DONG Bingjiang, LU Xinhua, YUAN Jing. A total variation diminishing scheme for two-dimensional shallow water equations on mixed unstructured grids[J]. Advances in Water Science, 2013, 24(1): 103-110.
Citation:
DONG Bingjiang, LU Xinhua, YUAN Jing. A total variation diminishing scheme for two-dimensional shallow water equations on mixed unstructured grids[J]. Advances in Water Science, 2013, 24(1): 103-110.
DONG Bingjiang, LU Xinhua, YUAN Jing. A total variation diminishing scheme for two-dimensional shallow water equations on mixed unstructured grids[J]. Advances in Water Science, 2013, 24(1): 103-110.
Citation:
DONG Bingjiang, LU Xinhua, YUAN Jing. A total variation diminishing scheme for two-dimensional shallow water equations on mixed unstructured grids[J]. Advances in Water Science, 2013, 24(1): 103-110.
Bureau of Hydrology Changjiang Water Resources Commission, Wuhan 430010, China;
2.
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
Funds: The study is financially supported by the National Basic Research Program of China (No.2012CB417001) and the Fundamental Research Funds for the Central Universities (No.206275798).
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.