A numerical scheme for simulating the dynamics of surface water on the basis of the combined SPH-TVD approach

A new numerical algorithm is developed for calculating the shallow water dynamics. The algorithm provides a cross-cutting computation on irregular or/and discontinuous reliefs with unsteady boundaries of the “water-dry bottom” type. The method is based on the combination of modified SPH and TVD approaches for the shallow water equations. A large number of classical problems is tested. The numerical results show that the combined SPH-TVD scheme is conservative, well-balanced, has the second order of accuracy on smooth solutions. This scheme has the first order of accuracy in the domains containing discontinuities of the flow parameters and kinks of the relief profile.