Advertisement

A multigrid factorization technique for the flux-split Euler equations

  • C. P. Li
Contributed Papers
Part of the Lecture Notes in Physics book series (LNP, volume 218)

Abstract

The Euler equations formulated in characteristic components are solved by a time-like finite-difference method based on implicit multilevel grid sequencing. The conservative equations are made quasi-linear in metric coefficients in order to use upwind difference approximation of second order for the entire domain. Inside the computation region, the appropriate difference formula is automatically selected in accordance with the sign of the characteristics. When the flux components are originated outside the region, they are discarded and boundary conditions are imposed. Because the propagation path of signals is properly accounted for, higher accuracies of the solution and greater robustness of the numerical procedure are obtained. The implicit factorization procedure, which relies on the solution of four scalar matrices rather than of one block pentadiagonal matrix to save computation time, has removed severe restrictions on the time-step increments. Further more, the convergence rate is accelerated by a multigrid algorithm that switches the implicit procedure from fine to successively coarser grid levels. Newton's method is used to linearize the difference equations at the beginning of each step, then the correction vector is determined from the factorization technique applied to each grid level. Two-dimensional examples of a supersonic inlet flow and a transonic airfoil flow are considered in this study.

Keywords

Grid Level Multigrid Algorithm Correction Vector Multigrid Technique Implicit Procedure 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Steger, J. L. and Warming, R. F., J. Comp. Phys., Vol. 40, 1981, pp. 263–293.CrossRefGoogle Scholar
  2. 2.
    Reklis, R. P. and Thomas, P. D., AIAA J., Vol. 20, Sept. 1982, pp. 1212–1218.Google Scholar
  3. 3.
    Li, C. P., Paper 83-0560, AIAA 21st Aerospace Sciences Meeting, 1983.Google Scholar
  4. 4.
    Brandt, A., AIAA J., Vol. 18, No. 10, Oct. 1980, pp. 1165–1172.Google Scholar
  5. 5.
    Ni, R. H., AIAA J., Vol. 20, No. 11, Nov. 1982, pp. 1565–1571.Google Scholar
  6. 6.
    Jameson, A. and Baker, T. J., Paper 84-0093, AIAA 22nd Aerospace Sciences Meeting, 1984.Google Scholar
  7. 7.
    Jespersen, D. C., Paper 83-0124, AIAA 21st Aerospace Sciences Meeting, 1983.Google Scholar
  8. 8.
    Sorenson, R. L., NASA TM-81198, 1980.Google Scholar
  9. 9.
    Holst, T. L., Lecture Series 1983-04, Von Karman Institute, Belgium, 1983.Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • C. P. Li
    • 1
  1. 1.NASA Johnson Space CenterHouston

Personalised recommendations