Well-balanced energy-stable residual distribution methods for the shallow water equations with varying bottom topography

This paper presents an alternative well-balanced and energy stable method for the system of non-homogeneous Shallow Water Equations (SWE) on unstructured grids based on the residual distribution (RD) approach. The motivation of the work is based on the grid insensitivity of RD method. The newly proposed method has a positive first order part, a linearity-preserving second order scheme as well as a limited scheme which works for both steady and unsteady problems using simple, explicit time integration techniques. Numerical results herein confirm the accuracy and efficacy of the new methods in preserving both energy stability and well-balancedness