We developed a three-dimensional global simulator of astrophysical rotational plasma which strongly interact with magnetic fields. The simulator consists of modules plugged-in to a platform of parallelized magneto-hydrodynamical code. High vector-parallel performance has been achieved for modules incorporating magnetic diffusion, thermal conduction, and self-gravity. We also developed web-based user interface and visualization modules. By applying the simulator to astrophysical disks, we showed that magnetic turbulence generated inside the torus efficiently transports angular momentum outward and enables accretion of the disk plasma. Furthermore, we successfully reproduced the 1/f noise-like X-ray time variability characteristic of black hole candidates, and well-collimated, bipolar jets.