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Journal of Hydrodynamics

, Volume 18, Issue 1, pp 151–156 | Cite as

Application of a three-point explicit compact difference scheme to the incompressible Navier-Stokes equations

  • Jian-guo Lin
  • Zhi-hua Xie
  • Jun-tao Zhou
Session B2
  • 1 Downloads

Abstract

A three-point explicit compact difference scheme with high order of accuracy for solving the unsteady incompressible Navier-Stokes equations was presented. Numerical solutions are obtained for the model problem of lid-driven cavity flow and are compared with benchmark solutions found in the literature. It is discovered that the proposed three point explicit compact scheme is not only simple to implement and economical to use, but also is effective to obtain high-order accurate solution in coarse grid systems.

Key words

incompressible Navier-Stokes equations lid-driven cavity flow high order compact scheme explicit finite difference method 

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References

  1. [1]
    Ghia U., Ghia K.N., Shin C.T. High-Re solutions for imcompressible flow using the Navier-Stokes equation and a multigrid method [J]. Journal of Computational Physics, 1982, 48(3): 387–411.CrossRefGoogle Scholar
  2. [2]
    Barragy E., Carey G.F. Stream function-vorticity driven cavity solutions using p finite elements [J]. Computers and Fluids, 1997; 26:453–468.CrossRefGoogle Scholar
  3. [3]
    Liao S. J. Higher-order streamfunction-vorticity formulation of 2-D steady state Navier–Stokes equations [J]. International Journal for Numerical Methods in Fluids, 1992; 15:595–612.CrossRefGoogle Scholar
  4. [4]
    Kim J., Moin P. Application of a fractional-step method to incompressible navier-stokes equations [J]. Journal of Computational Physics, 1985, 59: 308–323.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Botella O., Peyret R. Benchmark spectral results on the lid-driven cavity flow [J]. Computers and Fluids, 1998; 27:421–433.CrossRefGoogle Scholar
  6. [6]
    Gupta M.M. High accuracy solutions of incompressible Navier–Stokes equations [J]. Journal of Computational Physics, 1991; 93:343–359.MathSciNetCrossRefGoogle Scholar
  7. [7]
    Li M, Tang T, Fornberg B. A compact fourth-order finite difference scheme for the steady incompressible Navier–Stokes equations [J]. International Journal for Numerical Methods in Fluids, 1995; 20:1137–1151.MathSciNetCrossRefGoogle Scholar
  8. [8]
    Shankar P.N., Deshpande M.D. Fluid mechanics in the driven cavity [J]. Annual Review of Fluid Mechanics, 2000; 32:93–136.MathSciNetCrossRefGoogle Scholar
  9. [9]
    Erturk, E.; Corke, T.C.; Gokcol, C. Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers [J]. International Journal for Numerical Methods in Fluids, 2005; 48:747–774.CrossRefGoogle Scholar
  10. [10]
    Sousa E., Sobey I.J. Effect of boundary vorticity discretization on explicit stream-function vorticity calculations [J]. International Journal for Numerical Methods in Fluids, 2005; 49:371–393.MathSciNetCrossRefGoogle Scholar
  11. [11]
    Briley W.R. A numerical study of laminar separation bubbles using the Navier-Stokes equations [J]. Journal of Fluid Mechanics, 1971, 47: 713–736.CrossRefGoogle Scholar

Copyright information

© China Ship Scientific Research Center 2006

Authors and Affiliations

  1. 1.College of Environmental Science and EngineeringDalian Maritime UniversityDalianChina

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