A structure-preserving algorithm for surface water flows with transport processes (Q2667928)

The authors consider a system of coupled equations modeling a shallow water flow with solute transport. They propose an artificial dissipation parameter which improves numerically the original cell-vertex central-upwind scheme. This new formulation guarantees a consistency property between the continuity equation and the transport equation at the discrete level and also ensures the nonlinear stability and positivity of the scheme. A well-balanced positivity-preserving reconstruction is formulated in terms of the conservative variable describing the concentration. It is shown that the proposed scheme satisfies the discrete maximum/minimum principle for the scalar concentration. The numerical tests presented demonstrate that the central-upwind scheme with the proposed artificial dissipation performs well in terms of numerical dissipation in comparison to the standard central-upwind scheme. These tests also confirm the well-balanced and positivity-preserving properties of the scheme for the water depth and concentration, and it is of second-order accuracy.