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Solution of three-dimensional incompressible flow problems

Published online by Cambridge University Press:  12 April 2006

S. M. Richardson  and
A. R. H. Cornish
S. M. Richardson
Affiliation:
Department of Chemical Engineering and Chemical Technology, Imperial College, London Present address: Department of Chemical Engineering, University of Cambridge.
A. R. H. Cornish
Affiliation:
Department of Chemical Engineering and Chemical Technology, Imperial College, London
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Abstract

A method for solving quite general three-dimensional incompressible flow problems, in particular those described by the Navier–Stokes equations, is presented. The essence of the method is the expression of the velocity in terms of scalar and vector potentials, which are the three-dimensional generalizations of the two-dimensional stream function, and which ensure that the equation of continuity is satisfied automatically. Although the method is not new, a correct but simple and unambiguous procedure for using it has not been presented before.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 82 , Issue 2 , 7 September 1977 , pp. 309 - 319
Copyright
© 1977 Cambridge University Press

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