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On the well-balance property of Roe's method for nonconservative hyperbolic systems. applications to shallow-water systems

Published online by Cambridge University Press:  15 October 2004

Carlos Parés  and
Manuel Castro
Carlos Parés
Affiliation:
Dpto. Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, Campus de Teatinos s/n, 29080-Málaga, Spain. grupo@anamat.cie.uma.es.
Manuel Castro
Affiliation:
Dpto. Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, Campus de Teatinos s/n, 29080-Málaga, Spain. grupo@anamat.cie.uma.es.
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Abstract

This paper is concerned with the numerical approximations of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The first goal is to introduce a general concept of well-balancing for numerical schemes solving this kind of systems. Once this concept stated, we investigate the well-balance properties of numerical schemes based on the generalized Roe linearizations introduced by [Toumi, J. Comp. Phys.102 (1992) 360–373]. Next, this general theory is applied to obtain well-balanced schemes for solving coupled systems of conservation laws with source terms. Finally, we focus on applications to shallow water systems: the numerical schemes obtained and their properties are compared, in the case of one layer flows, with those introduced by [Bermúdez and Vázquez-Cendón, Comput. Fluids23 (1994) 1049–1071]; in the case of two layer flows, they are compared with the numerical scheme presented by [Castro, Macías and Parés, ESAIM: M2AN35 (2001) 107–127].

Keywords

Nonconservative hyperbolic systemswell-balanced schemesRoe methodsource termsshallow-water systems.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 5 , September 2004 , pp. 821 - 852
Copyright
© EDP Sciences, SMAI, 2004

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