A robust well-balanced model on unstructured grids for shallow water flows with wetting and drying over complex topography

Abstract

To simulate complex flows involving wet-dry fronts in irregular terrains over arbitrary beds, this paper presents a 2D well-balanced shallow water flow model, based on an unstructured cell-centered finite volume scheme. In this model, hydrostatic reconstruction is applied to reconstruct non-negative water depths at wet-dry interfaces. Harten, Lax and van Leer approximate Riemann solver with the contact wave restored is employed to compute the fluxes of mass and momentum. In addition, the splitting point-implicit method is utilized to solve the friction source terms. The novel aspects of the model include the adaptive method and the slope source term treatment. The former is devised to prevent unphysical high velocities occurring in the part of the domain with varying thin water and topography. The latter converts the slope source terms of a cell into fluxes through its edges and takes account of the influence of wet-dry fronts, so as to satisfy the C-property in any case on unstructured grids. The accuracy and robustness of the proposed model are extensively verified against several benchmark tests as well as a real dam-break event, where its superiority in simulating complex flows with wetting and drying over uneven bed is emphasized.