On the C-property and Generalized C-property of Residual Distribution for the Shallow Water Equations

In this paper we consider the discretization of the Shallow Water equations by means of Residual Distribution (RD) schemes. We review the conditions allowing the exact preservation of some exact steady solutions. These conditions are shown to be related both to the type of spatial approximation and to the quadrature used to evaluate the cell residual. Numerical examples are shown to validate the theory.