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

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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 one-dimensional 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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Authors and Affiliations

  1. Laboratoire d’Analyse et de Mathématiques Appliquées (UMR 8050), CNRS, UPEM, UPEC, Université Paris-Est, 77454, Marne-la-Vallée, France

    François Bouchut & Xavier Lhébrard

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  1. François Bouchut
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  2. Xavier Lhébrard
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Correspondence to François Bouchut.

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Bouchut, F., Lhébrard, X. A multi well-balanced scheme for the shallow water MHD system with topography. Numer. Math. 136, 875–905 (2017). https://doi.org/10.1007/s00211-017-0865-y

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  • DOI: https://doi.org/10.1007/s00211-017-0865-y

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