Abstract:
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.
Keywords:shallow water equations; numerical scheme; SPH; TVD; irregular bottom topography.