Fast triangulated vortex methods for the 2D Euler equations (Q1326685)

Vortex methods for inviscid incompressible two-dimensional fluid flow are usually based on blob approximations. This paper presents a vortex method in which the vorticity is approximated by a piecewise polynomial interpolant on a Delaunay triangulation of the vortices. An efficient reconstruction of the Delaunay triangulation at each step makes the method accurate for long times. The vertices of the triangulation move with the fluid velocity, which is reconstructed from the vorticity via a simplified fast multipole method for the Biot-Savart law with a continuous source distribution. Numerical results show that the method is highly accurate over long time intervals.