Approximate Riemann Solvers

AApproximate Riemann solver  full range of 10 approximate Riemann solvers for the shallow water equations written in conservative and non-conservative forms have been presented, along with a discussion on criteria to judge their quality in comparison with the exact solver. A first criterion is whether a solver is linear or non-linear and whether a linear solver is accompanied with an effective entropy fix to exclude unphysical entropy-violating shocks. A second criterion is whether a solver is complete, that is whether or not the number of waves W in its wave model matches that of the exact solver N. For incomplete Riemann solvers $$W