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Numerical Methods for Hyperbolic and Kinetic Problems
Edited by: Stéphane Cordier, Université d'Orléans, France, Thierry Goudon, Université Lille I, Villeneuve d'Ascq, France, and Michael Gutnic and Eric Sonnendrucker, Université Louis Pasteur, Strasbourg, France
A publication of the European Mathematical Society.
IRMA Lectures in Mathematics and Theoretical Physics
2005; 368 pp; softcover
Volume: 7
ISBN-10: 3-03719-012-4
ISBN-13: 978-3-03719-012-8
List Price: US$49
Member Price: US$39.20
Order Code: EMSILMTP/7
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Hyperbolic and kinetic equations arise in a large variety of industrial problems. For this reason, the Summer Mathematical Research Center on Scientific Computing and its Applications (CEMRACS), held at the Center of International Research in Mathematics (CIRM) in Luminy, was devoted to this topic. During a six-week period, junior and senior researchers worked full time on several projects proposed by industry and academia. Most of this work was completed later on, and the present book reflects these results.

The articles address modelling issues as well as the development and comparisons of numerical methods in different situations. The applications include multi-phase flows, plasma physics, quantum particle dynamics, radiative transfer, sprays, and aeroacoustics.

The text is aimed at researchers and engineers interested in applications arising from modelling and numerical simulation of hyperbolic and kinetic problems.

A publication of the European Mathematical Society. Distributed within the Americas by the American Mathematical Society.


Graduate students, research mathematicians, and engineers interested in applications arising from modelling and numerical simulation of hyperbolic and kinetic problems.

Table of Contents

Kinetic Problems
  • S. Cordier, T. Goudon, and E. Sonnendrücker -- Introduction
  • R. Barthelmé and C. Parzani -- Numerical charge conservation in Particle-In-Cell
  • J.-P. Chehab, A. Cohen, D. Jennequin, J. J. Nieto, Ch. Roland, and J. Roche -- An adaptive Particle-In-Cell method using multi-resolution analysis
  • M. Campos Pinto and M. Mehrenberger -- Adaptive numerical resolution of the Vlasov equation
  • N. Crouseilles and F. Filbet -- A conservative and entropic method for the Vlasov-Fokker-Planck-Landau equation
  • C. Besse, N. J. Mauser, and H. P. Stimming -- Numerical studies for nonlinear Schrödinger equations: the Schrödinger-Poisson-X \(\alpha\) model and Davey-Stewartson system
  • C. Besse, J. Claudel, P. Degond, F. Deluzet, G. Gallice, and C. Tessieras -- Ionospheric plasmas: model derivation, stability analysis and numerical simulations
  • L. Gosse -- A case study on the reliability of multiphase WKB approximation for the one-dimensional Schrödinger equation
Hyperbolic Problems
  • B. Desprès -- Introduction
  • C. Baranger, G. Baudin, L. Boudin, B. Desprès, F. Lagoutière, E. Lapébie, and T. Takahashi -- Liquid jet generation and break-up
  • B. Després, S. Jaouen, C. Mazeran, and T. Takahashi -- Numerical study of a conservative bifluid model with interpenetration
  • F. Caro, F. Coquel, D. Jamet, and S. Kokh -- DINMOD: A diffuse interface model for two-phase flows modelling
  • F. Coquel, D. Diehl, C. Merkle, and C. Rohde -- Sharp and diffuse interface methods for phase transition problems in liquid-vapour flows
  • J. Cartier and A. Munnier -- Geometric Eddington factor for radiative transfer problems
  • M. Dumbser and C.-D. Munz -- Arbitrary high order discontinuous Galerkin schemes
  • C.-D. Munz, M. Dumbser, and M. Zucchini -- The multiple pressure variables method for fluid dynamics and aeroacoustics at low Mach numbers
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