Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources

François Bouchut - Collection Frontiers in Mathematics

134 pages, parution le 12/07/2004

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Résumé

This book is devoted to finite volume methods for hyperbolic systems of conservation laws. It differs from previous expositions on the subject in that the accent is put on the development of tools and the design of schemes for which one can rigorously prove nonlinear stability properties. Sufficient conditions for a scheme to preserve an invariant domain or to satisfy discrete entropy inequalities are systematically exposed, with analysis of suitable CFL conditions.The monograph intends to be a useful guide for the engineer or researcher who needs very practical advice on how to get such desired stabilityproperties. The notion of approximate Riemann solver and the relaxation method, which are adapted to this aim, are especially explained. In particular, practical formulas are provided in a new variant of the HLLC solver for the gas dynamics system, taking care of contact discontinuities, entropy conditions, and including vacuum. In the second half of the book, nonconservative schemes handling source terms are analyzed in the same spirit. The recent developments on well-balanced schemes that are able to capture steady states are explained within a general framework that includes analysis of consistency and order of accuracy. Several schemes are compared for the Saint Venant problem concerning positivity and the ability to treat resonant data. In particular, the powerful and recently developed hydrostatic reconstruction method is detailed.

Sommaire

Quasilinear systems and conservation laws
Conservative schemes
Source terms
Nonconservative schemes
Multidimensional finite volumes with sources
Numerical test with source

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	François Bouchut
Collection	Frontiers in Mathematics
Parution	12/07/2004
Nb. de pages	134
Format	17 x 24
Couverture	Broché
Poids	410g
Intérieur	Noir et Blanc
EAN13	9783764366650