An Asymptotic Preserving scheme for the shallow-water equations with Manning friction using viscous correction of the HLL scheme

The aim of this paper is to propose a numerical scheme for the shallow-water equations with a Manning friction source term able to preserve the diffusive regime, namely the behavior of the solutions in long time and stiff friction limit. Because of the non-usual rescaling of the friction parameter, a strongly nonlinear derivative operator is involved in the diffusive limit and the development of a numerical scheme possessing this property is not straightforward. The scheme presented here is based on a perturbed HLL scheme with additional viscous terms.