Abstract: A well-balanced weighted average flux (WAF) scheme is proposed for the nonhomogeneous shallow water equations with pollutant transport. The water surface elevation and water discharge are used as the conserved variables in the shallow water equations, while the conserved variables and the bed elevation are set on the staggered mesh. Here, the WAF scheme combined with the HLLC Riemann solver is directly performed for the nonhomogeneous shallow water equations with pollutant transport and the spatial second order central difference approximation is applied to source terms. Then, it’s proved that the extended WAF scheme satisfies the equilibrium property in theory. Finally, several numerical tests about the steady and nonsteady flows over the irregular bottom or with the wet/dry front are simulated. The results obviously suggest that the WAF scheme is a well-balanced, robust, efficient, practical and high resolution scheme.

Key words: shallow water equations, WAF scheme, dam-break, pollutant transport