Efficient meshless method for water flows through channels with bottom topography

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.