A gas-kinetic scheme for shallow-water equations with source terms |
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Authors: | Huazhong Tang Tao Tang Kun Xu |
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Institution: | (1) LMAM & School of Mathematical Sciences, Peking University, 100871 Beijing, China;(2) Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong;(3) Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong |
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Abstract: | In this paper, the Kinetic Flux Vector Splitting (KFVS)
scheme is extended to solving the shallow water equations with
source terms. To develop a well-balanced scheme between the source
term and the flow convection, the source term effect is accounted
in the flux evaluation across cell interfaces. This leads to a
modified gas-kinetic scheme with particular application to the
shallow water equations with bottom topography. Numerical
experiments show better resolution of the unsteady solution than
conventional finite difference method and KFVS method with little
additional cost. Moreover, some positivity properties of the
gas-kinetic scheme is established. |
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Keywords: | 65M93 35L64 76N10 |
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