The Generalized Riemann Problem Method For The Shallow-Water Equations With Bottom Topography

This paper uses the generalized Riemann problem method (GRP) to solve the system of shallow water equations with bottom topography, then a Godunov-type scheme for the shallow water equations with bottom topography is obtained. The main contribution is that the bottom topography effect is included in numerical fluxes and the bottom topography is discretized with an interface method in the same step. This scheme proves to be well balanced between the flux gradient and the bottom topography for both 1-D and 2-D cases, as the water surface is chosen to be the basis of data reconstruction. Numerical results indicate that the scheme is accurate, efficient and robust in both steady and unsteady flow simulations.