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

Anne-Sophie Bonnet-BenDhia, Marie-Odile Bristeau, Edwige Godlewsk Godlewski,
Sébastien Imperiale, Anne Mangeney and Jacques Sainte-Marie
Publication type:
Paper in peer-reviewed journals
SEMA SIMAI Springer Series, pp. 209--250
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.
    author={Anne-Sophie Bonnet-BenDhia and Marie-Odile Bristeau and Edwige 
           Godlewsk Godlewski and Sébastien Imperiale and Anne Mangeney 
           and Jacques Sainte-Marie },
    title={Pseudo-compressibility, dispersive model and acoustic waves in 
           shallow water flows },
    journal={SEMA SIMAI Springer Series },
    year={2021 },