An application of adaptive grid method to shallow water equations on complex topography

The quality of terrain generalization has an important impact on the result of numerical simulations. Aiming at the practical issue associated with the coexistence of long narrow valleys and vast floodplain, an adaptive grid method with hierarchical structures (HAGM) is introduced. The adaptive criterion is made on the basis of the gradient of free surface elevation and the local Froude number. The local grid density can be adjusted automatically in response to a changing flow regime, which makes it possible to achieve a balance between accuracy and computational efficiency in numerical simulations. The finite volume method is used to solve the two-dimensional shallow water equations based on the HAGM. Gradient limiters and the two-step Runge-Kutta scheme are employed to improve the accuracy in space resolution and time marching, respectively. Results of numerical experiments show that the HAGM has good performance in adapting to a changing flow regime, in capturing sensitive zones for water level calculation, and in achieving local grid refinement. The proposed HAGM is thus suitable for a wide range of applications.