Simulating vortex motion by three-dimensional vortex method

A 3D vortex method was applied to several vortex motions to demonstrate its usefulness and difficulties. The viscous diffusion of vorticity was incorporated by the method of Winkelmans and Leonard (1989). Vortex motions discussed in this paper include the deformation of pseudo-elliptic vortex rings of various major-to-minor axis ratios, the interaction of multiple circular vortex rings which approximately reproduced the Kolmogorov energy spectrum, and the unsteady separated flow around a circular disk with an angle of attack to the main flow. These examples demonstrate aspects of usefulness of the vortex method. On the other hand, one of the difficulties of the 3D vortex method is that the vorticity of vortex elements tends to diverge at a certain stage of evolution of the vortex systems. This might suggest the inadequacy of the Winkelmans and Leonard's (1989) model of the viscous diffusion of vorticity. A few methods of avoiding the vorticity divergence are discussed.