A two-dimensional method for a family of dispersive shallow water model

Abstract : We propose a numerical method for a family of two-dimensional dispersive shallow water systems with topography. The considered models consist in shallow water approximations without the hydrostatic assumption-of the incompressible Euler system with free surface. Hence, the studied models appear as extensions of the classical shallow water system enriched with dispersive terms. The model formulation motivates to use a prediction-correction scheme for its numerical approximation. The prediction part leads to solving a classical shallow water system with topography while the correction part leads to solving an elliptic-type problem. The numerical approximation of the considered dispersive models in the two-dimensional case over unstructured meshes is described, it requires to combine finite volume and finite element techniques. A special emphasis is given to the formulation and the numerical resolution of the correction step (variational formulation, inf-sup condition, boundary conditions,.. .). The numerical procedure is confronted with analytical and experimental test cases. Finally, an application to a real tsunami case is given.
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https://hal.archives-ouvertes.fr/hal-01632522
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Submitted on : Thursday, November 7, 2019 - 11:36:35 AM
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  • HAL Id : hal-01632522, version 4

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Nora Aïssiouene, Marie-Odile Bristeau, Edwige Godlewski, Anne Mangeney, Carlos Parés, et al.. A two-dimensional method for a family of dispersive shallow water model. 2019. ⟨hal-01632522v4⟩

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