A new diffusion scheme in vortex methods for three-dimensional incompressible flows

Department of Mechanical Engineering FAMU/FSU College of Engineering PO Box 2175, Tallahassee, Florida, 32316, USA

Abstract

We propose and validate a new, accurate, robust, mesh-free method to represent diffusion processes in Lagrangian computations, called "vorticity redistribution". The basic idea of this method is to represent diffusion by modifying the strength of the vortices: circulation is exchanged between vortices in the immediate vicinity of one another in such a way that the correct diffusion is achieved. Our method resolves length scales up to the spacing of the vortices, and it has no inherent limitations on the order of accuracy. Moreover, conservation of circulation, linear and angular momentum are implicit in the formulation. For its validation, we compute the flow over an impulsively started cylinder at Re=9500 (based on diameter); we compare the vorticity field with another recent high resolution simulation. The method is extended to three-dimensions and tested on two linear problems.