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Pseudo-compressibility, dispersive model and acoustic waves in shallow water flows

Anne-Sophie Bonnet-Ben Dhia 1 Marie-Odile Bristeau 2, 3 Edwige Godlewski 3, 2 Sébastien Imperiale 4, 5 Anne Mangeney 6, 2 Jacques Sainte-Marie 2, 3 
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
2 ANGE - Numerical Analysis, Geophysics and Ecology
Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
4 M3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine
LMS - Laboratoire de mécanique des solides, Inria Saclay - Ile de France
Abstract : In this paper we study a dispersive shallow water type model derived from the free surface compressible Navier-Stokes system. The compressible effects allow to capture the acoustic-like waves propagation and can be seen as a relaxation of an underlying incompressible model. The first interest of such a model is thus to capture both acoustic and water waves. The second interest lies in its numerical approximation. Indeed, at the discrete level, the pseudo-compressibility terms circumvent the resolution of an elliptic equation to capture the non-hydrostatic part of the pressure. This drastically reduces the cost of the numerical resolution of dispersive models especially in 2d and 3d.
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Submitted on : Friday, May 29, 2020 - 3:20:12 PM
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Anne-Sophie Bonnet-Ben Dhia, Marie-Odile Bristeau, Edwige Godlewski, Sébastien Imperiale, Anne Mangeney, et al.. Pseudo-compressibility, dispersive model and acoustic waves in shallow water flows. SEMA SIMAI Springer Series, Springer International Publishing, 2021, pp.209--250. ⟨10.1007/978-3-030-72850-2_10⟩. ⟨hal-02493518v3⟩



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