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A numerical study of the two- and three-dimensional unsteady Navier-Stokes equations in velocity-vorticity variables using compact difference schemes

  • T. B. Gatski
  • C. E. Grosch
Contributed Papers
Part of the Lecture Notes in Physics book series (LNP, volume 218)

Abstract

A compact finite-difference approximation to the unsteady Navier-Stokes equations in velocity-vorticity variables is used to numerically simulate a number of flows. These include two-dimensional laminar flow of a vortex evolving over a flat plate with an embedded cavity, the unsteady flow over an elliptic cylinder, and aspects of the transient dynamics of the flow over a rearward facing step. The methodology required to extend the two-dimensional formulation to three-dimensions is presented.

Keywords

Unsteady Flow Vortical Structure Elliptic Cylinder Contour Level Vorticity Contour 
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References

  1. 1.
    Dennis, S. C. R.; Ingham, D. B.; and Cook, R. N.: J. Comp. Phys., Vol. 33, (1979), pp. 325–339.CrossRefGoogle Scholar
  2. 2.
    Fasel, H. F.: Lecture Notes in Mathematics, No. 771, Springer-Verlag, New York/Berlin, (1980), pp. 177–195.Google Scholar
  3. 3.
    Fix, G. J.; and Rose, M. E.: SIAM J. Numerical Analysis, (1984), to appear.Google Scholar
  4. 4.
    Gatski, T. B.; Grosch, C. E.; and Rose, M. E.: J. Comp. Phys., Vol. 48, No. 1, (1982), pp. 1–22.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • T. B. Gatski
    • 1
  • C. E. Grosch
    • 2
  1. 1.NASA Langley Research CenterHampton
  2. 2.Old Dominion UniversityNorfolk

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