One-dimensional conservative coupled discretization of the shallow-water with scalar transport equations

The quality of the solutions obtained by numerical methods in shallow-water equations is strongly dependent on the discretization used. This is the greatest difficulty in shallow-water simulations. In this work we showthat only a coupled discretization of the whole system of equations and a careful definition of the flux limiter function in second order TVD schemes are necessary in order to preserve uniform solute profiles in situations of 1D unsteady subcritical flow. An ideal dambreak with analytical solution and two practical applications on river flow and furrow