Accurate shock-capturing finite volume method for advection-dominated flow and pollution transport

This paper describes an accurate shock-capturing finite volume numerical method to solve a two-dimensional flow and solute transport problem in shallow water. Hydrodynamic and advection–diffusion equations are simultaneously solved by means of a Strang operator-splitting approach. The advective part is solved in time by a third-order TDV Runge–Kutta method and in space by a second-order WAF method coupled with a fifth-order WENO reconstruction. The diffusion part is solved in time and space by a second-order accurate method. Thus the overall accuracy is second-order both in time and space. Nevertheless the Strang splitting approach allows the advective part of the equations to be solved with a reconstruction of high order, where at lower orders it shows excessive numerical diffusion and damping, especially for very long time simulations. Very good results have been obtained applying the model to standard long time numerical tests.