Vortex rings have been a subject of interest in vortex dynamics due to a
plethora of physical phenomena revealed by their motions and interactions within
a boundary. The present paper is devoted to physics of a head-on collision of two
vortex rings in three dimensional space, simulated with a second order finite volume
scheme and compressible. The scheme combines non-iterative approximate Riemannsolver
and piecewise-parabolic reconstruction used in inviscid flux evaluation procedure.
The computational results of vortex ring collisions capture several distinctive
phenomena. In the early stages of the simulation, the rings propagate under their own
self-induced motion. As the rings approach each other, their radii increase, followed
by stretching and merging during the collision. Later, the two rings have merged into
a single doughnut-shaped structure. This structure continues to extend in the radial
direction, leaving a web of particles around the centers. At a later time, the formation
of ringlets propagate radially away from the center of collision, and then the effects of
instability involved leads to a reconnection in which small-scale ringlets are generated.
In addition, it is shown that the scheme captures several experimentally observed
features of the ring collisions, including a turbulent breakdown into small-scale structures
and the generation of small-scale radially propagating vortex rings, due to the
modification of the vorticity distribution, as a result of the entrainment of background
vorticity and helicity by the vortex core, and their subsequent interaction.