Explicit Residual Discretizations for Shallow Water Flows

Mario Ricchiuto 1, 2
1 BACCHUS - Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5800
Abstract : We describe an explicit residual based discretization of the Shallow Water equations. When based on a continuous polynomial approximation of the unknowns, these discretizations have remarkable properties in terms of preservation of steady equilibria. However, they are also implicit by nature due to the necessity of inverting a mass matrix. Following [Ricchiuto and Abgrall, J.Comput.Phys. 229, 2010], we present an approach to construct genuinely explicit schemes, which simply by properly choosing the approximation space, preserve steady equilibria at the discrete level on unstructured meshes. Numerical examples involving multidimensional perturbations of steady equilibria and wetting/drying are presented.
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https://hal.inria.fr/hal-00651806
Contributeur : Mario Ricchiuto <>
Soumis le : mercredi 14 décembre 2011 - 11:40:22
Dernière modification le : jeudi 11 janvier 2018 - 06:22:35

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Mario Ricchiuto. Explicit Residual Discretizations for Shallow Water Flows. AIP Conference Proceedings, American Institute of Physics, 2011, 1389 (1), pp.919-922. 〈10.1063/1.3636885〉. 〈hal-00651806〉

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