A third-order semidiscrete central scheme for conservation laws and convection-diffusion equations (Q2706445)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A third-order semidiscrete central scheme for conservation laws and convection-diffusion equations |
scientific article |
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19 March 2001
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hyperbolic systems
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convection-diffusion equations
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central difference schemes
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high-order accuracy
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nonoscillatory schemes
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weighted essentially nonoscillatory reconstruction
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semidiscretization
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numerical examples
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conservation laws
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A third-order semidiscrete central scheme for conservation laws and convection-diffusion equations (English)
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The authors present a third-order, semidiscrete central method for approximating solutions to multidimensional systems of hyperbolic conservation laws, convection-diffusion equations and related problems. The method is a high-order extension of a second-order scheme presented by \textit{A. Kurganov} and \textit{E. Tadmor} [J. Comput. Phys. 160, No. 1, 241-282 (2000; Zbl 0987.65085)]. The construction technique of the scheme is very flexible with respect to possible reconstruction steps. In particular, a third-order central weighted essentially nonoscillatory reconstruction technique is employed. The resulting scheme is applied to various test cases showing the desired behaviour of the scheme.
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