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Computing laminar boundary layers with the von Mises equation

Published online by Cambridge University Press:  04 July 2016

R. D. Mills  and
M. Z. Abedin
R. D. Mills
Affiliation:
Computing Science Department, Glasgow University
M. Z. Abedin
Affiliation:
Computing Science Department, Glasgow University
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Extract

There is much current interest in numerical methods of solution of the laminar boundary-layer equations. Methods used to date may generally be classified as

  • (i) explicit finite-difference methods (e.g. Refs. 1, 2, 3);

  • (ii) implicit finite-difference methods (e.g. Refs. 4, 5, 6, 7);

  • (iii) difference-differential methods (e.g. Ref. 8).

A method based on converting the boundary-layer problem into an integral equation and solving the latter by iteration has been developed by one of the present authors.

Type
Technical notes
Information
The Aeronautical Journal , Volume 78 , Issue 766 , October 1974 , pp. 476 - 479
Copyright
Copyright © Royal Aeronautical Society 1974 

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References

1. Baxter, D. C. and Flügge-Lotz, I. The solution of compressible laminar boundary layer problems by a finite difference method. Z angew Math Phys, Vol 9, p 81, 1958.Google Scholar
2. Mitchell, A. R. and Thompson, J. Y. Finite difference methods of solution of the von Mises boundary layer equation with special reference to conditions near a singularity. Z angew Math Phys, Vol 9, p 26, 1958.Google Scholar
3. Mitchell, A. R. The solution of the von Mises boundary layer equation using a high speed computer. Mathematics of Computation, Vol 15, p 238, 1961.Google Scholar
4. Leigh, D. C. F. The laminar boundary-layer equation: A method of solution by means of an automatic computer. Proc Camb Phil Soc, Vol 51, p 320, 1955.Google Scholar
5. Terrill, R. M. Laminar boundary-layer flow near separation with and without suction. Phil Trans Roy Soc A, Vol 253, p 55, 1961.Google Scholar
6. Schönauer, W. Ein Differenzenverfahren zur Lösung der Grenzschtgleichung fur Stationare, Laminare, Incompressible Strömung. Ingenieur-Archiv, Vol 33, p 173, 1964.Google Scholar
7. Sells, C. C. L. Two-dimensional laminar compressible boundary-layer programme for a perfect gas. ARC R and M 3533, 1966.Google Scholar
8. Smith, A. M. O. and Clutter, D. W. Solution of the incompressible laminar boundary layer equations. AIAA Journal, Vol 1. p 2062, 1963.Google Scholar
9. Mills, R. D. The steady laminar incompressible boundary-layer problem as an integral equation in Crocco variables: Investigations of the similarity flows. ARC R and M 3515, 1968.Google Scholar
10. Mills, R. D. The steady laminar incompressible boundary-layer problem as an integral equation in Crocco variables: The calculation of non-similar flows. ARC R & M 3742, 1974.Google Scholar
11. Abedin, M. Z. Investigations of numerical methods for solving the laminar boundary-layer equations, with some applications. PhD Thesis, University of Glasgow, 1973.Google Scholar
12. Stewartson, K. The theory of laminar boundary layers in compressible fluids. Oxford, 1964.Google Scholar
13. Fox, L. The numerical solution of two-point boundary problems in ordinary differential equations. Oxford. 1957.Google Scholar
14. Fox, L. An introduction to numerical linear algebra. Oxford, 1964.Google Scholar
15. Milne-Thompson, L. M. Theoretical hydrodynamics. MacMillan, 1938.Google Scholar
16. Hartree, D. R. A solution of the laminar boundarylayer equation for retarded flow. ARC R & M 2426, 1939.Google Scholar