The gas-kinetic scheme for shallow water equations*

In this paper, we introduce a finite-volume kinetic BGK scheme for the shallow water equations and its applications to the study of water waves. The current scheme is based on the numerical solution of the gas-kinetic Bhatnagar- Gross-Krook model in the flux evaluation across each cell interface. An intrinsic connection between the BGK model and time-dependent, non-linear, non-homogeneous shallow-water equations enables us to solve shallow-water equations automatically with our kinetic scheme. The numerical solution and experimental measurements associated with solitary waves incident on a sloped beach, are presented.