HLLC scheme with novel wave-speed estimators appropriate for two-dimensional shallow-water flow on erodible bed

This paper presents a first-order HLLC (Harten-Lax-Van Leer with contact discontinuities) scheme to solve the Saint-Venant shallow-water equations, including morphological evolution of the bed by erosion and deposition of sediments. The Exner equation is used to model the morphological evolution of the bed, while a closure equation is needed to evaluate the rate of sediment transport. The system of Saint-Venant-Exner equations is solved in a fully coupled way using a finite-volume technique and a HLLC solver for the fluxes, with a novel wave-speed estimator adapted to the Exner equation. Wave speeds are usually derived by computing the eigenvalues of the full system, which is highly time-consuming when no analytical expression is available. In this paper, an eigenvalue analysis of the full system is conducted, leading to simple but still accurate wave-speed estimators. The new numerical scheme is then tested in three different situations: (1) a circular dam-break flow over movable bed, (2) an one-dimensional bed aggradation problem simulated on a 2D unstructured mesh and (3) the case of a dam-break flow in an erodible channel with a sudden enlargement, for which experimental measurements are available. Copyright (C) 2010 John Wiley & Sons, Ltd.