Finite volume methods for pollutant transport in shallow water equations

Abstract

This paper is about a new hybrid finite volume method/particle method for the numerical solution of systems of shallow water equations featuring transport of passive pollutants. The proposed numerical scheme discretizes the system of shallow water equations with pollutant transport (SWEPT) in a special way that maintains steady state solutions and ensures a reduced dissipation in the concentration of the pollutant. Selected test cases are considered and the generated numerical solution is reported. The observed numerical results endorse the potential of the proposed scheme to handle SWEPT problems accurately.