Hostname: page-component-77c89778f8-vsgnj Total loading time: 0 Render date: 2024-07-16T19:04:49.289Z Has data issue: false hasContentIssue false
  • English
  • Français

An Improved Reversed-Flow Formulation of the Galerkin-Kantorovich-Dorodnitsyn Multi-Moment Integral Method

Published online by Cambridge University Press:  07 June 2016

Howard E. Bethel
Howard E. Bethel*
Affiliation:
Aerospace Research Laboratories, Wright-Patterson Air Force Base
Get access

Summary

An improved reversed-flow formulation of the Galerkin-Kantorovich-Dorodnitsyn multi-moment integral method is presented in this paper. Convergence and accuracy properties of the approximate solutions of the Stewartson lower branch similar flows are given. The approximate solutions obtained with the new formulation for the lower branch similar flows are, in general, more accurate than those obtained with the classical Pohlhausen method or either of the previous formulations used with the GKD method.

Type
Research Article
Information
Aeronautical Quarterly , Volume 20 , Issue 2 , May 1969 , pp. 191 - 202
Copyright
Copyright © Royal Aeronautical Society. 1969

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Bethel, H. E. On a convergent multi-moment method for the laminar boundary-layer equations. Aeronautical Quarterly, Vol. XVIII, pp. 332–353, November 1967.Google Scholar
2. Bethel, H. E. Approximate solution of the laminar boundary-layer equations with mass transfer. AIAA Journal, Vol. 6, pp. 220–225,1968.Google Scholar
3. Nielsen, J. N., Lynes, L. L. and Goodwin, F. K. Calculation of laminar separation with free interaction by the method of integral relations. Air Force Flight Dynamics Laboratory, AFFDL TR-65-107, 1965.Google Scholar
4. Holt, M. Separation of laminar boundary layer flow past a concave corner. AGARD Conference Proceedings No. 4, 1966.Google Scholar
5. Lees, L. and Reeves, B. L. Supersonic separated and reattaching laminar flows. AIAA Journal, Vol. 2, p. 1908, 1964.Google Scholar
6. Grabow, R. M. Finite difference methods. Von Kármán Institute Short Course on Separated Flows, Rhode-St.-Genèse, Belgium, 1967.Google Scholar
7. Reyhner, T. A. and Flügge-Lotz, I. The interaction of a shock wave with a laminar boundary layer. Stanford University, Division of Engineering Mechanics, TR 163, 1966.Google Scholar
8. Cooke, J. C. and Mangler, K. W. The numerical solution of the laminar boundary-layer equations for an ideal gas in two and three dimensions. RAE TM Aero 999, 1967.Google Scholar
9. Libby, P. A. and Liu, T. M. Some similar laminar flows obtained by quasilinearization. AGARD Seminar on Numerical Methods for Viscous Flows, 1967.Google Scholar
10. Catherall, D. and Mangler, K. W. The integration of the two-dimensional laminar boundary-layer equations past the point of vanishing skin friction. Journal of Fluid Mechanics, Vol. 26, pp. 163–182, 1966.Google Scholar
11. Quick, A. W. and Schröder, K. Verhalten der laminaren Grenzschicht bei periodisch schwankendem Druckverlauf. Mathematische Nachrichten, Vol. 8, pp. 217–238, 1953.CrossRefGoogle Scholar
12. Stewartson, K. Further solutions of the Falkner-Skan equation. Proceedings, Cambridge Philosophical Society, Vol. 50, pp. 454–465, 1954.CrossRefGoogle Scholar
13. Hankey, W. L. Solutions of laminar boundary-layer equations with emphasis on separation. Part II-Integral methods. USAF Aerospace Research Laboratories, ARL 67-0273, 1967.Google Scholar