A conservative well-balanced hybrid SPH scheme for the shallow-water model

Christophe Berthon (1) , Matthieu de Leffe (2) , Victor Michel-Dansac (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 HydrOcean

A scheme defined by a hybridization between SPH method and finite volume method is considered. The aim of the present communication is to derive a suitable discretization of the source term to enforce the required well-balanced property. To address such an issue, we adopt a relevant reformulation of the flux function by involving the free surface instead of the water height. Such an approach gives a natural discretization of the topography source term in order to preserve the lake at rest. Moreover, we prove that the scheme is in conservative form, which is, in general, a very difficult task since we do not impose restrictive assumptions on the SPH method. Several 1D numerical experiments are performed to exhibit the properties of the scheme.

Domaines: Analyse numérique [math.NA]

Christophe Berthon, Matthieu de Leffe, Victor Michel-Dansac. A conservative well-balanced hybrid SPH scheme for the shallow-water model. FVCA VII, Jun 2014, Berlin, Germany. pp.817-825, ⟨10.1007/978-3-319-05591-6_82⟩. ⟨hal-00960982⟩