An unstructured node-centered finite volume scheme for shallow water flows with wet/dry fronts over complex topography

Abstract

An unstructured high-resolution, node-centered finite volume algorithm for triangular grids is developed 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, using a slope limiter to control the total variation of the reconstructed field, and an explicit four stage Runge–Kutta time stepping. The novel aspects of the algorithm include the extension to second-order of the topography source term treatment and the wet/dry front treatment, using the MUSCL slope limiting method, within the node-centered finite volume formulation. The developed wet/dry treatment is found to ensure absolute mass conservation. At the beginning of the procedure a triangular grid is locally refined (performing h-enrichment) at regions with steep variations of the topography in order to obtain a better approximation of irregular terrain characteristics and improve the accuracy of the results in the flow for those regions in which a more complex flow is associated to more abrupt geometry without an excess in computational cost. The proposed numerical scheme is extensively validated, with respect to its effectiveness and robustness, against benchmark test cases and experimental data related to propagation and run-up of long waves over arbitrary topographies.