Local Time Stepping Scheme Using Structured Grids for Modelling of Shallow Water Flows

Numerical simulations of shallow water flows are widely used to predict global flows such as flood flows in the sea, river and reservoir flows, especially floods due to heavy rainfall and dam break. In particular, reducing the simulation time by applying the Local Time Stepping (LTS) scheme is one way to improve the practical efficiency of numerical simulation. In this paper, we proposed LTS scheme using a structured grid for the numerical simulation of shallow water system. When modeling any terrain, rectangular grid cells are used to facilitate grid generation. To estimate the momentum flux at the grid cell boundaries, we applied the second-order spatial accuracy Godunov finite volume algorithm with Roe approximation solver using the MUSCL method. The LTS scheme is applied to shallow water flow problems with tsunami reflection pattern and its accuracy and efficiency are compared with the traditional global time step (GTS) method. Results show that, with no loss of accuracy, the new LTS algorithm achieves 59-67% CPU time reduction when compared to the GTS method. The proposed LTS scheme accurately reflects time varying water regimes and reflected waves in shallow water flows and can be used for numerical simulations of the three-dimensional shallow water flows with arbitrary topography to reduce the simulation time significantly.