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

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- 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 38.5 (2010): 821-852. <http://eudml.org/doc/194242>.

@article{Parés2010,

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].
},

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

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

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

language = {eng},

month = {3},

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/194242},

volume = {38},

year = {2010},

}

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

DA - 2010/3//

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. 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].

LA - eng

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

UR - http://eudml.org/doc/194242

ER -

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- François Bouchut, Tomás Morales de Luna, An entropy satisfying scheme for two-layer shallow water equations with uncoupled treatment
- Ulrik Skre Fjordholm, Siddhartha Mishra, Accurate numerical discretizations of non-conservative hyperbolic systems
- Ulrik Skre Fjordholm, Siddhartha Mishra, Accurate numerical discretizations of non-conservative hyperbolic systems
- Jorge Balbás, Smadar Karni, A central scheme for shallow water flows along channels with irregular geometry
- Jorge Balbás, Smadar Karni, A central scheme for shallow water flows along channels with irregular geometry

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