The gas-kinetic scheme for shallow water equations
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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.
Key wordsshallow water equations gas-kinetic scheme
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