Development and verification of a finite volume model for hydraulics over multi-layered erodible beds

The accuracy and efficiency of a class of finite volume methods are investigated for numerical solution of morphodynamic problems in multi-layered beds. The governing equations consist of two components, namely an hydraulic part described by the shallow water equations and a sediment part described by the transport and suspended sediments equations. To allow exchange between layers in the bed we propose an equation of balance laws for the bed elevation. As a numerical solver we consider a modified Roe method in the finite volume framework. A well balanced discretization is also used for the treatment of the source terms. The method is well-balanced, non-oscillatory and suitable for both near- and far-bed simulations in sediment transport. The proposed model is verified for a dam-break problem over erodible multi-layered bed and the obtained results demonstrate it abilities to resolve the vertical features in multi-layered sediment transport problems.