Abstract
We present a class of finite volume methods for the numerical solution of Saint-Venant equations with variable horizontal density. The model is based on coupling the Saint-Venant equations for the hydraulic variables with a suspended sediment transport equation for the concentration variable. To approximate the numerical solution of the considered models we propose a generalized Rusanov method. The method is simple, accurate and avoids the solution of Riemann problems during the time integration process. Using flux limiters, a second-order accuracy is achieved in the reconstruction of numerical fluxes. The proposed finite volume method is well-balanced, conservative, non-oscillatory and suitable for Saint-Venant equations for which Riemann problems are difficult to solve. The numerical results are presented for two test examples.