A WELL BALANCED FVM WITH SCALAR DIFFUSION TO HYPERBOLIC BALANCE LAWS

The goal of this work is to extend a finite volume method with scalar diffusion to hyperbolic system of balance laws. This is made by reformulating the numerical scheme by adding a diffusive term to the numerical discretization of the source term in such a way that the obtained scheme is well-balanced for a wide range of stationary solutions of any hyperbolic systems with source term. The scheme is applied to Shallow Water Equations and the exact well-balanced property is established for the stationary solution of water at rest. Finally, some numerical tests are presented that exhibit the good performances of the scheme.