A Higher Order Vorticity Redistribution Method for 3-D Diffusion In Free Space

A 3-D Vortex Code for Parachute Flow Predictions: VIPAR Version 1.0

“…We note that the recently developed three-dimensional fast multipole method of Cheng, Greengard, and Rokhlin [21] that uses local expansions has a break even point on the order of 1,000 vortons and is approximately two orders of magnitude faster than our method for 10 6 vortons. Our aversion to using the "Greengard-Rokhlin Scheme" is that parallel efficiencies scale poorly for this scheme.…”

“…In future versions of VIPAR, we plan to implement merging and splitting algorithms to better manage vortex element strain and growth due to stretching and diffusion, respectively, as well as control the total number of vortons in the flow. We also plan to implement a Vortex Redistribution Method (VRM) for diffusion due to Shankar [5] that has been further developed by Gharakhani [6].…”

Gridless Compressible Flow: A White Paper

“…Gharakhani [15] suggests that a vorticity redistribution method (VRM) originally developed by Subramaniam [16] may prove superior to the PSE method with regard to reducing the number of elements and rediscretization requirements associated with the PSE method.…”

“…The diffusion velocity scheme originally developed by Ogami and Akamatsu [31] and further developed by Strickland, Kempka, and Wolfe [32] is a convenient scheme if a wall layer containing a moving grid is used to simulate the viscous boundary layer near the body surface. If particles are used, the PSE method [14] or the VRM [15,16] are more appropriate. Both the PSE method and the VRM redistribute the vorticity so as to account for the Laplacian on the right hand side of the vorticity evolution equation.…”

“…Gharakhani [33] provides a 1997 review of methods to model stretching and diffusion. Since that time, his version of the VRM for treating diffusion has become available [15].…”