Table Of ContentISNM
International Series of Numerical Mathematics
Vol. 130
Managing Editors:
K.-H. Hoffmann, MOnchen
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
Seventh International Conference in Zurich, February 1998
Volume II
Edited by
Michael Fey
Rolf Jeltsch
Springer Basel AG
Editors:
Rolf Jeltsch Michael Fey
Seminar for Applied Mathematics Seminar for Applied Mathematics
ETHZentrum ETHZentrum
8092 Ziirich 8092 Ziirich
1991 Mathematics Subject Classification 35LXX; 35L65; 65N 12
A CIP catalogue record for tbis book is available from tbe Library of Congress, Washington D.C., USA
Deutsche Bibliothek Cataloging-in-Publication Data
Hyperbolic problems: theory, numerics, applications : seventh international
conference in Ziirich, February 1998/ ed. by Michael Fey; Rolf Jeltsch.
Basel ; Boston; Berlin: Birkhăuser.
ISBN 978-3-0348-9744-0 ISBN 978-3-0348-8724-3 (eBook)
DOI 10.1007/978-3-0348-8724-3
VoI. 2. - (1999)
(International series of numerical mathematics ; VoI. 130)
ISBN 978-3-0348-9744-0
This work is subject to copyright. AII rights are reserved, whether the whole Of 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.
© 1999 Springer Basel AG
Originally published by Birkhăuser Verlag in 1999
Softcover reprint of tbe hardcover 1s t edition 1999
Printed on acid-free paper produced of chlorine-free pulp. TCF
00
Cover design: Heinz Hiltbrunner, Basel
987654321
Contents
Volume 2
Patrick Jenny and Bernhard Muller
A New Approach for a Flux Solver Taking into Account Source Terms,
Viscous and Multidimensional Effects .................................. 503
Helge Kristian Jenssen and Carlo Sinestrari
Blowup for Hyperbolic Equations....................................... 515
F. Jochmann
Some Analytical Results Concerning the Drift Diffusion Equations for
Semiconductor Devices Coupled with Maxwell's Equations ............. 525
Alexandre V. Kazhikhov and Alexandre E. Mamontov
Transport Equations and Orlicz Spaces ................................. 535
Runhild Aae Klausen and Nils Henrik Risebro
Well-posedness of a 2 x 2 System of Resonant Conservation Laws....... 545
Christian Klingenberg and Yun-Guang Lu
The Relaxation Limit for Systems of Broadwell Type ................... 553
Alfred Kluwick
Weakly-nonlinear Hyperbolic Waves in BZT-fluids ...................... 559
Martin K oeber
Inclusion of Solutions of Cauchy Problems for Quasilinear
Hyperbolic Equations .................................................. 569
Barry Koren and Arthur Venis
A Fed Back Level-Set Method for Moving Material-Void Interfaces 579
A.G. Kulikovskii, N. V. Pogorelov, and A. Yu. Semenov
Mathematical Aspects of Numerical Solution of Hyperbolic Systems 589
Philippe G. LeFloch
Existence of Entropy Solutions for the Compressible Euler Equations ... 599
Randall J. Le Veque and Derek S. Bale
Wave Propagation Methods for Conservation Laws
with Source Terms ..................................................... 609
M.P. Levin
Quasi-Characteristics Numerical Schemes.. . . . . . . . . .. . . . .. . . . . . . . . . . . ... 619
Jiequan Li and Tong Zhang
On the Initial-value Problem for Zero-pressure Gas Dynamics 629
vi Contents
Tong Li
Stability and Instability of Detonation Waves ........................... 641
Salvatore Fabio Liotta, Vittorio Romano and Giovanni Russo
Central Schemes for Systems of Balance Laws.......................... 651
Richard Liska and Burton Wendroff
Composite Centered Schemes for Multidimensional
Conservation Laws..................................................... 661
Hailiang Liu
On the Diffusion Limit of a Hyperbolic Relaxation System .............. 671
Tai-Ping Liu and Tong Yang
Well-Posedness Theory for System of Hyperbolic Conservation Laws.... 681
Tao Luo and Zhouping Xin
Nonlinear Stability of Shock Fronts for a Relaxation System
in Several Space Dimensions ............................................ 693
D.K. Mao
Front Tracking Based on Conservation in
One and Two Space Dimensions ........................................ 703
Jochen Maurer
A Genuinely Multi-dimensional Scheme for
Mixed Hyperbolic-Parabolic Systems................................... 713
Guy Metivier, Jean-Luc Joly and Jeffrey Rauch
Recent Results in Non Linear Geometric Optics 723
K. W. Morton
Evolution-Galerkin Methods: Algorithms and Analysis
from a Finite Difference Viewpoint ..................................... 737
Giovanni Naldi, Lorenzo Pares chi and Giuseppe Toscani
Hyperbolic Relaxation Approximation to Nonlinear
Parabolic Problems .................................................... 747
Sebastian Noelle
A Comparison of Third and Second Order Accurate Finite Volume
Schemes for the Two-dimensional Compressible Euler Equations........ 757
Daniel Ostrov
Unique Solutions to Discontinuous Hamilton-Jacobi Equations
in Shape-From-Shading ................................................ 767
Jochen Peitz and Stefan Appl
Relativistic Dissipative Hydrodynamics in the 3+ 1 Formulation 773
Contents vii
Yulian B. Radvogin and Nikolay A. Zaitsev
Absolutely Transparent Boundary Conditions for Time-Dependent
Wave-Type Problems ................................................... 783
Olga S. Rozanova
Blow-up of Solutions in System of Atmosphere Dynamics............... 793
M. Ruzhansky
Holomorphic Factorization for the Solution Operators
for Hyperbolic Equations ............................................... 803
Yurii G. Rykov
The Propagation of Shock Waves in 2-D System
of Pressureless Gas Dynamics .......................................... 813
H. Joachim Schroll and Jens Lorenz
Hyperbolic Systems with Relaxation: Symmetrizers and Entropies ...... 823
Igor Selezov
Some Hyperbolic Models for Wave Propagation ...... . . . . . . . . . . . . . . . . . .. 833
Denis Serre
Discrete Shock Profiles and Their Stability ............................. 843
J.A. Sethian
Advances in Fast Marching and Level Set Methods
for Propagating Interfaces .............................................. 855
Wen Shen, Aslak Tveito and Ragnar Winther
Rate of Convergence for the Zero Relaxation Limit ..................... 865
Spencer Sherwin
A High Order Fourier/Unstructured Discontinuous
Galerkin Method for Hyperbolic Conservation Laws 875
Armen Shirikyan and Leonid Volevich
Asymptotic Properties of Solutions to High-Order
Hyperbolic Equations Generalizing the Damped Wave Equation ........ 885
Keh-Ming Shyue
A Volume-of-fluid Type Algorithm for
Compressible Two-phase Flows......................................... 895
P.C. Sleziona, M. Auweter-Kurtz, C. Boie, J. Heiermann and S. Lenzner
Numerical Code for Magneto-Plasma Flows ............................ 905
Ivan L. Sofronov
Highly-Accurate Artificial Boundary Conditions for
Unsteady Transonic Flow Problems in Wind Tunnels................... 915
viii Contents
Eitan Tadmor and Tao Tang
Pointwise Convergence Rate for Nonlinear Conservation Laws 925
Tiana Tefy and Penelope Leyland
Newton-GMRES Resolution of III Conditioned Hyperbolic Systems
in Fluid Dynamics ..................................................... 935
Blake Temple and Joel Smoller
Applications of Shock-Waves in General Relativity 945
Vladimir M. Teshukov
The Riemann Problem for the Integrodifferential Equations
of the Shallow Water Theory ........................................... 953
K onstantina Trivisa
Decay and Uniqueness of Solutions of Nonlinear Hyperbolic
Conservation Laws via Generalized Characteristics ..................... 963
Rolf Walder and Doris Folini
Radiative Shocks, Supersonic Turbulence and
Structure Formation in Space .......................................... 973
Michael Westdickenberg and Sebastian Noelle
ANew Convergence Proof for FV Schemes 983
Harry Yserentant
The Particle Model of Compressible Fluids 993
Susanne Amy Zimmermann
The Method of Transport for the Euler Equations
Written as a Kinetic Scheme ........................................... 999
List of Participants ....................................................... 1009
Contents IX
Volume 1
D. Aregba-Driollet and R. Natalini
Discrete Kinetic Schemes for Systems of Conservation Laws 1
Paul Arminjon and Aziz Madmne
A Mixed Finite Volume/Finite Element Method for 2-dimensional
Compressible Navier-Stokes Equations on Unstructured Grids .......... 11
Fumioki Asakum
Large Time Stability of Propagating Phase Boundaries 21
B. Ben Moussa, N. Lanson and J.P. Vila
Convergence of Meshless Methods for Conservation Laws
Applications to Euler equations ........................................ 31
Sylvie Benzoni
Multi-dimensional Stability of Propagating Phase Boundaries 41
Christophe Berthon and Fn!deric Coquel
Travelling Wave Solutions of a Convective Diffusive System with
First and Second Order Terms in Nonconservation Form................ 47
Fmnca Bianco, Gabriella Puppo and Giovanni Russo
High Order Central Schemes for Hyperbolic Systems
of Conservation Laws .................................................. 55
G. Billet and O. Louedin
A Simple Algorithm to Improve the Accuracy
of TVD-MUSCL Schemes .............................................. 65
Alexander M. Blokhin and Yuri L. Tmkhinin
Hyperbolic Initial Boundary Value Problems on the Stability
of Strong Discontinuities in Continuum Mechanics ...................... 77
Igor Bock
On Hyperbolic Integro-differential von Karman Equations
for Viscoelastic Plates .................................................. 87
Oleg 1. Bogoyavlenskij
Courant's Problems and Their Extensions 97
Carles Bona
Old and New Hyperbolic Approaches in General Relativity 105
Fmnr;ois Bouchut and Fmnr;ois James
Differentiability with Respect to Initial Data
for a Scalar Conservation Law .......................................... 113
x Contents
Manfred Braun and Slawomir Kosinski
Evolution Behavior of Transverse Shocks in a
Nonlinear Elastic Layer ................................................ 119
Thierry Buffard, Thierry Gallouet and Jean-Marc Herard
A Naive Riemann Solver to Compute a Non-conservative
Hyperbolic System ..................................................... 129
Gui-Qiang Chen
Compactness and Asymptotic Behavior of Entropy Solutions without
Locally Bounded Variation for Hyperbolic Conservation Laws .......... 139
Shuxing Chen
Non-symmetric Conical Supersonic Flow 149
Sebastien Clerc
On the Preconditioning of Finite Volume Schemes 159
Bernardo Cockburn, Pierre-Alain Gremaud, and Jimmy X. Yang
A Priori Error Estimates for Nonlinear Scalar Conservation Laws ....... 167
J. da Mota, W. Dantas and D. Marchesin
Traveling Waves for Combustion in Porous Media 177
Raphael Danchin
Evolution of a Cusp-like Singularity in a Vortex Patch .................. 189
H. De Sterck, H. Deconinck, S. Poedts and D. Roose
A Bow Shock Flow Containing (Almost) All Types of ('Exotic')
MHD Discontinuities ................................................... 195
S.M. Deshpande
Application of Kinetic Schemes to All Types of Meshes ................. 205
Benoit Desjardins
On the Regularity of Solutions of the Compressible Isentropic
Navier-Stokes Equations. . . . .. .. . .. . . . . . . . . . . . .. .. . .. . .. . . . . . . . . . . .. . ... 215
Bruno Despres
Entropy Inequality for High Order Discontinuous Galerkin
Approximation of Euler Equations ..................................... 225
Wlodzimierz Domanski
Asymptotic Equations for Weakly Nonlinear Elastic Waves
in a Cubic Crystal ..................................................... 233
Rosa Donat and Antonio Marquina
Computing Strong Shocks in Ultrarelativistic Flows:
A Robust Alternative .................................................. 243
