Hyperbolic Problems: Theory, Numerics, Applications: Seventh International Conference in Zürich, February 1998 Volume II PDF
Preview Hyperbolic Problems: Theory, Numerics, Applications: Seventh International Conference in Zürich, February 1998 Volume II
ISNM 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
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