Well-balanced schemes for free surface fluid models
We consider here integrated models for free surface flows (extensions of the Saint-Venant system). These models have in common the presence of source terms which result in the existence of non-trivial stationary states, in the sense that the unknowns of the system (flow depth and velocity unknowns) are not constant. After having shown why classical schemes require very fine meshes to obtain accurate results, we will present two methods to build efficient schemes around these stationary states, even on coarse meshes. We will first focus on the theory of approximate Riemann solvers to build schemes adapted to one-dimensional equilibria and then we will present a work on the preservation of the two-dimensional geostrophic equilibrium.
