Development of a cell-centered Godunov-type finite volume model for shallow water flow based on unstructured mesh

Abstract

Based on the Godunov-type cell-centered finite volume method, this paper presents a two-dimensional well-balanced shallow water model for simulating flows over arbitrary topography with wetting and drying. The central upwind scheme is used for the computation of mass and momentum fluxes on interface. The novel aspect of the present model is a robust and accurate nonnegative water depth reconstruction method which is implemented in the unstructured mesh to achieve second-order accuracy in space and to track the moving wet/dry fronts of the flow over irregular terrain. By defining the bed elevation and primary flow variables at the cell center in the nonstaggered grid system, all computational cells are either fully wet or dry to avoid the problem of being partially wetted. The developed model is capable of being well balanced and preserving the computed water depth to be nonnegative under a certain CFL restriction, which makes it robust and stable. The present model is validated against three benchmark tests and two laboratory dam-break cases. Finally, the good agreement between the numerical results by the established model and measured data of the Malpasset dam break event on a 1/400 scale physical model demonstrates the capability of the model for the real-life applications. © 2014 Gangfeng Wu et al.