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Numerische Mathematik

, Volume 136, Issue 4, pp 875–905 | Cite as

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

  • François BouchutEmail author
  • Xavier Lhébrard
Article
  • 166 Downloads

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.

Mathematics Subject Classification

76W05 76M12 35L65 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Laboratoire d’Analyse et de Mathématiques Appliquées (UMR 8050), CNRS, UPEM, UPECUniversité Paris-EstMarne-la-ValléeFrance

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