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.
CITATION STYLE
Bonnet-Ben Dhia, A. S., Bristeau, M. O., Godlewski, E., Impériale, S., Mangeney, A., & Sainte-Marie, J. (2021). Pseudo-compressibility, Dispersive Model and Acoustic Waves in Shallow Water Flows. In SEMA SIMAI Springer Series (Vol. 28, pp. 209–250). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-72850-2_10
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