A Compact Fourth-Order Finite Difference Scheme for Unsteady Viscous Incompressible Flows

Ming Li*, Tao Tang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

62 Citations (Scopus)
5 Downloads (Pure)


In this paper, we extend a previous work on a compact scheme for the steady Navier-Stokes equations [Li, Tang, and Fornberg (1995), Int. J. Numer. Methods Fluids, 20, 1137-1151] to the unsteady case. By exploiting the coupling relation between the streamfunction and vorticity equations, the Navier-Stokes equations are discretized in space within a 3 x 3 stencil such that a fourth order accuracy is achieved. The time derivatives are discretized in such a way as to maintain the compactness of the stencil. We explore several known time-stepping approaches including second-order BDF method, fourth-order BDF method and the Crank-Nicolson method. Numerical solutions are obtained for the driven cavity problem and are compared with solutions available in the literature. For large values of the Reynolds number, it is found that high-order time discretizations outperform the low-order ones.

Original languageEnglish
Pages (from-to)29-45
Number of pages17
JournalJournal of Scientific Computing
Issue number1
Publication statusPublished - Mar 2001

Scopus Subject Areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Navier–Stokes equations
  • streamfunction
  • vorticity
  • compact scheme


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