Collision of Vortex Rings by Vortex Method
Details
Numerical simulation of the collision of two vortex rings is a classic problem. The vortex reconnection or/and the merging phenomena of the vortex rings has been often simulated by the spectral method or LES modeling, etc. In the aspect of the discrete vortex method, it seems to be much difficult in this flow to satisfy the necessary conditions in which the Navier-Stokes equations have a strong solution when the vorticity vector is satisfied with sinβ(x, x', t) ⩽ |x - x'|/ρ (see Constantin, SIAM Review, 36, 1994). In the previous paper, the clear vortex reconnection did not occur in the numerical results which was simulated by the dynamic Smagorinsky model proposed by Cottet et al. (see M2AN, 37, 2003, 187-207). In this paper, we investigate the filtering model in which each cutoff radius is locally increased by taking account of the necessary condition of Constantin.
