A fully well-balanced and asymptotic preserving scheme for the shallow-water equations with a generalized Manning friction source term (Q2240640)

The authors improves a Godunov-type scheme to preserve the steady states of the shallow-water equations with Manning-type friction. The preservation of the diffusive asymptotic regime by this scheme is proved. A spatial higher-order version of this scheme is proposed. Using some suitable linearizations, the obtained higher-order scheme exactly preserves the steady states and the diffusive behavior. Some numerical tests are presented to show the efficiency of the proposed method.