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Numerical solution of the Navier-Stokes equations for symmetric laminar incompressible flow past a parabola

Published online by Cambridge University Press:  29 March 2006

R. T. Davis
R. T. Davis
Affiliation:
Department of Aerospace Engineering and Applied Mechanics, University of Cincinnati
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Abstract

Symmetric laminar incompressible flow past a parabolic cylinder is considered for all Reynolds numbers. In the limit as the Reynolds number based on nose radius of curvature goes to zero, the solution for flow past a semi-infinite flat plate is obtained. All solutions are found by using an implicit alternating direction method to solve the time-dependent Navier-Stokes equations. The solutions found are compared with various other exact and approximate solutions. Results are presented for skin friction, surface pressure, friction drag and pressure drag. The numerical method developed is of particular interest since it combines the alternating direction method with the implicit method for solving the boundary-layer equations. This leads to fast convergence and may be of use in other problems.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 51 , Issue 3 , 8 February 1972 , pp. 417 - 433
Copyright
© 1972 Cambridge University Press

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References

Blottner, F. G. & Flügge-Lotz I.1963 J. de Mécanique, 2, 397–423.
Botta X., Dijkstra, D. & Veldman J.1971 To appear in J. Engng. Math.
Cheng H. K.1963 Cornell Aero. Lab. Report, no. AF-1284-A-10.
Cheng H. K., Chen S. H., Mobley, P. & Huber C. P.1970 Rand Report, RM-6193-PR.
Davis R. T.1967 J. Fluid Mech. 27, 691–704.
Davis R. T.1970 A.I.A.A. J. 8, 843–851.
Dean W. R.1954 Mathematika, 1, 443–456.
Dennis, S. C. R. & Chang G. Z.1969 Phys. Fluids Supp. 11, 11-88-93.
Dennis, S. C. R. & Walsh, E. D. 1971 J. Fluid. Mech. 50, 801–814.
Dijkstra D.1969 Mathematisch Instituut Rijksuniwersiteit Groningen Report, TW-72.
Douglas J.1955 J. Soc. Indust. Appl. Math. 3, 42–65.
Imai I.1957 Aeron. Sci. 24, 155–156.
Thomas L. H.1949 Watson Science Computing Lab. Report, Columbia University.
Van Dyke M.1964 J. Fluid Mech. 19, 145–159.
Van Dyke M.1972 Submitted to J. Fluid Mech.
Van de Vooren, A. I. & Dijkstra, D. 1970 J. Engr. Math. 4, 9–27.
Yoshizawa A.1970 J. Phys. Soc. Japan, 28, 776–779.