A method of local corrections for computing the velocity field due to a distribution of vortex blobs

Very large vortex calculations in two dimensions

“…The first step finishes by inverting the right hand side with a Poisson solver, and then interpolating the resultant far-field velocity field onto the center of the vortex. We used the Lagrange interpolation formula for complex analytic functions used by Anderson [2].…”

“…Most interactions, involving distant length scales, can then be effectively lumped or averaged since the the induced velocity field will be a harmonic function. We use one strategy that takes advantage of that fact, known as Anderson's Method of Local Corrections (MLC) [2]. Another such strategy, the multipole expansion method of Rokhlin and Greengard [11], appears elsewhere in this proceedings .…”

A Deterministic Vortex Sheet Method for Boundary Layer Flow

“…In the present scheme, approximate solutions to (1) are obtained in the form of collections of N vortex sheets or "tiles" of large aspect ratio ldhi, where 2li and 2hi are the width and height of the ith tile, respectively. The vortex sheets are assumed to have uniform vorticity, wi(t), and convect with the velocity of their centers -generally without change of size and shape.…”

“…Recent advances in developing fast vortex methods [1,2,16,17] and the parallel implementation of vortex algorithms on supercomputers (23] have effectively eliminated many past limitations on the number of vortex elements that can be reasonably employed in simulations. It has also become increasingly evident [9] that simulations of three-dimensional turbulence may not require resolution beyond that of the principal energy containing vortical structures.…”

Potential Flow in Channels.

“…The governing equation is the Poisson equation, (1) A= subject to an appropriate boundary condition. In this paper, we will restrict our attention to two-dimensional models and will consistently use the terminology of fluid dynamics.…”