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Article Dans Une Revue AIP Conference Proceedings Année : 2011

Explicit Residual Discretizations for Shallow Water Flows

Résumé

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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Dates et versions

hal-00651806 , version 1 (14-12-2011)

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Mario Ricchiuto. Explicit Residual Discretizations for Shallow Water Flows. AIP Conference Proceedings, 2011, 1389 (1), pp.919-922. ⟨10.1063/1.3636885⟩. ⟨hal-00651806⟩
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