Explicit smooth velocity kernels for vortex methods
Abstract
Recently the authors showed the convergence of a class of vortex methods for incompressible, inviscid flow in two or three space dimensions. These methods are based on the fact that the velocity can be determined from the vorticity by a singular integral. The accuracy of the method depends on replacing the integral kernel with a smooth approximation. The purpose of this note is to construct smooth kernels of arbitrary order of accuracy which are given by simple, explicity formulas.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 February 1983
 Bibcode:
 1983STIN...8332007B
 Keywords:

 Differential Equations;
 Functions (Mathematics);
 Incompressible Flow;
 Inviscid Flow;
 Vortices;
 Accuracy;
 Computation;
 Convergence;
 Formulas (Mathematics);
 Stability;
 Three Dimensional Flow;
 Two Dimensional Flow;
 Fluid Mechanics and Heat Transfer