A mass-conservative centered finite volume model for solving two-dimensional two-layer shallow water equations for fluid mud propagation over varying topography and dry areas

In this paper we develop a finite volume model to solve the two-dimensional shallow water equations governing the propagation of two superimposed layers, with the upper water layer carrying a dilute sediment suspension, and the underlaying layer being a high concentration non-Newtonian fluid mud mixture. The model formulation contains non-conservative terms as well as source terms. We propose a scheme able to deal with varying topography and dry areas, providing well-balanced solutions when both water and fluid mud are quiescent. The model is tested against both exact solutions and numerical examples. The results show the ability of the model to deal with wetting and drying of both water and fluid mud layers, providing mass-conservative solutions. Moreover, the model solves discontinuities and steep fronts, computing accurate and oscillation-free solutions.