Boundary Conditions for the Shallow Water Equations solved by Kinetic Schemes
Résumé
We consider the Saint-Venant system for Shallow Water which is an usual model to describe the flows in rivers, coastal areas or floodings. The hyperbolic system of conservation laws is solved on unstructured meshes using a finite volume method together with a kinetic solver.We add to this system a friction term, the role of which is important when small water depths are considered. In this paper we address the treatment of the boundary conditions, the difficulty is due to the fact that in some cases (fluvial flows) the given boundary conditions are not sufficient to apply directly the scheme, we discuss here how to treat these boundary conditions using a Riemann invariant.Some numerical results illustrate the ability of the method to treat complex problems like the filling up or the draining off of a river bed.