Séance Séminaire

Séminaire ACSIOM

Residual Distribution schemes for Shallow Water simulations: C-property, generalized C-property dry areas, and relations with Finite Volumes

In this talk we discuss the construction of residual based discretizations for the Shallow Water equations. After recalling the basic properties of the Shallow Water system some exact solutions and to notion of C and generalized C-properties, we review the basics of the construction of Residual Distribution discretization. We show how the Residual Based idea can be used to obtain schemes satisfying both the C and generalized C-properties on two-dimensional unstructured grids. The treatment of wet-dry fronts is also discussed. Finally, we highlight the relations with finite volume discretizations and also show how to construct FV schemes verifying the C and generalized C-property using the RD approach. Numerical results are presented all along the talk to clarify and illustrate the theoretical constructions.