Table Of ContentFlow Simulation
with High-Performance
Computersll
Edited by
Ernst Heinrich Hirschel
Notes on Numerical Fluid Mechanics (NNFM) Volume 52
Series Editors: Ernst Heinrich Hirschel, Miinchen (General Editor)
Kozo Fujii, Tokyo
Bram van Leer, Ann Arbor
Michael Leschziner, Manchester
Maurizio Pandolfi, Torino
Arthur Rizzi, Stockholm
Bernard Roux, Marseille
Volume 51 Numerical Treatment of Coupled Systems. Proceedings of the Eleventh GAMM-Seminar, K
January 20-22,1995 (W. Hackbusch I G. Wittum, Eds.)
Volume 50 Computational Fluid Dynamics on Parallel Systems. Proceedings of a CNRS-DFG Symposil
in Stuttgart, December 9 and 10, 1993 (S. Wagner, Ed.)
Volume 49 Fast Solvers for Flow Problems. Proceedings of the Tenth GAMM-Seminar, Kiel,
January 14-16, 1994 (W. Hackbusch I G. Wittum, Eds.)
Volume 48 Numerical Simulation in Science and Engineering. Proceedings of the FORTWIHR
Symposium on High Performance Scientific Computing, Miinchen, June 17-18, 1993
(M. Griebel I Ch. Zenger, Eds.)
Volume 47 Numerical Methods for the Navier-Stokes Equations (F.-K. Hebeker, R. Rannacher,
G. Wittum, Eds.)
Volume 46 Adaptive Methods - Algorithms, Theory, and Applications. Proceedings of the Ninth GAM]
Seminar, Kiel, January 22-24,1993 (w. Hackbusch I G. Wittum, Eds.)
Volume 45 Numerical Methods for Advection - Diffusion Problems (c. B. Vreugdenhil I B. Koren, Eds.
Volume 44 Multiblock Grid Generation - Results of the EClBRlTE-EURAM Project EUROMESH,
1990-1992 (N. P. Weatherilll M. J. Marchant I D. A. King, Eds.)
Volume 43 Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects
Proceedings of the Fourth International Conference on Hyperbolic Problems, Taormina,
Italy, April 3 to 8, 1992 (A. Donato I F. Oliveri, Eds.)
Volume 42 EUROVAL - A European Initiative on Validation of CFD Codes .
(w. Haase I F. Brandsma I E. Elsholz 1M. Leschziner I D. Schwamborn, Eds.)
Volume 41 Incomplete Decompositions (ILU) - Algorithms, Theory, and Applications
(w. Hackbusch I G. Wittum, Eds.)
Volume 40 Physics of Separated Flow - Numerical, Experimental, and Theoretical Aspects
(K. Gersten, Ed.)
Volume 39 3-D Computation of Incompressible Internal Flows (G. Sottas II. L. Ryhming, Eds.)
Volume 38 Flow Simulation on High-Performance Computers I (E. H. Hirschel, Ed.)
Volume 37 Supercomputers and Their Performance in Computational Fluid Mechanics
(K. Fujii, Ed.)
Volume 36 Numerical Simulation of 3-D Incompressible Unsteady Viscous Laminar Flows
(M. Deville IT.-H. L! I Y. Morchoisne, Eds.)
Volume 35 Proceedings of the Ninth GAMM-Conference on Numerical Methods in Fluid Mechanio
(J. B. Vos I A. Rizzi II. L. Ryhming, Eds.)
Volume 34 Numerical Solutions of the Euler Equations for Steady Flow Problems
(A. Eberle I A. Rizzi I E. H. Hirschel)
Volume 33 Numerical Techniques for Boundary Element Methods (w. Hackbusch, Ed.)
Volume 32 Adaptive Finite Element Solution Algorithm for the Euler Equations (R. A. Shapiro)
Volume 31 Parallel Algorithms for Partial Differential Equations (w. Hackbusch, Ed.)
Volumes 1 to 25, 45 are out of print.
The addresses of the Editors and further titles of the series are listed at the end of the book.
Flow Simulation
with High-Performance
ComputersD
DFG Priority Research Programme
Results 1993-1995
Edited by
Ernst Heinrich Hirschel
Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Flow simulation with high performance computers:
DFG priority research programme results / ed. by
Ernst Heinrich Hirschel. - Braunschweig; Wiesbaden:
Vieweg.
Frtiher u. d. T.: Flow simulation on supercomputers
NE: Hirschel, Ernst Heinrich [Hrsg.]:
Deutsche Forschungsgemeinschaft
2. 1993-1995. -1996
(Notes on numerical fluid mechanics; Vol. 52)
NE:GT
All rights reserved
© Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, BraunschweigIWiesbaden, 1996
Softcover reprint of the hardcover 1st edition 1996
Vieweg ist a subsidiary company of Bertelsmann Professional Information.
No part of this publication may be reproduced, stored in a retrieval
system or transmitted, mechanical, photocopying or otherwise,
without prior permission of the copyright holder.
Produced by Langeltiddecke, Braunschweig
Printed on acid-free paper
ISSN 0179-9614
ISBN 978-3-322-89851-7 ISBN 978-3-322-89849-4 (eBook)
DOl: 10.1007/ 978-3-322-89849-4
Foreword
This volume contains thirty-seven reports on work, which was conducted between 1993 and
1995 in the Priority Research Programme "Flow Simulation with High-Perfonnance
Computers" of the Deutsche Forschungsgemeinschaft (DFG, Gennan Research Society), 1989
to 1995.
The main purpose of this pUblication is to give an overview over the work conducted in the
second half of the programme, and to make the results obtained available to the public. The
reports are grouped under the four headings "Flow Simulation with Massively Parallel
Systems", "Direct and Large-Eddy Simulation of Turbulence", "Mathematical Foundations,
General Solution Techniques and Applications" and "Results of Benchmark Computations".
All contributions to this publication have been reviewed by a board consisting of F. Durst
(Erlangen), R. Friedrich (Miinchen), D. Hanel (Duisburg), R. Rautmann (Paderbom),
H. Wengle (Mtinchen), and the editor. The responsibility for the contents of the reports
nevertheless lies with the authors.
E.H. Hirschel
Editor
Preface
The Deutsche Forschungsgemeinschaft (DFG) sponsored the development of numeri
cal simulation techniques in fluid mechanics since 1989 in a Priority Research Program
"Flow Simulation with High-performance Computers". The major results obtained in this
program until 1992 were published in summarizing articles in Volume 38 of the "Notes on
Numerical Fluid Mechanics" of the Vieweg Verlag. The present volume summarizes the
results of the second half of the program, which completed its investigations December 1995.
The problems studied included developments of solution techniques as well as ap
plications. Altogether 35 projects were supported. It is worthwhile to point out, that 13
projects concentrated on the parallelization of algorithms and related work. The program
thereby stimulated research in this relatively new branch of computational fluid dynamics in
Germany with marked success. Development of general solution techniques and their
application were pursued in 17 projects, and the remainder 5 projects were devoted to the
development of simulation techniques for transitional and turbulent flows.
The work on parallel solution techniques included development of a time and space
multi-grid method, of parallel finite element methods for the solution of the Navier-Stokes
equations, performance enhancement of parallelized algorithms, adaptive operator techniques,
and parallel interactive and integrated visualization techniques. The applications of par
a1lelized algorithms comprised simulation of turbulent flow, of various viscous incompress
ible flows, of unsteady flows in turbomachinery, of chemically reacting flow, and of aerody
namic .f lows.
The work on other solution techniques included approximations in high order norms,
low Mach number solutions based on asymptotic analysis, solutions based on the artificial
compressibility concept, on higher order upwind schemes on unstructured grids, and others.
The applications included simulation of aerodynamic and of hypersonic flows, of flows in
turbomachinery and other complex internal flows. The investigations of transitional and
turbulent flows were aimed at direct simulation of internal compressed turbulent flow and of
separated flows; at large-eddy simulation of near-wall turbulence, of turbulent flows in
curved pipes, and of turbulent boundary-layer flow over a hemisphere.
The cooperation with the Groupment de Recherche Mecanique des Fluides Numerique
of the French Centre National de la Recherche Scientifique (CNRS) was continued. The
second joint workshop was held May 3 -5 1993 in Lambrecht (Pfalz) on the topic "Three
Dimensional Flow -Alternative Formulations and Solution of the Conservation Equations".
At this occasion several representatives of the CNRS and the DFG under the chairmanship
of one of the vice presidents of the DFG, Prof. S. Wittig, met and discussed possibilities of
cooperation. Agreement was reached on the following points: Cooperation in 10 joint
projects within the frame of existing programs; participation of a French representative in the
meetings of the German reviewing board and vice versa; organization of a joint meeting in
Sophia-Antipolis at the end of 1994 with the aim of preparing a joint CNRS-DFG research
program on computational fluid dynamics.
A third joint CNRS-DFG workshop was organized December 9 - 10, 1993 at Stutt
gart University under the topic "Computational Fluid Dynamics on Parallel Systems". The
contributions were published in volume 50 of the "Notes on Numerical Fluid Dynamics" of
the Vieweg Verlag under the title of the workshop. They were edited by S. Wagner of
Stuttgart University. The fourth workshop was held in Sophia-Antipolis November 25 -26,
1994. As proposed in Lambrecht one year earlier, 20 projects for a prospective joint
program entitled "Numerical Flow Simulation, A French -German Research Initiative" were
discussed in the presence of official representatives of the CNRS and the DF G, and in March
1995 a proposal for such a program was submitted to the CNRS and the DFG under the title
"Joint French - German Research Program: Numerical Flow Simulation". The individual
proposals were reviewed by a French -German reviewing board November 27, 1995 and
submitted for final decision to the CNRS and the DFG.
The DFG Priority Research Program "Flow Simulation on High-Performance
Computers" substantially stimulated and fostered research in this field over a long period of
time. It was a safe stepping stone for initiating and supporting work on paralellization. It
brought together engineers and applied mathematicians in fruitful cooperation. The program
helped to maintain international competiveness in flow research and markedly fastened the
ties to the corresponding French program.
It is with great pleasure, that the undersigned take this opportunity to thank: the DFG
for supporting work on numerical flow simulation over more than six years. The efforts of
the reviewers, Profs. Dr. G. Bohme and Dr. R. Rannacher are gratefully acknowledged.
Their invaluable expertise helped to shape the program in many ways. They stimulated
interdisciplinary discussion between engineers and mathematicians, who participated in the
program. Their efforts are reflected in the articles published in this volume. Without the
continuous help and far-sighted administering of the program by Dr. W. Lachenmeier it
would have been impossible to maintain continuity in the research activities over the years.
We thank: him for his efforts.
Finally the Vieweg Verlag is gratefully acknowledged for publishing the results in the
Notes on Numerical Fluid Mechanics, and Prof. Dr. E. H. Hirschel for editing this volume.
Bonn-Bad Godesberg, January 1996
E.Krause E. A. Muller
COmENTS
Page
I. FLOW SIMULATION WITH MASSIVELY PARALLEL SYSTEMS ..... .
M. Schafer: Introduction to Part I ................................................................................. 3
1. Burmeister, W. Hackbusch: On a Time and Space Parallel Multi-Grid Method
Including Remarks on Filtering Techniques .................................................................... 5
O. Dorok, V. John, U. Risch, F. Schieweck, L. Tobiska: Parallel Finite Element
Methods for the Incompressible Navier-Stokes Equations ............................................. 20
M. Griebel, W. Huber, C. Zenger: Numerical Turbulence Simulation on a Parallel
Computer Using the Combination Method ...................................................................... 34
F. Lohmeyer, O. Vornberger: CFD with Adaptive FEM on Massively Parallel
Systems .............................................................................................................................. 48
M. Lenke, A. Bode, T. Michl, S. Wagner: On the Performance Enhancements
of a CFD Algorithm in High Performance Computing .................................................. 64
F. Durst, M. Schafer, K. Wechsler: Efficient Simulation of Incompressible Viscous
Flows on Parallel Computers ........................................................................................... 87
J. Hofhaus, M. Meinke, E. Krause: Parallelization of Solution Schemes for the
Navier-Stokes Equations ................................................................................................... 102
K. Engel, F. Eulitz, S. Pokorny, M. Faden: 3-D Navier-Stokes Solver for the
Simulation of the Unsteady Turbomachinery Flow on a Massively Parallel
Hardware Architecture .................................... .................................................................. 117
H. Rentz-Reichert, G. Wittum: A Comparison of Smoothers and Numbering
Strategies for Laminar Flow Around a Cylinder ............................................................. 134
G. Bader, E. Gehrke: Simulation of Detailed Chemistry Stationary Diffusion
Flames on Parallel Computers .......................................................................................... 150
I.S. Doltsinis, J. Urban: An Adaptive Operator Technique for Hypersonic Flow
Simulation on Parallel Computers ................................................................................... 165
J. Argyris, H.U. Schlageter: Parallel Interactive and Integrated Visualisation ............ 184
C. Meiselbach, R. Bruckschen: Interactive Visualization: On the Way to a Virtual
Wind Tunnel ....................... " ............................................................................................ 203
CONTENTS (continued)
Page
IL DIRECT AND LARGE·EDDY SIMULATION OF TURBULENCE .......... 209
C. Hartel: Introduction to Part IT ............ .............. ............................ ...... .............. ......... 211
E. Giintsch, R. Friedrich: Direct Numerical Simulation of Turbulence Compress sed
in a Cylinder ..................................................................................................................... 213
C. MaaS, U. Schumann: Direct Numerical Simulation of Separated Turbulent Flow
Over a Wavy Boundary .................................................................................................... 227
C. Hartel, L. Kleiser: Large-Eddy Simulation of Near-Wall Turbulence ..................... 242
M. Breuer, W. Rodi: Large Eddy Simulation for Complex Turbulent Flows of
Practical Interest ................................................................................................................ 258
M. Manhart, H. Wengle: Large-Eddy Simulation and Eigenmode Decomposition of
Turbulent Boundary Layer Flow Over a Hemisphere ..................................................... 275
m.
MATHEMATICAL FOUNDATIONS, GENERAL SOLUTION
TECHNIQUES AND APPLICATIONS ........................................................... 291
M. Meinke: Introduction to Part ITI .............................................................................. 293
R. Rautmann: Navier-Stokes Approximations in High Order Norms ........................... 295
S. Blazy, W. Borchers, U. Dralle: Parallelization Methods for a Characteristic's
Pressure Correction Scheme ................. .................. .................................. .............. .......... 305
K. Steiner: Weighted Particle Method Solving Kinetic Equations for Dilute Ionized
Gases ................................................................................................................................. 322
KJ. Geratz, R. Klein, C.D. Munz, S. Roller: Multiple Pressure Variable (MPV)
Approach for Low Mach Number Flows Based on Asymptotic Analysis ..................... 340
M. Weimer, M. Meinke, E. Krause: Numerical Simulation of Incompressible Flows
with the Method of Artificial Compressibility .............................................. .................. 355
M. Wierse, D. Kroner: Higher Order Upwind Schemes on Unstructured Grids
for the Nonstationary Compressible Navier-Stokes Equations in Complex
Timedependent Geometries in 3-D .................................................................................. 369
CONlENTS (continued)
Page
L. Xue, T. Rung, F. Thiele: Improvement and Application of a Two Stream-
Function Fonnulation Navier-Stokes Procedure .............................................................. 385
R. Hentschel, E.H. Hirschel: AMRFLEX3D-Flow Simulation Using a Three-
Dimensional Self-Adaptive, Structured Multi-Block Grid System ................................. 400
Z. Lilek, M. Peric, V. Seidl: Development and Application of a Finite Volume
Method for the Prediction of Complex Flows ................................................................. 416
R. Vilsmeier, D. Hanel: Computational Aspects of Flow Simulation on 3-D,
Unstructured, Adaptive Grids ........................................................................................... 431
C. Roehl, H. Simon: Flow Simulations in Aerodynamically Highly Loaded
Turbomachines Using Unstructured Adaptive Grids ....................................................... 446
W. Evers, M. Heinrich, I. Teipel, A.R. Wiedermann: Flow Simulation in a High
Loaded Radial Compressor .............................................................................................. 461
H. Greza, S. Bikker, W. Koschel: Efficient FEM Flow Simulation on Unstructured
Adaptive Meshes ............................................................................................................... 476
J. Gronner, E. von Lavante, M. Hilgenstock, M. Kallenberg; Numerical Methods
for Simulating Supersonic Combustion ..... ,..................................................................... 491
D. Nellessen, O. Britten, S. Schiechtriem, J. Ballmann: Aeroelastic Computations
of a Fokker-Type Wing in Transonic Flow..................................................................... 501
E. Laurin, J. Wiesbaum: Three-Dimensional Numerical Simulation of the
Aerothermodynamic Reentry ........ .................. ........ ...... .............. .......................... ............ 517
S. Briick, O. Brenner, D. Rues, D. Schwam born: Investigations of Hypersonic
Flows Past Blunt Bodies at Angle of Attack .................................................................. 530
IV. RESULTS OF BENCHMARK COMPUTATIONS ....................................... 545
M. Schafer, S. Turek (and F. Durst, E. Krause, R. Rannacher): Benchmark
Computations of Laminar Flow Around a Cylinder ....................................................... 547
F. Durst, M. Fischer, 1. Jovanovic, H. Kikura, C. Lange: LOA Measurements
in the Wake of a Circular Cylinder ................................................................................. 556
