Benoit Perthame

Upwinding Sources at Interfaces for hyperbolic systems with sources

We consider computational aspects of Saint-Venant's shallow water sytem (usual for many applications like rivers flow, tidal waves, but also narrow tubes). This hyperbolic system requires specific algorithms for because the topography driven source term also regulate the steady states of the flow. We will show how this leads to algorithms where the source is better 'upwindinded' at the interfaces rather than cell-centred. On unstructured grids, this poses new questions in terms of stability, consistency. We will illustrate the methods with other multiscale problems and numerical computations.

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