A simple multi-layer finite volume solver for density-driven shallow water flows

Abstract

A simple solver is proposed for the numerical solution of density-driven multi-layer shallow water flows. The governing equations consist on coupling the multi-layer shallow water equations for the hydraulic variables with suspended sediment transport equations for the concentration variables. The layers can be formed in the shallow water model based on the variation of water density which may depend on the water temperature and salinity. At each time step, the method consists of two stages to update the numerical solution. In the first stage, the multi-layer shallow water equations are rewritten in a non-conservative form and the intermediate solutions are calculated using the modified method of characteristics. In the second stage, the numerical fluxes are reconstructed from the intermediate solutions in the first stage and used in the conservative form of the multi-layer shallow water equations. The proposed method avoids Riemann problem solvers and it is suitable for multi-layer shallow water equations on non-flat topography. Several numerical results are presented to illustrate the performance of the proposed finite volume method. The computed results confirm its capability to solve multi-layer shallow water equations for density-driven flows over flat and non-flat bottom topography.