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A multi well-balanced scheme for the shallow water MHD system with topography

Abstract : The shallow water magnetohydrodynamic system involves several families of physically relevant steady states. In this paper we design a well-balanced numerical scheme for the shallow water magnetohydrodynamic system with topography, that resolves exactly a large range of steady states. Two variants are proposed with slightly different families of preserved steady states. They are obtained by a generalized hydrostatic reconstruction algorithm involving the magnetic field and with a cutoff parameter to remove singularities. The solver is positive in height and semi-discrete entropy satisfying, which ensures the robustness of the method.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-01131297
Contributor : François Bouchut Connect in order to contact the contributor
Submitted on : Wednesday, January 6, 2016 - 6:13:34 PM
Last modification on : Thursday, September 29, 2022 - 2:21:15 PM

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  • HAL Id : hal-01131297, version 2

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François Bouchut, Xavier Lhébrard. A multi well-balanced scheme for the shallow water MHD system with topography. 2016. ⟨hal-01131297v2⟩

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