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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, LondonPresent 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.

Information

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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References

Aris, R. 1962 Vectors, Tensors, and the Basic Equations of Fluid Mechanics. Prentice-Hall.
Aziz, K. & Hellums, J. D. 1967 Numerical solution of the three-dimensional equations of motion for laminar natural convection. Phys. Fluids 10, 314.Google Scholar
Bykhovski, E. B. & Smirnov, N. V. 1960 On orthogonal expansions of the space of vector functions which are square-summable over a given domain. Trudy Mat. Inst. Steklova 59, 5.Google Scholar
Hirasaki, G. J. 1967 A general formulation of the boundary conditions on the vector potential in three-dimensional hydrodynamics. Ph.D. thesis, Rice University.
Hirasaki, G. J. & Hellums, J. D. 1968 A general formulation of the boundary conditions on the vector potential in three-dimensional hydrodynamics. Quart. Appl. Math. 26, 331.Google Scholar
Hirasaki, G. J. & Hellums, J. D. 1970 Boundary conditions on the vector and scalar potentials in viscous three-dimensional hydrodynamics. Quart. Appl. Math. 28, 293.Google Scholar
Holst, P. H. & Aziz, K. 1972 Transient three-dimensional natural convection in confined porous media. Int. J. Heat Mass Transfer 15, 73.Google Scholar
Mallinson, G. D. & de Vahl Davis, G. 1973 The method of the false transient for the solution of coupled elliptic equations. J. Comp. Phys. 12, 435.Google Scholar
Moreau, J. J. 1959 Une spécification du potentiel-vecteur en hydrodynamique. C. R. Acad. Sci. Paris 248, 3406.Google Scholar
Richardson, S. M. 1976 Numerical solution of the three-dimensional Navier — Stokes equations. Ph.D. thesis, University of London.
Roache, P. J. 1972 Computational Fluid Dynamics. Hermosa.
Spiegel, M. R. 1959 Vector Analysis. McGraw-Hill.
Timman, R. 1954 Le potentiel vecteur et son application à l'analyse harmonique d'un écoulement à trois dimensions. In Mémoires Sur la Mécanique des Fluides Offerts à D. P. Riabouchinsky (ed. H. Villat), p. 351. Publ. Sci. Tech. Min. Air.