ON THE ROKHLIN-GREENGARD METHOD WITH VORTEX BLOBS FOR PROBLEMS POSED IN ALL SPACE OR PERIODIC IN ONE DIRECTION

In this paper we consider the Rokhlin-Greengard (R-G) fast multipole a lgorithm when used to evaluate vortex blob interactions in a two-dimen sional fluid. We use exact solutions of the incompressible Euler equat ions to demonstrate that the R-G algorithm can compute vortex blob int eractions accurately. However, we also show that the structure of vort ex blobs forces a practical limitation on the highest (finest) bisecti on level one can use in the R-G algorithm, a restriction which does no t apply when point vortices are used. If this maximum bisection level is exceeded, then the accuracy of the R-G algorithm with blobs may be significantly reduced. A similar constraint should hold in three dimen sions. We also extend the R-G algorithm with blobs to problems which a re periodic in one spatial dimension and unbounded in the other, and w e document the performance of the resulting algorithm using some exact periodic solutions of the incompressible Euler equations. (C) 1995 Ac ademic Press, Inc.