A New Implementation of the Vortex Method for Elliptical Vortex Evolution

We discuss a new implementation of the vortex method for the incompressible Euler equations. This work focuses on smooth vorticity distributions as opposed to vortex sheets. As usual the vorticity is carried by Lagrangian particles and the velocity is recovered by the Biot-Savart law. The new implementation combines remeshing, adaptive refinement, and treecode acceleration to resolve complex features of the flow. Applications are given to vortex dynamics in two-dimensional free-space.