Numerical solution of Stokes flow generated by vortices: part 1: around an elliptical cylinder |
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Authors: | T B A El Bashir |
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Affiliation: | 1. Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Al-Khod 123, Muscat, Sultanate of Oman
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Abstract: | In this paper, the Stokes flow outside a two-dimensional elliptical cylinder is considered for a highly viscous, incompressible
fluid flow, driven by a pair of vortices placed at different positions. Relating the coefficients of some of the terms in
the asymptotic expansion of the stream function to the force components and the torque on the combined system, together with
the imposition of integral constraints, enables the boundary element method to provide a closed system of equations. It is
found that excellent agreement is obtained between the numerical results for a single vortex and all the previous analytical
expressions. Some new results relating to forces and torques on the elliptical cylinder are presented. The analytical closed-form
expression for the single vortex is provided. |
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Keywords: | |
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