Generalized Riemann Problems in Computational Fluid Dynamics

Matania Ben-Artzi, Joseph Falcovitz

366 pages, parution le 25/03/2003

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Résumé

Numerical simulation of compressible, inviscid, time-dependent flow is a major branch of computational fluid dynamics. Its primary goal is to obtain accurate representation of the time evolution of complex flow patterns, involving interactions of shocks, interfaces, and rarefaction waves. The Generalized Riemann Problem (GRP) algorithm, developed by the authors for this purpose, provides a unifying 'shell' which comprises some of the most commonly used numerical schemes of this process. This monograph gives a systematic presentation of the GRP methodology, starting from the underlying mathematical principles, through basic scheme analysis and scheme extensions (such as reacting flow or two-dimensional flows involving moving or stationary boundaries). An array of instructive examples illustrates the range of applications, extending from (simple) scalar equations to computational fluid dynamics. Background material from mathematical analysis and fluid dynamics is provided, making the book accessible to both researchers and graduate students of applied mathematics, science and engineering.

Contents

Part I. Basic Theory

Scalar conservation laws
The GRP method for scalar conservation laws
Systems of conservation laws
The generalized Riemann problem (GRP) for compressible fluid dynamics
Analytical and numerical treatment of fluid dynamical problems

Part II. Numerical Implementation

From the GRP algorithm to scientific computing
Geometric extensions
A physical extension: reacting flow
Wave interaction in a duct - A comparative study

Appendices

A- Entropy Conditions For Scalar Conversation Laws
B- Convergence of the Godunov Scheme
C- Riemann Solver for a γ-Law Gas
D- The MUSCL Scheme

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Matania Ben-Artzi, Joseph Falcovitz
Parution	25/03/2003
Nb. de pages	366
Format	15,7 x 23,5
Couverture	Relié
Poids	692g
Intérieur	Noir et Blanc
EAN13	9780521772969
ISBN13	978-0-521-77296-9