Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws

François Bouchut

ISBN 10: 3764366656 / ISBN 13: 9783764366650

Editore: Springer, Basel, Birkhäuser Basel, Birkhäuser Jun 2004, 2004

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This item is printed on demand - it takes 3-4 days longer - Neuware -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 stability properties. 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. 134 pp. Englisch. Codice articolo 9783764366650

Dati bibliografici

Titolo: Nonlinear Stability of Finite Volume Methods...

Casa editrice: Springer, Basel, Birkhäuser Basel, Birkhäuser Jun 2004

Data di pubblicazione: 2004

Legatura: Taschenbuch

Condizione: Neu

Descrizione articolo

Riassunto:

The schemes are analyzed regarding their nonlinear stability

Recently developed entropy schemes are presented

A formalism is introduced for source terms

Recensione:

From the reviews:

“This is a very interesting and useful book which provides a systematic presentation of the theory of finite volume methods and numerical simulations for hyperbolic systems of conservation laws. The author provides a unified approach and notation to the study of nonlinear stability of finite volume methods for hyperbolic systems of conservation laws as the accent is put on the development of tools and design of schemes. The exposition of the book is very clear. It will be a very useful tool for the researchers in this field as well as for engineers.”(ZENTRALBLATT MATH)