Table Of ContentISNM
International Series of Numerical Mathematics
Vol. 129
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 I
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; 65N12
A CIP catalogue record for this book is avaiIabIe from the Library of Congress, Washington D.C., USA
Die Deutsche Bibliotbek - CIP-Einheitsaufnahme
Byperbolic problems: theory, numerics, applications : seventb international
conference in Ziirich, February 1998/ ed. by Michael Fey ; Rolf Jeltsch.
Basel ; Boston; Berlin: Birkhauser.
VoI. 1. -(1999)
(International series of numerical matbematics ; VoI. 129)
ISBN 978-3-0348-9742-6 ISBN 978-3-0348-8720-5(eBook)
DOI 10.1007/978-3-0348-8720-5
This work is subject to copyright. Ali rights are reserved, whether tbe whole or part of tbe material is concerned,
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© 1999 Springer Basel AG
Originally published by Birkhăuser Verlag,Basel, Switzerland 1999
Printed on acid-free paper produced of chlorine-free pulp. TCF
00
Cover design: Heinz Hiltbrunner, Basel
987654321
Contents
Volume 1
D. Aregba-Driollet and R. Natalini
Discrete Kinetic Schemes for Systems of Conservation Laws 1
Paul Arminjon and Aziz Madrane
A Mixed Finite Volume/Finite Element Method for 2-dimensional
Compressible Navier-Stokes Equations on Unstructured Grids .......... 11
Fumioki Asakura
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 Frederic Coquel
Travelling Wave Solutions of a Convective Diffusive System with
First and Second Order Terms in N onconservation Form ................ 47
Franca 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. Trakhinin
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 I. Bogoyavlenskij
Courant's Problems and Their Extensions 97
Carles Bona
Old and New Hyperbolic Approaches in General Relativity............. 105
vi Contents
Franr;ois Bouchut and Franr;ois James
Differentiability with Respect to Initial Data
for a Scalar Conservation Law .......................................... 113
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
Thaveling 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
Contents Vll
Rosa Donat and Antonio Marquina
Computing Strong Shocks in Ultrarelativistic Flows:
A Robust Alternative .................................................. 243
Cleb C. Doronin and Aparecido J. Souza
A Free Boundary Problem for an Elastic-Plastic Flow Model 253
Cunilla Efraimsson and Cunilla Kreiss
Numerical Errors Downstream of Slightly Viscous Shocks. . . . . . . . . . . . . .. 263
Bjorn Engquist and Olof Runborg
Multiphase Computations in Geometrical Optics 273
Steinar Evje and Kenneth Hvistendahl Karlsen
Degenerate Convection-Diffusion Equations and Implicit
Monotone Difference Schemes .......................................... 285
Michael Fey
On the Numerical Solution of Multi-dimensional Non-linear
Systems of Conservation Laws 295
Doris Folini and Rolf Walder
3D Radiative Transfer Under Conditions of Non-local Thermodynamic
Equilibrium: A Contribution to the Numerical Solution. . . . . . . . . . . . . . . .. 305
Hans Forrer and Marsha Berger
Flow Simulations on Cartesian Grids Involving
Complex Moving Geometries........................................... 315
J. Fort, J. Furst, J. Halama, M. Hrusova and K. Kozel
Comparisons of Cell Centered and Cell Vertex Finite Volume
Methods for Internal Flow Problems .......................... . . . . . . . . .. 325
Heinrich Preistuhler and Christian Rohde
Numerical Methods for Viscous Profiles of
Non-classical Shock Waves 333
H ermano Frid
On the Asymptotic Behavior of Solutions of Certain Multi-D
Viscous Systems of Conservation Laws ................................. 343
Christian Fries
Stability of General Shock profiles - a Novel Weight Function
for the Non-convex Case ............................................... 353
V.A. Calkin
Global Correctness of Cauchy Problem for Nonlinear Conservation
Laws Systems and one Example for the Gas Dynamics ................. 361
viii Contents
Isabelle Gallagher
Asymptotics for Hyperbolic Equations with a
Skew-symmetric Perturbation .......................................... 369
Guido Giese
Decomposition of the Elastic-plastic Wave Equation
into Advection Equations .............................................. 375
Birgit Gottschlich-Muller and Siegfried Muller
Adaptive Finite Volume Schemes for Conservation Laws
Based on Local Multiresolution Techniques ............................. 385
M. Grassin
Existence of Global Smooth Solutions to Euler Equations
for an Isentropic Perfect Gas ........................................... 395
Rainer Grauer
Adaptive Mesh Refinement for Singular Structures in Incompressible
Hydro- and Magnetohydrodynamic Flows .............................. 401
Michael Griebel and Gerhard Zumbusch
Adaptive Sparse Grids for Hyperbolic Conservation Laws ............... 411
G. Guiochon, F. James and M. Sepulveda
Numerical Results for the Flux Identification in a
System of Conservation Laws ........................................... 423
Tim Gutzmer
Adaptive Mesh Coarsening in CFD 433
D. Hanel, P. Roth, M. Rose, C. Thill, U. Uphoff, and R. Vilsmeier
Adaptive Grid Methods for Reactive Flows ............................. 445
H arumi Hattori
The Riemann Problem of a System for a Phase Transition Problem ..... 455
S.B. Hazra
Computation of High-speed Flow Using Non-Oscillatory Scheme........ 465
Alan W. Hood
Nonlinear MHD Processes in the Sun's Atmosphere 475
Ling Hsiao and Ronghua Pan
The Relaxation Approximation to Hyperbolic System
of Conservation Laws .................................................. 485
K. Hvistendahl Karlsen, K.-A. Lie and N.H. Risebro
A Front Tracking Method for Conservation Laws
with Boundary Conditions ............................................. 493
Contents IX
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 Sinestmri
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 Koeber
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
Tong Li
Stability and Instability of Detonation Waves ........................... 641
x Contents
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 Pareschi 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
Yulian B. Radvogin and Nikolay A. Zaitsev
Absolutely Transparent Boundary Conditions for Time-Dependent
Wave-Type Problems ................................................... 783
