An asymptotic preserving scheme for the shallow‐water equations with Manning friction using viscous correction of the HLL scheme

Abstract

AbstractThe aim of this article is to propose a numerical scheme for the shallow‐water equations with a Manning's 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.