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

470 Pages·2001·17.197 MB·English

by  Bernard Haasdonk (auth.), Heinrich Freistühler, Gerald Warnecke (eds.)

ISNM
International Series of Numerical Mathematics
Vol. 141
Managing Editors:
K.-H. Hoffmann, MGnchen
D. Mittelmann, Tempe
Associate Editors:
R. E. Bank, La Jolla
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 II
Edited by
Heinrich FreistGhler
Gerald Warnecke
Springer Basel AG
Editors:
Heinrich Freistiihler Gerald Wamecke
Max Planck Institute for Mathematics Institute of Analysis and Numerical Mathematics
in the Sciences Otto-von-Guericke-Un i versity
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 / ed. by Heinrich Freistiihler;
Gerald Wamecke. -Basel ; Boston; Berlin: Birkhiiuser
ISBN 978-3-0348-9538-5 ISBN 978-3-0348-8372-6 (eBook)
DOI 10.1007/978-3-0348-8372-6
VoI. 2 . - (2001)
(International series of numeric al mathematics ; VoI. 141)
ISBN 978-3-0348-9538-5
ISBN 978-3-0348-9538-5
This work is subject to copyright. Ali 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 kind of use whatsoever, permission from the copyright owner must be obtained.
© 2001 Springer Basel AG
Originally published by Birkhiiuser Verlag, Basel-Boston -Berlin in 2001
Softcover reprint of the hardcover 1s t edition 200 1
Printed on acid-free paper produced of chlorine-free pulp
ISBN 978-3-0348-9538-5
987654321 www.birkhasuer-science.com
Contents
Volume 2
B. Haasdonk
Convergence of a Staggered Lax-Friedrichs Scheme
on Unstructured 2D-grids .......................................... 475
J. Hiirterich
Viscous and Relaxation Approximations to Heteroclinic Traveling Waves
of Conservation Laws with Source Terms ............................. 485
R. Hartmann
Adaptive FE Methods for Conservation Equations .................... 495
H. Hattori
The Entropy Rate Admissibility Criterion
for a Phase Transition Problem ..................................... 505
c. Helling, R. Klein, M. Liittke, and E. Sedlmayr
Dust Formation in TUrbulent Media ................................. 515
A. Hertzog and A. Mondoloni
Existence of a Weak Solution for a Quasilinear Wave Equation
with Boundary Condition .......................................... 525
L. Hsiao and H. L. Li
Asymptotic Behavior of Entropy Weak Solution for Hyperbolic System
with Damping .................................................... 535
P. Huot
On the Existence of Semi discrete Shock Profiles ....................... 543
E. R. Jakobsen, K. H. Karlsen, and N. H. Risebro
On the Convergence Rate of Operator Splitting for Weakly Coupled
Systems of Hamilton-Jacobi Equations ............................... 553
M. Janda, K. Kozel, and R. Liska
Composite Schemes on Triangular Meshes ............................ 563
S. Jin and L. Pares chi
Asymptotic-Preserving (AP) Schemes for Multiscale Kinetic Equations:
A Unified Approach ............................................... 573
M. Junk
A Kinetic Approach to Hyperbolic Systems and the Role of Higher Order
Entropies ........................................................ 583
vi Contents
S. Kawashima and S. Nishibata
Stationary Waves for the Discrete Boltzmann Equations
in the Half Space ................................................. 593
F. Kemm, C.-D. Munz, R. Schneider, and E. Sonnendriicker
Divergence Corrections in the Numerical Simulation of Electromagnetic
Wave Propagation ................................................ 603
G. Kreiss and M. Liefvendahl
Numerical Investigation of Examples of Unstable Viscous Shock Waves .. 613
G. Kreiss and M. Siklosi
Proving Existence of Nonlinear Differential Equations Using Numerical
Approximations ................................................... 623
W. Kress
Asymptotic Behavior of Hyperbolic Boundary Value Problems
with Relaxation Term ............................................. 633
R. J. Le Veque and J. A. Rossmanith
A Wave Propagation Algorithm for the Solution of PDEs
on the Surface of a Sphere ......................................... 643
M. Lewicka
On the L1 Stability of Multi-shock Solutions to the Riemann Problem ... 653
S. Liebscher
Stable, Oscillatory Viscous Profiles of Weak Shocks
in Systems of Stiff Balance Laws .................................... 663
R. Liska and B. Wendroff
Shallow Water Conservation Laws on a Sphere ........................ 673
D. Marchesin, J. da Mota, and A. de Souza
Riemann Solutions for a Model of Combustion in Two-Phase Flow
in Porous Media .................................................. 683
D. Marchesin and B. Plohr
Theory of Three-Phase Flow Applied to Water-Alternating-Gas Enhanced
Oil Recovery ..................................................... 693
A. Meister and C. Vomel
Preconditioned Krylov Subspace Methods
for Hyperbolic Conservation Laws ................................... 703
J.-M. Mercier and B. Piccoli
The Riemann Problem for Nonlinear Elasticity ....................... 713
Contents VB
R. C. Millington, V. A. Titarev and E. F. Toro
ADER: Arbitrary-Order Non-Oscillatory Advection Schemes ........... 723
1. Muller
Extended Thermodynamics - the Physics and Mathematics of the
Hyperbolic Equations of Thermodynamics ........................... 733
C.-D. Munz, P. Omnes, and R. Schneider
Enforcing Gauss' Law in Computational Electromagnetics
within a Finite-volume Framework .................................. 755
R. Natalini and S. Tang
Discrete BGK Models for Dynamic Phase Transitions in One-Dimension. 765
S. Noelle, W. Rosenbaum, and M. Rumpf
An Adaptive Staggered Grid Scheme for Conservation Laws ............ 775
D. N. Ostrov
Solutions to Scalar Conservation Laws Where the Flux is Discontinuous
in Space and Time ................................................ 785
S. Poedts and H. De Sterck
Overcompressive Shocks and Compound Shocks
in 2D and 3D Magnetohydrodynamic Flows .......................... 791
J. E. Romate
Aspects of a Numerical Procedure for Two-Phase Flow Models ......... 801
O. S. Rozanova
On a Nonexistence of Global Smooth Solutions
to Compressible Euler Equations .................................... 811
G. Russo
Central Schemes for Balance Laws .................................. 821
M. Ruzhansky
Estimates for Pseudo-differential and Hyperbolic Differential Equations
via Fourier Integrals with Complex Phases ........................... 831
H. R. Schwetlick
Existence of Travelling Fronts for Nonlinear Transport Equations ....... 841
1. Selezov
Nonlinear Wave Propagation in Close to Hyperbolic Systems ........... 851
J. A. Smoller and J. B. Temple
Shock-Wave Cosmology ............................................ 861
viii Contents
T. Sonar and 1. Thomas
On a Second Order Residual Estimator for Nonlinear Conservation Laws. 863
T. Tang
Error Estimates of Approximate Solutions for Nonlinear Scalar
Conservation Laws ................................................ 873
F. G. Tcheremissine
Solution of the Boltzmann Equation in Stiff Regime ................... 883
v. M. Teshukov
Characteristics and Riemann Invariants of the Kinetic Integrodifferential
Equations of Bubbly Flow ......................................... 891
S. Tiwari
A LSQ-SPH Approach for Solving Compressible Viscous Flows ......... 901
Yu. L. Trakhinin
On Stability of Fast Shock Waves in Classical and Relativistic MHD .... 911
W.-A. Yong
Remarks on Hyperbolic Relaxation Systems .......................... 921
R. Young
Wave Interactions in Nonlinear Strings .............................. 931
List of Participants ................................................... 941
Author Index ....................................................... 945
Contents ix
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 of Smoothness 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 of Maxwell 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. Helzel
Crossflow Instabilities in the Approximation of Detonation Waves ....... 119
x Contents
D. S. Bale and R. J. Le Veque
Wave Propagation Algorithms for Hyperbolic Systems
on Curved Manifolds .............................................. 129
W. Bao and S. Jin
The Random Projection Method
for Stiff Multi-species Detonation Computation ....................... 139
S. Benzoni-Gavage
On the Stability of Large Amplitude Semi-discrete Shock Profiles
by Means of an 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 of the Godunov Scheme for Straight Line Systems ......... 187
A. Bressan and W. Shen
The Convergence of Multicomponent Chromatography with Relaxation .. 197
R. Burger and K. H. Karlsen
A Strongly Degenerate Convection-diffusion Problem Modeling
Centrifugation of Flocculated 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 of Abdominal 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