Improved Local Time Step for 2D Shallow-Water Modeling Based on Unstructured Grids

Shallow-water models suffer from relatively high computational costs owing to the Courant-Friedrichs-Lewy (CFL) constraint and (in most cases) the adopted global minimum time step for variable updating. Here, an improved local time step (LTS) scheme is proposed by introducing slight but useful modifications to the Sanders LTS scheme for two-dimensional (2D) shallow-water modeling based on unstructured triangular meshes. The modifications include (1) avoiding an unrealistically large LTS in the case of a vanishing water depth for near-static cells and (2) avoiding spatial variation of the LTS level around a wet/dry front or dynamic/static front. A series of numerical tests show that the improved LTS gives stable and accurate solutions, along with significant reductions in the computational cost. Moreover, the computational overhead due to the aforementioned modifications is negligible. It is expected that the improved LTS scheme will find wide application in 2D shallow-water modeling.