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.
CITATION STYLE
Berthon, C., de Leffe, M., & Michel-Dansac, V. (2014). A conservativewell-balanced hybrid sph scheme for the shallow-water model. In Springer Proceedings in Mathematics and Statistics (Vol. 78, pp. 817–825). Springer New York LLC. https://doi.org/10.1007/978-3-319-05591-6_82
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