Fully well-balanced, positive and simple approximate Riemann solver for shallow water equations

Christophe Berthon 1 S. Cornet G. Sperone Christophe Chalons 2
1 LMJL - Laboratoire de Mathématiques Jean Leray
2 LMV - Laboratoire de Mathématiques de Versailles
Abstract : The present work is focused on the numerical approximation of the shallow water equations. When studying this problem, one faces at least two important issues, namely the ability of the scheme to preserve the positiveness of the water depth, along with the ability to capture the stationary states.We propose here aGodunov-typemethod that fully satisfies the previous conditions, meaning that the method is in particular able to preserve the steady states with non-zero velocity.
Keywords : positive preserving scheme well-balanced property Shallow-water equations steady states finite volume schemes
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Journal articles
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https://hal.uvsq.fr/hal-02166377
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Submitted on : Wednesday, June 26, 2019 - 5:15:57 PM
Last modification on : Friday, January 10, 2020 - 3:42:28 PM

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UVSQ | LM-VERSAILLES | INSMI | CNRS | CHL | UNIV-NANTES | LMJL | UNIV-PARIS-SACLAY

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Christophe Berthon, S. Cornet, G. Sperone, Christophe Chalons. Fully well-balanced, positive and simple approximate Riemann solver for shallow water equations. Boletim da Sociedade Brasileira de Matemática / Bulletin of the Brazilian Mathematical Society, Springer Verlag, 2016, 47 (1), pp.117-130. ⟨10.1007/s00574-016-0126-1⟩. ⟨hal-02166377⟩

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