• THE LOCALIZED RADIAL BASIS FUNCTION MESHLESS METHOD FOR SOLVING TWO–DIMENSIONAL SHALLOW WATER EQUATIONS

Abstract

Proposed to demonstrate the localized radial basis function (LRBF) is a stable and accurate tool for simulating two–dimensional shallow water equations (SWEs) (de Saint Venant equation). There are three unknowns in SWEs. Which the water depth h and the water fluxes uh,vh are firstly estimated directly by their values and spatial derivatives in the previous time step. Comparing with global–type meshless methods, the present methods are more appropriate to large–scale problem with complex shapes. For real hydraulic engineering applications, this numerical model is applied to simulate a dam–break problem.