Schéma semi-implicite sur maillages décalés pour le système shallow water multi-couches

Abstract : We present a semi-implicit scheme for a two-dimensional multilayer shallow water system with density stratification, formulated on general staggered meshes. The main result of the present note concerns the control of the mechanical energy at the discrete level, principally based on advective fluxes implying a diffusion term expressed in terms of the gradient pressure. The scheme is also designed to capture the dynamics of low-Froude number regimes and offers interesting positivity and well-balancing results. A numerical test is proposed to highlight the scheme's efficiency in the one layer case.
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Arnaud Duran, Jean Paul Vila, Rémy Baraille. Schéma semi-implicite sur maillages décalés pour le système shallow water multi-couches. Comptes Rendus Mathématique, Elsevier Masson, 2017, 355 (12), pp.1298-1306. ⟨10.1016/j.crma.2017.09.011⟩. ⟨hal-02081576⟩

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