Advances in the Application of Fast Semidirect Computational Methods in Transonic Flow

  • E. Dale Martin
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)

Abstract

This paper is intended as a review and summary of the advances made in a recently developed approach for rapid numerical solution of the equations of inviscid transonic aerodynamics. The investigation has been limited to two-dimensional, steady, inviscid flow over airfoils in a subsonic free stream, with emphasis on development of a rapid computational technique, rather than on generality of application.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Buzbee, B. L.; Golub, G. H.; Nielson, C. W.: On direct methods for solving Poisson’s Equations. SIAM J. Numer. Anal. 7 (1970) 627–656.MathSciNetMATHCrossRefADSGoogle Scholar
  2. 2.
    Martin, E. D.: A generalized-capacity-matrix technique for computing aerodynamic flows. Computers and Fluids 2 (1974) 79–97.MATHCrossRefGoogle Scholar
  3. 3.
    Lomax, H.; Martin, E. D.: Fast direct numerical solution of the nonhomogeneous Cauchy-Riemann equations. J. Comp. Phys. 15 (1974) 55–80.MATHCrossRefADSGoogle Scholar
  4. 4.
    Fromm, J. E.: A numerical study of buoyancy driven flows in room enclosures. Lecture Notes in Physics 8 (ed. by M. Holt). Springer-Verlag, Berlin, 1971; 120–126.Google Scholar
  5. 5.
    Widlund, O. B.: On the use of fast methods for separable finite difference equations for the solution of general elliptic problems. Sparse Matrices and Their Applications (ed. by D. J. Rose and R. A. Willoughby). Plenum Press, New York, 1972; 121–134.CrossRefGoogle Scholar
  6. 6.
    Concus, P.; Golub, G. H.: Use of fast direct methods for the efficient numerical solution of nonseparable elliptic equations. SIAM J. Numer. Anal. 10 (1973) 1103–1120.MathSciNetMATHCrossRefADSGoogle Scholar
  7. 7.
    Martin, E. D.; Lomax, H.: Rapid finite-difference computation of subsonic and slightly supercritical aerodynamic flows. AIAA Paper No. 74-11, 1974. Also AIAA Jour. 13 (1975) 579–586.MathSciNetMATHCrossRefADSGoogle Scholar
  8. 8.
    Murman, E. M.: Analysis of embedded shock waves calculated by relaxation methods. AIAA Jour. 12 (1974) 626–633.MATHCrossRefADSGoogle Scholar
  9. 9.
    Martin, E. D.: Progress in application of direct elliptic solvers to transonic flow computations. Aerodynamic Analyses Requiring Advanced Computers, NASA SP-347, 1975.Google Scholar
  10. 10.
    Lomax, H.; Martin, E. D.: Variants and extensions of a fast direct numerical Cauchy-Riemann solver, with illustrative applications. NASA TN D-7934, 1975.Google Scholar
  11. 11.
    Martin, E. D.: A fast semidirect method for computing transonic aerodynamic flows. AIAA 2nd Computational Fluid Dynamics Conference Proceedings, 1975; 162-174.Google Scholar
  12. 12.
    Murman, E. M.; Bailey, F. R.; Johnson, M. H.: TSFOIL — A computer code for 2-D transonic calculations, including wind-tunnel wall effects and wave-drag evaluation. Aerodynamic Analyses Requiring Advanced Computers, NASA SP-347, 1975.Google Scholar
  13. 13.
    Aitken, A. C.: On Bernoulli’s numerical solution of algebraic equations. Proc. Royal Soc. Edinburgh 46 (1926) 289–305.MATHGoogle Scholar
  14. 14.
    Shanks, D.: Nonlinear transformations of divergent and slowly convergent sequences. J. Math. and Phys. 34 (1955) 1–42.MathSciNetMATHGoogle Scholar
  15. 15.
    Bellman, R.: Perturbation Techniques in Mathematics, Physics, and Engineering. Holt, Rinehart and Winston, New York, 1964.Google Scholar

Copyright information

© Springer-Verlag, Berlin/Heidelberg 1976

Authors and Affiliations

  • E. Dale Martin
    • 1
  1. 1.NASA Ames Research CenterMoffett FieldCaliforniaUSA

Personalised recommendations