A robust and well-balanced scheme for the 2D Saint-Venant system on unstructured meshes with friction source term

Abstract

In the following lines, we propose a numerical scheme for the shallow-water system supplemented by topography and friction source terms, in a 2D unstructured context. This work proposes an improved version of the well-balanced and robust numerical model recently introduced by Duran et al. (J. Comp. Phys., 235, 565-586, 2013) for the pre-balanced shallow-water equations, accounting for varying topography. The present work aims at relaxing the robustness condition and includes a friction term. To this purpose, the scheme is modified using a recent method, entirely based on a modified Riemann solver. This approach preserves the robustness and well-balanced properties of the original scheme and prevents unstable computations in the presence of low water depths. A series of numerical experiments are devoted to highlighting the performances of the resulting scheme. Simulations involving dry areas, complex geometry and topography are proposed to validate the stability of the numerical model in the neighbourhood of wet/dry transitions.