  In two dimensional superfluid, annihilation processes of vortices are
investigated by numerical simulation within the dissipative Gross-Pitaevskii
equation (GPE) model. First, quantum vortex solution is obtained and its
fitting function is found. Second, the simulation show that positive and
negative vortices accelerate in both x,y directions, until they annihilate into
a soliton and then a crescent-shaped shock wave. The processes are found to be
controlled by the dissipative parameter and the general Magnus force. For the
behavior of separation distance between vortices d(t), an universal scaling
exponent 1/2 is found which is same with the three dimensional cases. Third,
system's energy is surprisingly found to be determined by system's
configuration and their relation are obtained. Then we derive the general
Magnus force which decreases with the increases of d(t) for large d(t) and
increases with the increases of d(t) for small d(t).
