Numerical simulation of interaction between elliptic rings by discrete vortex method

In present paper a three dimensional discrete vortex filament method is proposed to simulate unsteady incompressible vortical flows, through which the interaction of two coaxial vortex rings was studied. First the process of head-on collision of two circular rings was reproduced and compared with experimental result. The good agreement between numerical work and experiment verified our model. Then the motion of single elliptic ring was studied and a fit expression was given, through which the axis-switching period of single elliptic ring can be calculate effectively. At last the head-on collision and leapfrogging process of two coaxial elliptic rings was studied respectively. For the case of head-on collision of two elliptic rings, the shape of new generated ring was similar but larger than initial elliptic ring. While for case of two elliptic rings moving in same direction, the axis-switching process of elliptic ring is accompanied with the leapfrogging process.