A projection method based on Gaussian quadratures with application to compressible Navier-Stokes equations

  • K. C. Reddy
Contributed Papers
Part of the Lecture Notes in Physics book series (LNP, volume 141)


A projection method based on Gauss-Legendre quadratures for solving hyperbolic and parabolic partial differential equations is proposed. It is comparable to spectral methods in accuracy and convergence, and is more convenient to implement for non-linear problems. Results obtained with a wave equation and Burgers equation modeling a flow with sharp gradients show the high resolution achieved for a given number of nodes by using this method. Time-split implicit techniques are used for approximating the compressible Navier-Stokes equations.


Projection Method Burger Equation Parabolic Partial Differential Equation Gaussian Node Implicit Trapezoidal Rule 
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.
    Orszag, S. A. “Numerical Simulation of Incompressible Flows within Simple Boundaries: Accuracy.” J. Fluid Mechanics, 49, 1971, p. 75.Google Scholar
  2. 2.
    Gottlieb, D. and Orszag, S. A. Numerical Analysis of Spectral Methods: Theory and Applications. SIAM, Philadelphia, PA, 1977.Google Scholar
  3. 3.
    Orszag, S. A. “Numerical Simulation of Turbulent Flows.” Handbook of Turbulence, Plenum Press, New York, 1977, p. 281.Google Scholar
  4. 4.
    Murdock, J. W. “A Numerical Study of Nonlinear Effects on Boundary Layer Stability.” AIAA Journal, August 1977, p. 1167.Google Scholar
  5. 5.
    Warming, R. F. and Beam, R. M. “On the Construction and Application of Implicit Factored Schemes for Conservation Laws.” SIAM-AMS Proceedings, Vol. 11, Symposium on Computational Fluid Dynamics, New York, April 1977.Google Scholar
  6. 6.
    Beam, R. M. and Warming, R. F. “An Implicit Factored Scheme for the Compressible Navier-Stokes Equations,” AIAA Journal, April 1978, p. 393.Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • K. C. Reddy
    • 1
  1. 1.Sverdrup/ARO, Inc.AFDC Division Arnold Engineering Development CenterArnold Air Force Station

Personalised recommendations