# Numerical study of the three-dimensional incompressible flow between closed rotating cylinders

• Avi Lin
• G. de Vahl Davis
• E. Leonardi
• J. A. Reizes
Contributed Papers
Part of the Lecture Notes in Physics book series (LNP, volume 218)

## Abstract

A new method for the solution of the vector potential — vorticity formulation of the equations of a fluid motion is presented in this paper. The fully coupled finite difference approximations to these equations have been solved using a general block tri - diagonal scheme. New boundary conditions for the vector potential are also presented. These conditions enables to satisfy exactly the conditions at the boundaries of the solution domain, like the mass flow through the boundaries. The method is found to converge more rapidly, and to be more accurate than previous solutions of the three dimensional vector potential - vorticity equations.

## Keywords

Vector Potential Outer Cylinder Finite Difference Approximation Vorticity Component Boundary Condition Formulation
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## References

1. [1]
Hirasaki, G.J. and Hellums, J.D., (1970), “Boundary Conditions on the Vector and Scalar Potentials in Viscous Three-Dimensional Hydro dynamics”, Quart.Appl.Math,, XXVIII, 2 pp. 293–296.Google Scholar
2. [2]
Richardson, S.M. and Cornish, A.R.H., (1977), “Solutions of ThreeDimensional Incompressible Flow Problems”, J Fluid Mech., 82, 2, pp.309–319.Google Scholar
3. [3]
Reizes, J.A., Leonardi, E. and de Vahl Davis, G., (1984), “Problems with Derived Variable Methods for the Numerical Solution of Three-Dimensional Flows”, Techniques and Applications, John Noye and Clive Fletcher eds., North-Holland Publ. Co., pp.909–913.Google Scholar
4. [4]
Pepper, D.W. and Copper, R.E., (1979), ASME J. of Heat Transfer, 101, 4,pp.739–741.Google Scholar
5. [5]
Lin, A., (1964), “ A Primitive Variables Scheme For Solving the Navier Stokes Eauations”, in preparation.Google Scholar

## Copyright information

© Springer-Verlag 1985

## Authors and Affiliations

• Avi Lin
• 1
• G. de Vahl Davis
• 2
• E. Leonardi
• 2
• J. A. Reizes
• 2
1. 1.Computer Science DepartmentTechnion - Israel Institute of TechnologyHaifaIsrael
2. 2.School of Mechanical and Industrial EngineeringThe University of New South Walse, KensingtonN.S.W.Australia