A fully well-balanced scheme for the shallow-water model with topography and bottom friction

The shallow-water equations are widely used to model the free surface of a fluid in motion. However, when introducing the friction source term in the equations, the well-balanced property (preservation of the steady states) becomes harder to ensure. The aim of this talk is, after presenting the equations, to find the steady states for the shallow-water equations with friction, and show how to numerically preserve them. Numerical experiments will be shown to illustrate such a result.