Efficient meshless method for water flows through channels with bottom topography

Abstract

─ This paper aims to build an efficient radial basis function method to simulate the shallow water flow in an open channel with bottom topography. A special source term approximation, which represents an artificial viscosity, is introduced so that the proposed methods can preserve the still water steady state exactly and acquire Shock-capturing capabilities. Furthermore, the non-negativity of the water height is preserved and the method is well-balanced for the still water steady-state solutions. Promising numerical results are obtained at the end to verify these properties for problems involving transcritical flow.