Numerical solution of Stokes flow generated by vortices: Part 1: Around an elliptical cylinder

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.