A New Diffusion Procedure for Vortex Methods

• Published in: Journal of computational physics Vol. 127; no. 1; pp. 88 - 109
• Main Authors: Shankar, S., Dommelen, L.van
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.08.1996
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1006/jcph.1996.0160

A new method is proposed for simulating diffusion in vortex methods for two-dimensional incompressible flows. The method resolves length scales up to the spacing of the vortices. The grid-free nature of vortex methods is fully retained and the distribution of the vortices can be irregular. It is shown for the Stokes equations that in principle, the method can have any order of accuracy. It also conserves circulation, linear, and angular momentum. The method is based on exchanging a conserved quantity between arbitrary computational points. This suggests that extensions to more general flows may be possible. For the two-dimensional incompressible flows studied, circulation is exchanged between vortices to simulate diffusion. The amounts of circulation exchanged must satisfy a linear system of equations. Based on stability considerations, the exchanged amounts should further be positive. A procedure to find a solution to this problem is formulated using linear programming techniques. To test the method, the decay processes of a single point vortex and of a counterrotating pair of point vortices are computed. Current limitations of the method are discussed.