Journal of Hydrodynamics

, Volume 18, Supplement 1, pp 73–76 | Cite as

The gas-kinetic scheme for shallow water equations

Session B1


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 words

shallow water equations gas-kinetic scheme 


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    P.L. Bhatnagar, E.P. Gross, and M. Krook, A model for collision processes in gases. I: Small amplitude processes in charged and neutral one-component systems, Phys. Rev. 94, 511–525 (1954).CrossRefGoogle Scholar
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    K. Xu, A well-balanced gas-kinetic scheme for the shallow-water equations with source terms, J. Comput. Phys. 178, 533–562 (2002).MathSciNetCrossRefGoogle Scholar
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    C.E. Synolakis, The run-up of solitary waves, J. Fluid Mech. 185, 523–545 (1987).CrossRefGoogle Scholar

Copyright information

© China Ship Scientific Research Center 2006

Authors and Affiliations

  1. 1.Department of MathematicsHong Kong University of Science & TechnologyKowloonHong Kong

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