Application of weighted-least-square local polynomial approximation to 2D shallow water equation problems

In this study, a numerical model based on shallow water equations (SWE) is developed. An explicit predictor–corrector approach is adopted for the time marching process. Using the leap-frog formulae, the three unknowns in SWE, which are the water depth h, and the water fluxes uh, vh, are firstly estimated directly by their values and their spatial derivatives in the previous time step. Then they are corrected by the Crank-Nicolson formulation. The spatial derivatives of h, uh and vh for the further time marching processes are calculated by using the Weighted Least Square (WLS) local polynomial approximation, which is a kind of meshless method. This model is applied to the simulations of dam break flows and tidal currents.