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)


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.


Unsteady Flow Vortical Structure Elliptic Cylinder Contour Level Vorticity Contour 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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

Personalised recommendations