Applied Mathematics and Mechanics

, Volume 28, Issue 7, pp 943–953

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

• Lin Jian-guo  (林建国)
• Xie Zhi-hua  (谢志华)
• Zhou Jun-tao  (周俊陶)
Article

## 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.

## Key words

arbitrary order of accuracy compact scheme three-point stencil explicit lid-driven cavity flow

O241.82 X145

35Q30

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© Editorial Committee of Appl. Math. Mech. 2007

## Authors and Affiliations

• Lin Jian-guo  (林建国)
• 1
Email author
• Xie Zhi-hua  (谢志华)
• 1
• Zhou Jun-tao  (周俊陶)
• 1
1. 1.College of Environmental Science and EngineeringDalian Maritime UniversityDalianP. R. China