based on the conservation equations for momentum and heat transfer combined with mass transferThe heat conduction includes thermal solid/fluid interactions between the gas and solid parts of the reactor. The radiation heat transfer is coupled with convection and conduction. The radiation heat transfer modelling approach is based on the exchange of radiative heat fluxes between the internal solid surfaces in the computational domain using diffuse view-factors. The calculation of view factors is based on a double contour integral method. A shadowing algorithm is implemented for the calculation of view factors in complex geometriesThe model is implemented in a finite volume numerical solution procedure, incompressible or low Mach number flow on block-structured non-orthogonal grids for three-dimensional laminar flowsIn order to demonstrate the ability of the present method to analyse complex problems, investigations for horizontal MOCVD reactor configurations are presented. The simulated temperature distribution is compared with well-known temperature measurements and good agreement with them is achievedThe growth of GaAs from trimethyl gallium (TMGa), arsine, and hydrogen was considered where the deposition process is assumed to be in the transport-limited regime. The predicted deposition rates in the reactor fairly well compare with the available experimental results from literature

L. Kadinski, P. Kaufmann, C. Lindner, F. Durst

Electromagnetic Control of Electron Beam Evaporation: Numerical Simulation

During electron beam evaporation of liquid metals, the strong energy input induces strong temperature gradients along the free surface and in the interior of the melt. Thus, the liquid metal is subject to both thermocapillary and natural convection. The vigorous convective motion within the melt leads to highly unwelcome heat losses through the walls of the crucible. The strong convective heat transfer limits the temperature rise in the hot spot and, therefore, the thermodynamic efficiency of the evaporation process. The present paper aims to demonstrate that melt-flow can be effectively controlled by using external magnetic fields in order to considerably reduce the convective heat losses. We employ numerical simulations based on the finite element method to study the effects of a rotating magnetic field on convective heat transfer in a liquid metal heated locally at its free surface

U. Lüdtke, Ch. Karcher

Solution of a Hard Flight Path Optimization Problem by Different Optimization Codes

Solar electric propulsion is the key technology to reduce propellant consumption for interplanetary missions. A number of studies of interplanetary and lunar missions are currently performed by the European Space Agency (ESA), which exploit the benefits of solar electric propulsion (e.g., [11,8]). Although solar electric propulsion has the disadvantage of low-thrust levels the high specific impulse leads to considerable reduction of propellant mass and therefore to an increase in payload mass. Trajectory optimization problems with solar electric propulsion are known to be extremly difficult (e.g., [3]). They have in the past been successfully solved by indirect methods while direct methods usually failed. Nevertheless the sophistication of direct solution methods has also permanently increasedThe interesting question is: Can low-thrust missions be solved today by direct methods? How precise are these solutions compared with an indirect solution? What time and requirements does it take for a successful solution?A detailed numerical comparison of the direct solution code NUDOCCCS (Büskens [11]) and the indirect multiple shooting code MUMUS (Hiltmann [7]) is presented for a reference problem (a low thrust orbital transfer problem of a LISA spacecraft with constraints on the solar aspect angle) from [11]

K. Chudejl, Ch Biiskensl, T. Graf

Adaptive Data Structures and Algorithms for Efficient Visualization and Data Management at Runtime of Terrain and Feature Data

An approach is presented for rendering terrain and feature data in real time, applicable to flight simulators and to cockpit displays for generating synthetic vision. Basically, a hierarchical adaptive triangulation technique is used for dealing with the terrain elevation data in the memory. The interpolation hierarchical surplus is used as a criterion to detect redundant data and serves to control the error of the terrain approximation. With this level-of-detail mechanism and an easy visibility check due to the hierachical adaptive strategy, a high frame rate can be reached. A special organisation of the data is developed to exchange parts of the data at runtime in order to limit the required memory. On multiprocessor computer architectures, the reloading data process can be performed in the background without interrupting the rendering by starting parallel running tasks (threads)

K. Nothnagel, A. Paul, G. Sachs

Recent Improvements in the Trajectory Optimization Software ASTOS

The Aerospace Trajectory Optimization Software ASTOS is using direct optimization methods such as multiple shooting and collocation to calculate the optimal control time history for an optimal control problem. The mathematical model is completely data driven, which means that the end-user need not write any code to specify the problem to solveThis paper will describe some of the major technical improvements recently made to ASTOS, as there are: initial guess generation, branched trajectories and new optimization methods. In addition, some new applications are discussed which demonstrate the flexibility of the ASTOS Model Libary

P. Gath, A. Wiegand, A. Markl, K. H. Well

Optimal Design of the Power Train of Vehicles: Modelling, Simulation and Optimization

In the early stage of development of a vehicle, the design of the power train is encouraged by numerical simulations. Virtual testing of different variants and configurations of a car can be well-investigated without constructing any prototype. The mathematical models used to calculate the fuel consumption and driving power differ. Therefore, there exist different program packages to calculate these qualifying criteria of a vehicle. A standard interface between these packages and the optimization program has to be developed. Different, partly antagonistic objective functions are presented to optimize the design of the power train. The most important of the criteria are driving power and fuel consumption. The aim of development of new vehicles is to reduce the fuel consumption without loss of driving power. To fulfil these requirements it is not enough to investigate on each part of the power train separately. It is more efficient to optimize the whole system, using a mathematical model of the power train. The aim of the investigations is to find optimal characteristics of the torque converter, automatic gear transmissions, and the transmission of the rear axle differential, using mathematical methods for systematic optimization. In this paper methods are developed which can be used to optimize both model parameters and whole characteristics. The investigations are split up into the topics: mathematical description of objective functions, appropriate parameterization of characteristics, sensitivity analyses of the objective function. Some results are presented

D. Tscharnuter

Unsteady Heat Load Simulation for Hypersonic Cruise Optimization

Unsteady heat loads during the range cruise of a hypersonic vehicle propelled by a turbo/ram jet engines combination are considered. The unsteady heat load effects are simulated using a a realistic mathematical model. This model is coupled to the equations of motion of the vehicle. A two step technique for generating a solution is applied. First, an efficient optimization technique is used and, second, the obtained results are recalculated with an ODE-Solver. It is shown that the heat input can be significantly reduced, with only a small increase in fuel consumption

M. Wächter, G. Sachs

Modeling Techniques and Parameter Estimation for the Simulation of Complex Vehicle Structures

The numerical simulation of complex vehicle structures requires dynamic models for passenger cars as well as for trucks and vehicles with trailers. Tailored numerical modeling and integration techniques must be employed to achieve real-time capability of the considered vehicle dynamics program which is vital for its use within hardware-in-the-loop test-benches. To efficiently calibrate the vehicle model a parameter estimation tool was developed which relies on observations obtained from driving tests. Combining robust nonlinear optimization algorithms and careful numerical differentiation it is well suited for low-cost parallel computing platforms, such as heterogeneous PC clusters, which are usually available for automotive suppliers and industries employing vehicle dynamics simulations

T. Butz, O. vonStryk, C. Chucholowski, St. Truskawa, T. M Wolter

Numerical Techniques for Different Time Scales in Electric Circuit Simulation

The simulation of integrated circuits demands an increasing amount of computational resources, since systems become more and more complex and parasitic effects are included to a larger extent. However, the number of active elements keeps relatively small: less than 10%. In other settings digital and analog circuits are coupled, which yields systems with largely differing time scales. We will discuss two techniques, which are adapted to those cases. One approach is based on multirate Rosenbrock-Wanner schemes, the other leads to a PDE-model for driven oscillators

A. Bartel, M. Günther, R. Pulch, P. Rentrop

Transient Noise Analysis in Circuit Simulation

Circuit simulation is one of the most important steps during the development of electronic circuits. A standard task for circuit simulation is the transient analysis, the simulation of the chip on transistor level in the time domain. Normally, this simulation does not include noise source. As the supply voltage decreases, the signal-to-noise ratio also decreases and noise effects become more and more important. In this paper the modeling of noise in the time-domain will be described. Especially for flicker noise, new and efficient approaches are presented. For a numerical treatment of the resulting stochastic differential-algebraic equations, a new numerical scheme is given for the charge-oriented formulation of the circuit equations. Finally, the results of numerical experiments are presented

G. Denk

Realistic Step Flow Model for Orientation-Dependent Wet Etching

We present a new simulation tool for orientation-dependent etching of silicon. The implemented algorithm is based on a model proposed by Schröder [1], which can explain the convex corner undercutting in pure aqueous KOH solutions. Essential is the experimental observation that the so called fast etching planes, which hitherto were assumed to cause the characteristic shape of under-etched convex etchmask corners, are not really crystallographic planes. Referring to some basic examples we demonstrate that our simulation approach using this “step flow model of 3D structuring” is able to reproduce the detailed morphology of the etched structures

A. Horn, G. Wachutka

Modeling of Ion-Induced Charge Generation in High Voltage Diodes

Additional terms have to be added to the right-hand sides of the carrier balance equations for electrons and holes in order to describe the initial injection of charge caused by the loss of kinetic energy of a single ion penetrating a semiconductor device. Two-dimensional simulations of a reverse biased power diode yield the temporal and spatial distribution of the device-internal electric field initiated by an intruding ion. For small reverse biases the charge generated within the device corresponds to the total absorption of the ion’s kinetic energy. Applying a sufficiently high reverse bias a steep field peak forms which is able to propagate through the whole device with an undiminished peak height. Due to the corresponding strong avalanche multiplication a large amount of additional charge can be generated. The results obtained from our device simulations conform well to recent experimental findings

W. Kaindl, G. Sölkner, G. Wachutka

Modelling and Simulation of the Transient Electromagnetic Behavior of High Power Bus Bars

An extended concept for the characterization of the electromagnetic behavior of high power bus bars in high power semiconductor modules is presented. Based on a three-dimensional transient finite element analysis of the electromagnetic field under realistic switching conditions, the eigendynamics of interconnects is evaluated. It is demonstrated that the investigation of distributed parasitic effects caused by short switching times and steep current or voltage ramps complements the common circuit analysis approach. The different modelling and simulation techniques in use are discussed focusing on specific numerical requirements. The capabilities of the method are demonstrated by some illustrative numerical examples

P. Böhm, G. Wachutka, R. H. W. Hoppe

Modeling and Simulation of Electrothermomechanical Coupling Phenomena in High Power Electronics

High power electronic devices based on innovative semiconductor technology play a significant role in technical applications. A robust operating behavior of such devices can be achieved by an optimal design taking into account the presence of coupled physical effectsIn this contribution, we focus on electrothermomechanical coupling phenomena in Integrated-High-Voltage Modules with housing and cooling mechanisms that are used as electric drives for high power electromotors. For the numerical solution of the underlying coupled systems of partial differential equations we consider efficient algorithmic tools such as domain decomposition techniques

P. Böhm, Y. C. Gerstenmaier, R. H. W. Hoppe, Y. Iliash, G. Mazurkevitch, G. Wachutka

Heat Conduction as Eigenvalue Problem

The time dependent solution of the heat conduction equation is represented by expandingTin terms of eigenfunctions and eigenvalues (= inverse time constants). Once these are known, the time evolution ofTcan be computed readily for arbitrary heat sources. A method is presented for computing eigenfunctions and eigenvalues for a multilayer structure, where all layers have the same lateral extension and differ vertically in thickness and material parameters. Those structures are encountered in modeling IC packages and multichip modules in power electronic applications. Examples will be given for the temperature evolution calculated for the time dependent heat distribution in power converter applications. However, computation time and storage demands will be high if high spatial and temporal resolution for the temperature field is needed. Using effective time constants and functions the numerical effort can be reduced considerably

Y. C. Gerstenmaier, G. Wachutka


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