# On the well-balance property of Roe’s method for nonconservative hyperbolic systems. Applications to shallow-water systems

- Volume: 38, Issue: 5, page 821-852
- ISSN: 0764-583X

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topParés, Carlos, and Castro, Manuel. "On the well-balance property of Roe’s method for nonconservative hyperbolic systems. Applications to shallow-water systems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 38.5 (2004): 821-852. <http://eudml.org/doc/244896>.

@article{Parés2004,

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. Fluids 23 (1994) 1049–1071]; in the case of two layer flows, they are compared with the numerical scheme presented by [Castro, Macías and Parés, ESAIM: M2AN 35 (2001) 107–127].},

author = {Parés, Carlos, Castro, Manuel},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {nonconservative hyperbolic systems; well-balanced schemes; Roe method; source terms; shallow-water systems},

language = {eng},

number = {5},

pages = {821-852},

publisher = {EDP-Sciences},

title = {On the well-balance property of Roe’s method for nonconservative hyperbolic systems. Applications to shallow-water systems},

url = {http://eudml.org/doc/244896},

volume = {38},

year = {2004},

}

TY - JOUR

AU - Parés, Carlos

AU - Castro, Manuel

TI - On the well-balance property of Roe’s method for nonconservative hyperbolic systems. Applications to shallow-water systems

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2004

PB - EDP-Sciences

VL - 38

IS - 5

SP - 821

EP - 852

AB - 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. Fluids 23 (1994) 1049–1071]; in the case of two layer flows, they are compared with the numerical scheme presented by [Castro, Macías and Parés, ESAIM: M2AN 35 (2001) 107–127].

LA - eng

KW - nonconservative hyperbolic systems; well-balanced schemes; Roe method; source terms; shallow-water systems

UR - http://eudml.org/doc/244896

ER -

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