Abstract
Abstract : A fast vortex method was developed for solving the incompressible Euler equations in three dimensions. It is based on a combination of Anderson's Method of Local Corrections, which uses a hybrid of a finite difference representation and a particle representation to compute the velocity field induced on the vortices, and of adaptive mesh refinement for the finite difference calculation, The resulting algorithm is faster than any other existing finite difference or multipole - based algorithm for this problem and is 10-20 times faster than the direct N-body method for problems of current research interest. In addition, a good deal of technology was developed for finite-difference Poisson solvers of independent interest and usefulness, such as a multigrid-based local refinement algorithm for Mehrstellen discretizations of Poisson's equation in three dimensions, and efficient treatment of boundary conditions for boundaries that have infinite extent in one or more of the coordinate directions.
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