A Weil-Balanced Node-Centered Finite Volume Scheme for Shallow Water Flows with Wetting and Drying

We present a conservative, node-centered finite-volume (FV) algorithm for triangular grids in order to simulate unsteady, two-dimensional, shallow-water flows over arbitrary topography with wetting and drying. The algorithm utilizes Roe's approximate Riemann solver to compute the numerical fluxes, while second-order spatial accuracy is achieved with a MUSCL reconstruction technique. The novel aspects of the algorithm include the extension to second order of the topography source term treatment and the wet/dry front treatment, within the node-centered FV formulation. The numerical scheme is validated against benchmark test cases and experimental data related to propagation and run-up of long waves.