Hyperbolic Problems: Theory, Numerics, Applications: Eighth International Conference in Magdeburg, February/March 2000 Volume 1

481 Pages·2001·18.432 MB·English

by  Rémi Abgrall, Smadar Karni (auth.), Heinrich Freistühler, Gerald Warnecke (eds.)

ISNM
International Series of Numerical Mathematics
Vol. 140
Managing Editors:
K.-H. Hoffmann, MOnchen
D. Mittelmann, Tempe
Associate Editors:
R. E. Bank, LaJolla
H. Kawarada, Chiba
R. J. LeVeque, Seattle
C. Verdi, Milano
Honorary Editor:
J.Todd,Pasadena
Hyperbolic Problems:
Theory, Numerics,
Applications
Eighth International Conference in Magdeburg, February/March 2000
Volume I
Edited by
Heinrich Freistuhler
Gerald Warnecke
Springer Base! AG
Editors:
Heinrich Freistiihler Gerald Wamecke
Max Planck Institute for Mathematics Institute of Analysis and Numerical Mathematics
in the Sciences Otto-von-Guericke-University
Inselstrasse 22-26 PSF4120
04103 Leipzig 39106 Magdeburg
Germany Germany
e-mail: [email protected] e-mail: [email protected]
2000 Mathematics Subject Classification 35LXX; 65MXX, 74B20, 76E25, 76TXX, 83F05
A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA
Deutsche Bibliothek Cataloging-in-Publication Data
Hyperbolic problems: theory, numerics, applications : eighth international
conference in Magdeburg, February, March 2000 led. by Heinrich Freistiihler ;
Gerald Wamecke. -Basel ; Boston; Berlin: Birkhliuser
ISBN 978-3-0348-9537-8 ISBN 978-3-0348-8370-2 (eBook)
DOI 10.1007/978-3-0348-8370-2
VoI. 1 . - (2001)
(International series of numerical mathematics ; VoI. 140)
ISBN 978-3-0348-9537-8
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned,
specifically the rights of translation, reprinting, re-use of illustrations, broadcasting, reproduction on microfilms or in other
ways, and storage in data banks. For any !tind of use whatsoever, permission from the copyright owner must be obtained.
© 2001 Springer Basel AG
Originally published by Birkhliuser Verlag in 2001
Softcover reprint of the hardcover 1s t edition 2001
Printed on acid-free paper produced of chlorine-free pulp
ISBN 978-3-0348-9537-8
Dedicated to Professor Constantine Dafermos
on the occasion of his 60th birthday
Editors' Preface
The Eighth International Conference on Hyperbolic Problems- Theory, Nu
merics, Applications,washeldinMagdeburg,Germany,fromFebruary27toMarch
3, 2000. It was attended by over 220 participants from many European countries
as well as Brazil, Canada, China, Georgia, India, Israel, Japan, Taiwan, und the
USA. Therewere 12plenary lectures, 22 further invitedtalks, and around 150con
tributed talks in parallel sessions as well as posters. The speakers in the parallel
sessions were invited to provide a poster in order to enhance the dissemination of
information.
Hyperbolic partial differential equations describe phenomena of material or
wave transport in physics, biology and engineering, especially in the field offluid
mechanics. Despite considerable progress, the mathematical theory is still strug
gling with fundamental open problems concerning systems of such equations in
multiple space dimensions. For various applications the development of accurate
and efficient numerical schemes for computation is offundamental importance.
Applicationstouched in these proceedings concernone-phase and multiphase
fluid flow, phase transitions, shallow water dynamics, elasticity, extended ther
modynamics, electromagnetism, classical and relativistic magnetohydrodynamics,
cosmology. Contributions to the abstract theory of hyperbolic systems deal with
viscous and relaxation approximations, front tracking and wellposedness, stability
ofshock profilesand multi-shock patterns,travelingfronts for transportequations.
Numerically oriented articles study finite difference, finite volume, and finite ele
ment schemes, adaptive, multiresolution, and artificial dissipation methods.
The biannual series of International Conferences on Hyperbolic Problems
began in 1986 with a meeting in St. Etienne, France. Further conferences took
place in Aachen in Germany, Uppsala in Sweden, Taormina in Italy, Stony Brook,
New York, in the USA, Hongkong in China, and Zurich in Switzerland.
The conference in Magdeburg was held under the auspices of the German
priority research programme "Analysis and Numerics for Conservation Laws"
(ANumE) and the European research network "Hyperbolic Conservation Laws"
(HCL). ANumE is a sixyear (1997-2003) programme ofthe Deutsche Forschungs
gemeinschaft (DFG, Germany's national science foundation), in which over 30 re
search projects in mathematics, astrophysics, and engineering have received fund
ing. HCL, financed by the Commission ofthe European Union, gathered pertinent
groups all over Europe during the years 1996-2000, prompting a number of novel
achievements in the theory ofhyperbolic systems.
At the conference, the scientific committee felt that the field is still strongly
thriving and offers a multitude of interesting challenges for scientific research to
warrant a continuationofthe conference series. The next meetingin theseries will
beorganized in 2002 by T. Hou and E. Tadmor at Caltech inPasadena, USA. The
conference in 2004 is planned to be held in Japan.
viii Editor's Preface
The scientific committee of the Magdeburg conference consisted of J. Ball
mann (Germany), A. Bressan (Italy), C. Dafermos (USA/Greece), B. Engquist
(USA/Sweden), M. Feistauer (Czech Republic), J. Glimm (USA), L. Hsiao
(China),R. Jeltsch (Switzerland),P. Lax (USA),T.-P. Liu (USA/Taiwan),P. Mar
cati (Italy), D. Marchesin (Brazil), K.W. Morton (United Kingdom), B. Perthame
(France), D. Serre (France), E. Tadmor (USA/Israel), A. Tveito (Norway), and
the local organizers. The latter two thank the others for their much appreciated
work.
These conference proceedings were refereed, each submitted paper was read
by at least two experts. We would like to thank all the referees for this work.
Theconferencereceivedconsiderablefinancial support. Themaingrantswere
provided by the DFG and the StateofSachsen-Anhalt, ofwhich Magdeburg is the
capital. They provided funds for invited speakers as well as special support for
participants from eastern European countries. The Otto-von-Guericke-University
hosted the conference, provided rooms and lecture halls as well as staff support,
especially for theconference office. Aconsiderable number ofparticipants received
support from the programmes ANumE and HCL mentioned above. Some partic
ipants were supported through money which was left from the previous Aachen
conference. Further support was given by Commerzbank Magdeburg, the com
puter company Hewlett-Packard, the publisher Birkhauser and Coca Cola. We are
grateful to all sponsors for their generous support.
The performance ofthe meeting depended very much on many helpers that
we had, in particular Nikolai Andrianov, Claudia Bieder, Ines Bruckner, Bar
baraFischbach, LiborGrigerek, WolframHeineken, ChristianeHelzel,IlonaHesse,
Maria Lukacova, Rudiger Muller, Jitka Saibertova and Yousef Zahaykah. We ap
preciate their assistance in making conference organization a success.
Finally agreat thanks to Nikolai Andrianov, ClaudiaBieder, WolframHeine
ken, Stefan Kleeberg, Rudiger Muller and Yousef Zahaykah for the considerable
work they put into producing the final layout ofthese proceedings.
September 2001 Heinrich Freisttihler and Gerald Warnecke
Local conference organizers
Contents
Volume 1
R. Abgrall and S. Karni
Ghost-Fluids for the Poor: A Single Fluid Algorithm for Multifluids ..... 1
R. Airapetyan and 1. Witt
Propagation ofSmoothness for Edge-degenerate Wave Equations. ....... 11
F. Ancona and A. Marson
Front Tracking for Non Genuinely Nonlinear Conservation Laws. ....... 19
F. Ancona and A. Marson
Well-Posedness for Non Genuinely Nonlinear Conservation Laws 29
S. Andreae, J. Ballmann, and U. Specht
Wave Phenomena at Liquid-solid Interfaces 39
D. Aregba-Driollet, R. Natalini, and S. Tang
Diffusive Discrete BGK Schemes for Nonlinear Hyperbolic-parabolic
Systems 49
P. Arminjon, A. Madrane, and A. St-Cyr
Non-oscillatory Lax-Friedrichs type Central Finite Volume Methods
for 3-D Flows on Unstructured Tetrahedral Grids 59
F. Asakura
Stability ofMaxwell States in Thermo-Elasticity. ..................... 69
J. D. Au, D. Reitebuch, M. Torrilhon, and W. Weiss
The Riemann-Problem in Extended Thermodynamics 79
M. Auweter-Kurtz, C. A. Coclici, J. Heiermann, and W. L. Wendland
Heterogeneous Domain Decomposition Methods
for Compressible Magneto-plasma Flows ............................. 89
M. Auweter-Kurtz, C. A. Coclici, J. Heiermann, C.-D. Munz, and C. Sleziona
Magnetoplasmadynamic Rocket Thruster Simulation .................. 99
P. Bagnerini, P. Hoch, and M. Rascle
The Eikonal Equation on a Manifold. Applications to Grid Generation
or Refinement 109
D. S. Bale and C. Hetzel
Crossflow Instabilities in the Approximation ofDetonation Waves 119
x Contents
D. S. Bale and R. J. LeVeque
Wave Propagation Algorithms for Hyperbolic Systems
on Curved Manifolds 129
W. Bao and S. Jin
The Random Projection Method
for StiffMulti-species Detonation Computation 139
S. Benzoni-Gavage
On the Stability ofLarge Amplitude Semi-discrete Shock Profiles
by Means ofan Evans Function in Infinite Dimensions 149
S. Bianchini and A. Bressan
Viscosity Solutions for Hyperbolic Systems
where Shock Curves are Straight Lines 159
M. Braack
Adaptive Finite Elements for Stationary Compressible Flows
at Low Mach Number '" 169
Y. Brenier
A Monge-Kantorovich Approach to the Maxwell Equations 179
A. Bressan and H. K. Jenssen
Convergence ofthe Godunov Scheme for Straight Line Systems 187
A. Bressan and W. Shen
The Convergence ofMulticomponent Chromatography with Relaxation .. 197
R. Burger and K. H. Karlsen
A Strongly Degenerate Convection-diffusion Problem Modeling
Centrifugation ofFlocculated Suspensions 207
S. Canic, B. L. Keyjitz, and E. H. Kim
Weak Shock Reflection Modeled by the Unsteady Transonic Small
Disturbance Equation 217
S. Canic and D. Mirkovic
A Hyperbolic System of Conservation Laws in Modeling
Endovascular Treatment ofAbdominal Aortic Aneurysm 227
S. Chen
Study on Supersonic Flow Past a Pointed Body 237
G. Chiavassa, R. Donat, and A. Marquina
Fine-Mesh Numerical Simulations for 2D Riemann Problems
with a Multilevel Scheme 247