Point vortex dynamics simulation

Integration of N 2D point vortices in a cylinder, using an adaptive 4th order Runge-Kutta scheme.

The point vortex model was introduced by Helmholtz in 1867 and it was subsequently proved by Lin in 1942 that the motion of N vortices in a bounded domain is a Hamiltonian system (sometime called the `Kirchhoff-Routh path function'). The statistical mechanics of the N vortices is remarkable due to the fact that the system exhibits negative temperature.
The integrator used is a custom adaptive 4th order Runge-Kutta scheme which ensures the convergence of vortex positions to below a tolerance parameter before advancing to the next time step. In this way the energy and angular momentum of the system (the only two invariants) are conserved to high precision.