NUMERICAL DISCRETIZATIONS FOR SHALLOW WATER EQUATIONS WITH SOURCE TERMS ON UNSTRUCTURED MESHES

摘要

In the following lines we introduce two frictional schemes for the discretization of the 2D Shallow Water system, on unstructured meshes. The starting point consists in writing both of them as convex combinations of 1D schemes. Then, we propose to include the resistance effects proceeding to a slight adaptation of the gathered convex components, using the frictional approach recently developed in [2]. This method turns out to provide an excellent behavior for vanishing water heights, and does not require a modification of the CFL. Numerical experiments will be performed in order to assess the capacity of the two schemes in dealing with wetting and drying, complex geometry and topography.