Point vortex dynamics simulation in a conformally mapped domain

Integration of N 2D point vortices in a Neumann oval domain, conformally mapped from the unit circle

CC Lin showed in 1942 that the point vortex Hamiltonian can be solved in any simply connected domain using the conformal map to the unit circle. Here we choose the Neumann oval domain (relevant to ocean basins) to demonstrate the dynamics of the vortices governed by the mapped Hamiltonian.
To derive the mapped Hamiltonian and corresponding equations of motion the so-called Routh rule is used and details of which are given in the included readme.pdf file.

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 of the system (the only known invariant) can be conserved to high precision.