Application of dual time-step algorithm for 2-D shallow water equations

Aiming at the problem of low efficiency of traditional explicit schemes, an efficient finite volume scheme is proposed by applying an implicit dual time-step algorithm to discretize the two-dimensional shallow water equations on unstructured grids. An implicit non-linear lower-upper symmetric Gauss-Seidel (LU-SGS) solution algorithm is used as the iteration solver for the inner steady problems. The model's accuracy, efficiency, and capability of dealing with practical problems are validated through its application to four typical examples and comparison with an explicit algorithm. In addition, the effects of physical time step and maximum iteration number on the model's accuracy and efficiency are assessed. Numerical results from the test examples show that the dual time-step approach eases the restrictions on the sizes of time steps, which can be more than 10 times that of explicit algorithms, and that the reduction in run-time can be more than 50%. The proposed model is found to be accurate and efficient, thus having a good potential for popularization.