A gas-kinetic scheme for shallow-water equations with source terms

Huazhong Tang; Tao TANG; Kun Xu

doi:10.1007/s00033-003-1119-7

A gas-kinetic scheme for shallow-water equations with source terms

Huazhong Tang^*, Tao TANG, Kun Xu

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

40 Citations (Scopus)

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.

Original language	English
Pages (from-to)	365-382
Number of pages	18
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	55
Issue number	3
DOIs	https://doi.org/10.1007/s00033-003-1119-7
Publication status	Published - May 2004

User-Defined Keywords

Gas-kinetic schemes
Shallow water equations
Source terms

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10.1007/s00033-003-1119-7

Cite this

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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.",

keywords = "Gas-kinetic schemes, Shallow water equations, Source terms",

author = "Huazhong Tang and Tao TANG and Kun Xu",

note = "The research of HZT is partially supported by the National Natural Science Foundation of China (No. 19901031), the Special Funds for Major State Basic Research Projects of China, and Alexander von Humboldt Foundation. The research of TT and KX is partially supported by RGC Grants of Hong Kong Research Grants Council.",

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AU - Tang, Huazhong

AU - TANG, Tao

AU - Xu, Kun

N1 - The research of HZT is partially supported by the National Natural Science Foundation of China (No. 19901031), the Special Funds for Major State Basic Research Projects of China, and Alexander von Humboldt Foundation. The research of TT and KX is partially supported by RGC Grants of Hong Kong Research Grants Council.

PY - 2004/5

Y1 - 2004/5

N2 - 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.

AB - 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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DO - 10.1007/s00033-003-1119-7

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SN - 0044-2275

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JF - Zeitschrift fur Angewandte Mathematik und Physik

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A gas-kinetic scheme for shallow-water equations with source terms

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