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

Carlos Parés; Manuel Castro

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

Abstract

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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].

How to cite

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Parés, 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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Citations in EuDML Documents

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  1. Marica Pelanti, François Bouchut, Anne Mangeney, A Roe-type scheme for two-phase shallow granular flows over variable topography
  2. François Bouchut, Tomás Morales de Luna, An entropy satisfying scheme for two-layer shallow water equations with uncoupled treatment
  3. María Luz Muñoz-Ruiz, Carlos Parés, Godunov method for nonconservative hyperbolic systems
  4. Ulrik Skre Fjordholm, Siddhartha Mishra, Accurate numerical discretizations of non-conservative hyperbolic systems
  5. Ulrik Skre Fjordholm, Siddhartha Mishra, Accurate numerical discretizations of non-conservative hyperbolic systems
  6. Jorge Balbás, Smadar Karni, A central scheme for shallow water flows along channels with irregular geometry
  7. Jorge Balbás, Smadar Karni, A central scheme for shallow water flows along channels with irregular geometry

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