Abstract
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.
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Project supported by the Hong Kong Research Grant Council (HKUST6102/04E, 6210/05E).
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Xu, K. The gas-kinetic scheme for shallow water equations. J Hydrodyn 18 (Suppl 1), 73–76 (2006). https://doi.org/10.1007/BF03400426
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DOI: https://doi.org/10.1007/BF03400426