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

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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.

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Authors and Affiliations

  1. Laboratoire de Mathématiques Jean Leray, CNRS UMR 6629, Université de Nantes, 2 rue de la Houssinière, BP 92208, 44322, Nantes, France

    C. Berthon

  2. Laboratoire de Mathématiques de Versailles, UMR 8100, UFR des Sciences, bâtiment Fermat, Université de Versailles Saint-Quentin-en-Yvelines, 45 avenue des Etats-Unis, 78035, Versailles cedex, France

    C. Chalons

  3. École Centrale Paris, Grande Voie des Vignes, 92290, Châtenay-Malabry, France

    S. Cornet

  4. Departamento de Ingeniería Matemática, Universidad de Chile, Beauchef 851, Santiago, Chile

    G. Sperone

Authors
  1. C. Berthon
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  2. C. Chalons
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  3. S. Cornet
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  4. G. Sperone
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Corresponding author

Correspondence to C. Chalons.

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Berthon, C., Chalons, C., Cornet, S. et al. Fully well-balanced, positive and simple approximate Riemann solver for shallow water equations. Bull Braz Math Soc, New Series 47, 117–130 (2016). https://doi.org/10.1007/s00574-016-0126-1

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  • DOI: https://doi.org/10.1007/s00574-016-0126-1

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