Simulation of interaction between two vortex rings

In this paper, a three-dimension vortex filament method is proposed to simulate the interaction between two vortex rings. The propagation velocity of single circular ring was first studied and then the head-on collision and the leapfrogging process of two circular vortex rings were then reproduced, respectively. The well agreement between present simulation and literature proved the correctness of our model. After this, the model is used to simulate the interaction of two coaxial elliptical or circular rings travelling in same or opposite direction. Some interesting phenomena were found and discussed in detail.