A Well-Balanced FVC Scheme for 2D Shallow Water Flows on Unstructured Triangular Meshes

Abstract

We consider in this work the numerical resolution of a 2D shallow water system with a Coriolis effect and bottom friction stresses on unstructured meshes by a new Finite Volume Characteristics (FVC) scheme, which has been introduced in the preliminary works that will be cited below. Our main goal is to extend this approach to 2D unstructured formalism while preserving the physical and mathematical properties of the system, including the C-property. First, we present our extension by preserving the advantages of the finite volume discretization such as conservation property and the method of characteristics such as elimination of Riemann solvers. Afterward, an approach was applied to the topography source term that leads to a well-balanced scheme satisfying the steady-state condition of still water. A semi-implicit treatment will also be presented in this study to avoid stability problems for the other source terms. Finally, the proposed finite volume method is verified on several benchmark tests and shows good agreement with analytical solutions and experimental results; moreover, it gives a noticeable accuracy and rapidity improvement compared to the original approaches.