A low numerical diffusive scheme for pollutant transport in shallow water

An Eulerian numerical scheme is proposed for the solution of the two-dimensional pollutant transport equation coupled with hydrodynamic shallow water equations. The model is based on a second-order approximate Riemann solver used to integrate the advective part of the equations on non uniform quadrangular grids. To reduce the numerical diffusion that arises in pure second order schemes, a fifth order one-dimensional WENO reconstruction is introduced. The one-dimensional WENO reconstruction applied to two-dimensional problems does not increase the overall convergence rate, nevertheless it leads to a sensible improvement of the results in terms of numerical diffusion in comparison to pure second order schemes. Besides, the proposed scheme comes out to be computationally more advantageous in comparison to pure two-dimensional WENO reconstruction. Finally, the model is verified on standard tests documented in literature.