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

In this paper we consider the discretization the Shallow Water equations by means of Residual Distribution (RD) schemes, and review the conditions allowing the exact preservation of some exact steady solutions. These conditions are shown to be related to both the type of spatial approximation and to the quadrature used to evaluate the cell residual. Numerical examples are shown to validate the theory. Key-words: numerical analysis, second order schemes, hyperbolic problems, residual distribution, C-property, unstructured grids ∗ INRIA Bordeaux Sud-Ouest On the C-property and generalized C-property of Residual Distribution for the Shallow Water equations Résumé : In this paper we consider the discretization the Shallow Water equations by means of Residual Distribution (RD) schemes, and review the conditions allowing the exact preservation of some exact steady solutions. These conditions are shown to be related to both the type of spatial approximation and to the quadrature used to evaluate the cell residual. Numerical examples are shown to validate the theory. Mots-clés : numerical analysis, second order schemes, hyperbolic problems, residual distribution, C-property, unstructured grids