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Journal Articles SEMA SIMAI Springer Series Year : 2021

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

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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Dates and versions

hal-02493518 , version 1 (27-02-2020)
hal-02493518 , version 2 (18-03-2020)
hal-02493518 , version 3 (29-05-2020)

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Cite

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, 2021, pp.209--250. ⟨10.1007/978-3-030-72850-2_10⟩. ⟨hal-02493518v3⟩
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