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Three-point explicit compact difference scheme with arbitrary order of accuracy and its application in CFD

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Abstract

Based on the successive iteration in the Taylor series expansion method, a three-point explicit compact difference scheme with arbitrary order of accuracy is derived in this paper. Numerical characteristics of the scheme are studied by the Fourier analysis. Unlike the conventional compact difference schemes which need to solve the equation to obtain the unknown derivatives in each node, the proposed scheme is explicit and can achieve arbitrary order of accuracy in space. Application examples for the convection-diffusion problem with a sharp front gradient and the typical lid-driven cavity flow are given. It is found that the proposed compact scheme is not only simple to implement and economical to use, but also is effective to simulate the convection-dominated problem and obtain high-order accurate solution in coarse grid systems.

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Authors and Affiliations

  1. College of Environmental Science and Engineering, Dalian Maritime University, Dalian, 116026, P. R. China

    Lin Jian-guo Doctor  (林建国) (Professor), Xie Zhi-hua  (谢志华) & Zhou Jun-tao  (周俊陶)

Authors
  1. Lin Jian-guo Doctor  (林建国)
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  2. Xie Zhi-hua  (谢志华)
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  3. Zhou Jun-tao  (周俊陶)
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Corresponding author

Correspondence to Lin Jian-guo Doctor  (林建国).

Additional information

Communicated by LIN Jian-zhong

Project supported by the National Natural Science Foundation of China (No. 50479053)

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Lin, Jg., Xie, Zh. & Zhou, Jt. Three-point explicit compact difference scheme with arbitrary order of accuracy and its application in CFD. Appl Math Mech 28, 943–953 (2007). https://doi.org/10.1007/s10483-007-0711-x

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  • DOI: https://doi.org/10.1007/s10483-007-0711-x

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Chinese Library Classification

2000 Mathematics Subject Classification

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