Numerical Methods for Hyperbolic and Kinetic Problems: CEMRACS 2003 (IRMA Lectures in Mathematics & Theoretical Physics, 7)

✍ Scribed by Stephane Cordier, Thierry Goudon, Michael Gutnic, Eric Sonnendrucker

• Publisher: European Mathematical Society
• Year: 2005
• Tongue: English
• Leaves: 369
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Cover......Page 1
IRMA Lectures in Mathematics and Theoretical Physics 7......Page 2
Previously published in this series......Page 3
Title......Page 4
ISBN 3-03719-012-4......Page 5
Preface......Page 6
Table of Contents......Page 8
Kinetic problems......Page 10
Introduction......Page 12
Numerical charge conservation in Particle-In-Cell codes......Page 16
An adaptive Particle-In-Cell method using multi-resolution analysis......Page 38
Adaptive numerical resolution of the Vlasov equation......Page 52
A conservative and entropic method for the Vlasov–Fokker–Planck–Landau equation......Page 68
Numerical studies for nonlinear Schrödinger equations: the Schrödinger–Poisson-X\alpha model and Davey–Stewartson systems......Page 80
Ionospheric plasmas: model derivation, stability analysis and numerical simulations......Page 110
A case study on the reliability of multiphase WKB approximation for the one-dimensional Schrödinger equation......Page 140
Hyperbolic problems......Page 152
Introduction......Page 154
Liquid jet generation and break-up......Page 158
Numerical study of a conservative bifluid model with interpenetration......Page 186
DINMOD: A diffuse interface model for two-phaseflows modelling......Page 218
Sharp and diffuse interface methods for phase transition problems in liquid-vapour flows......Page 248
Geometric Eddington factor for radiative transfer problems......Page 280
Arbitrary high order discontinuous Galerkin schemes......Page 304
The multiple pressure variables method for fluid dynamics and aeroacoustics at low Mach numbers......Page 344
Back Cover......Page 369

✦ Subjects

Математика;Вычислительная математика;