A total variation diminishing scheme for two-dimensional shallow water equations on mixed unstructured grids

Unstructured grids are usually adopted in the solution of complex boundary flows. In this study, a depth-averaged two-dimensional (2-D) flow model is developed for mixed unstructured grids. The model uses both triangular cells and quadrilaterals, which ensures an accurate representation of irregular boundaries and at the same time, achieving a high computational efficiency. The unsteady term in the 2-D shallow water equations is treated implicitly. While the convection and diffusion terms are respectively approximated using the TVD (Total Variation Diminishing) algorithm and the auxiliary-point method. The depth-averaged standard k-ε model is used for turbulent closure. Two classical test cases are chosen for model verification. The first one is a 2-D diversion flow case, and the second is a 90 degree bend-flow case. Results show that the proposed model performs well in terms of accuracy and presents good convergence characteristics.