Concurrent Implementation of a Fast Vortex Method

v2u = -V x (we,) . (3) Vortex methods are a powerfil tool for the numerical simulation of incompressible flows at high Reynolds number. They are based on a discrete representation of the vorticity field and in the inviscid limit, the computational elements, or vortices, are simply advected at the local fluid velocity. The numerical approximations transform the vorticity equation, a non-linear PDE, into a N-body problem. The S(N2) time complexity usually associated with these problems has limited the number of computational elements to a few thousands. This paper is concerned with the concurrent implementation of fast vortex methods that reduce the time complexity to U(N1ogN). The fast algorithm that is used combines a binary tree data structure with high order expansions for the induced velocity field. The implementation of this particular algorithm on an MIMD archilecture is discussed. Vortex Methods