An efficient two-dimensional Vortex method with long time accuracy

Abstract

This paper deals with efficient techniques for the numerical solution of two-dimensional free-space incompressible Euler equations. We develop an algorithm for fast computation of velocity in a vortex method based upon discretization of vorticity by finite elements. We prove that the method with fast computation of velocity is numerically stable and convergent with second-order accuracy. Some standard numerical tests show that the algorithm with Delaunay regridding bears good stability and accuracy properties for long integration times, with a relatively low computational cost. Moreover, the algorithm is found to be more accurate than high-order vortex-blob methods with regridding for long enough integration times.