A spectral element method applied to unsteady flows at moderate Reynolds number

  • K. Z. Korczak
  • A. T. Patera
Contributed Papers
Part of the Lecture Notes in Physics book series (LNP, volume 218)


The spectral element method is a high-order technique for solution of the incompressible Navier-Stokes equations which combines spectral expansions with finite element methodology to give high accuracy in general geometries. In the spectral element discretization, the computational domain is broken up into macro-elements, and the velocity and pressure in each element are represented as high-order Lagrangian inter polants. The nonlinear terms in the equation are then treated with explicit collocation, while the pressure and viscous contributions are handled implicitly with variational projection operators. Parallel static condensation applied to the implicit equations gives an operation count commensurate with that for low-order sub-structure techniques at the same resolution. A time-splitting technique is presented for solution of the Navier-Stokes equations, and results are given for linear and (three dimensional) secondary spatial stability of plane Poiseuille flow, and for steady and unsteady separated channel flows at Reynolds numbers of several thousand.


Reynolds Number Spectral Element Spectral Element Method Plane Poiseuille Flow Spanwise Wavenumber 
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.
    D.O. Gottlieb and S.A. Orszag, “Numerical Analysis of Spectral Methods”, SIAM, Philadelphia, 1977.Google Scholar
  2. 2.
    F. Thomasset, “Implementation of Finite Element Methods for Navier-Stokes Equations,” Springer-Verlag, New York/Berlin, 1981.Google Scholar
  3. 3.
    A.T. Patera, J. Comput. Phys., 54, 1984.Google Scholar
  4. 4.
    N. Ghaddar, A.T. Patera, and B.B. Mikic, AIAA Paper No. 84-0495, 1984.Google Scholar
  5. 5.
    A. McKerrell, C. Phillips, and L.M. Delves, J. Comput. Phys., 40, 1981, 444.CrossRefGoogle Scholar
  6. 6.
    L. Adams and R.G. Voigt, ICASE Nasa Contractor Report 172219, 1983.Google Scholar
  7. 7.
    S.A. Orszag and A.T. Patera, J. Fluid Mech., 128, 1983, 347.Google Scholar
  8. 8.
    M. Nishioka, S. Iida, and Y. Ichikawa, J. Fluid Mech., 72, 1975, 731.Google Scholar
  9. 9.
    U.B. Mehta and Z. Lavan, J. Appl. Mech., December, 1969Google Scholar
  10. 10.
    M. Greiner, Ph.D. Thesis, Dept. of Mech. Engr., M.I.T., in progress.Google Scholar
  11. 11.
    G.A. Osswald, K.N. Ghia, and U. Ghia, in Proc. AIAA 6th Comp. Fluid Dyn. Conf., Danvers, 686 (1983).Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • K. Z. Korczak
    • 1
  • A. T. Patera
    • 1
  1. 1.Department of Mechanical EngineeringMassachusetts Institute of TechnologyCambridge

Personalised recommendations