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An all-regime and well-balanced Lagrange-projection type scheme for the shallow water equations on unstructured meshes

Abstract : In this work, we focus on the numerical approximation of the shallow water equations in two space dimensions. Our aim is to propose a well-balanced, all-regime and positive scheme. By well-balanced, it is meant that the scheme is able to preserve the so-called lake at rest smooth equilibrium solutions. By all-regime, we mean that the scheme is able to deal with all flow regimes, including the low-Froude regime which is known to be challenging when using usual Godunov-type finite volume schemes. At last, the scheme should be positive which means that the water height stays positive for all time. Our approach is based on a Lagrange-projection decomposition which allows to naturally decouple the acoustic and transport terms. Numerical experiments on unstructured meshes illustrate the good behaviour of the scheme.
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https://hal.archives-ouvertes.fr/hal-02004835
Contributor : Maxime Stauffert <>
Submitted on : Saturday, February 2, 2019 - 4:35:27 PM
Last modification on : Tuesday, November 17, 2020 - 1:50:04 PM
Long-term archiving on: : Friday, May 3, 2019 - 3:59:27 PM

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  • HAL Id : hal-02004835, version 1
  • ARXIV : 1902.01067

Citation

Christophe Chalons, Samuel Kokh, Maxime Stauffert. An all-regime and well-balanced Lagrange-projection type scheme for the shallow water equations on unstructured meshes. 2019. ⟨hal-02004835⟩

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