12
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 in the Sciences
Institute of Analysis and Numerical Mathematics Otto-von-Guericke-U ni versity
Inselstrasse 22-26 04103 Leipzig Germany
PSF4120 39106 Magdeburg 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 1 st 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
Contents xi
A. Cohen, S. M. Kaber, and M. Postel Multiresolution Analysis on Triangles: Application to Gas Dynamics ..... 257
V. G. Danilov and V. M. Shelkovich Propagation and Interaction of Nonlinear Waves to Quasilinear Equations ........................................... 267
A. Dedner, D. Kroner, C. Rohde, and M. Wesenberg MHD Instabilities Arising in Solar Physics: A Numerical Approach ...... 277
A. Dedner and M. Wesenberg Numerical Methods for the Real Gas MHD Equations ................. 287
P. Degond and M. Lemou Towards a Kinetic Model of Turbulent Incompressible Fluids ........... 297
D. Donatelli and P. Marcati Parabolic Relaxation of Semilinear Multidimensional Hyperbolic Systems ............................................... 307
G. Duro and E. Zuazua Large Time Asymptotics in Contaminant Transport in Porous Media with Variable Diffusion ............................................ 317
A. Eberle A Nonlinear Flux Vector Split Defect Correction Scheme for Fast Solutions of the Euler and Navier-Stokes Equations ............ 327
S. Evje, K. H. Karlsen, and N. H. Risebro A Continuous Dependence Result for Nonlinear Degenerate Parabolic Equations with Spatially Dependent Flux Function .................... 337
R. Fazio and G. Russo A Lagrangian Central Scheme for Multi-Fluid Flows ................... 347
E. Feireisl Ultimate Boundedness, Propagation of Oscillations, and the Long-time Behaviour of Solutions to the Navier-Stokes Equations of Compressible Fluid Flows ...................................................... 357
M. Feistauer and A. Klikova Adaptive Methods for the Solution of Compressible Flow .............. 363
M. Fey, S. Noelle, and C. v. Tome The MoT-ICE: A New Multi-dimensional Wave-propagation-algorithm Based on Fey's Method of Transport. With Application to the Euler-and MHD-equations ............................................... 373
xii Contents
M. Fey and S. A. Zimmermann Positive Decompositions of the Euler Equations into Advection Equations .......................................... 381
F. Finster The Einstein-Dirac-Yang/Mills Equations: Black Holes ................ 391
H. Preistiihler and C. Rohde A Numerical Study on Viscous Profiles of MHD Shock Waves .......... 399
I. Gasser and P. Marcati A Vanishing Debye Length Limit in a Hydrodynamic Model for Semiconductors ................................................ 409
T. Gefiner and D. Kroner Dynamic Mesh Adaption for Supersonic Reactive Flow ................ 415
G. Giese and R. Jeltsch A High-Resolution Scheme for the Elastic-Plastic Wave Equation ....... 425
P. Goatin Stability for Temple Class Systems with £00 Boundary Data ........... 435
P. Godillon Linear Stability of Shock Profiles for Systems of Conservation Laws with Semi-linear Relaxation ........................................ 445
L. Gosse A Nonconservative Numerical Approach for Hyperbolic Systems with Source Terms: The Well-Balanced Schemes ........................... 453
T. Grahs and T. Sonar Multidimensional Artificial Dissipation for the Numerical Approximation of Conservation Laws .............................................. 463
Author Index ....................................................... 473
