The research aims were to solve the 3D complex flows, in particular, investigating the high-Reynolds-number effects by isolating the error from boundary effect. Vortex ring is an important element in turbulent flows and the studies of their interaction may be applicable to the complex fluid flows. The possibility of further acceleration has been investigated by a simultaneous use of the FMM and the MDGRAPE-3. Several issues regarding the optimum level of the FMM, and the use of PPM have been addressed. We have chosen the collision of vortex rings as a test case. The following characteristics of this flow allow focusing on the assessment of the proposed acceleration technique. The flow does not involve solid or periodic boundaries, and thus poses minimal complications in the implementation of the FMM itself. Also, the initial condition is simple enough to generate by using vortex methods. The initial flow field is quite simple, the collision of the rings results in a strong turbulent state, and the resulting flow field is greatly affected by the initial Reynolds number. This character enabled me to demonstrate the ability to handle high-Reynolds-number flows.