A two-dimensional compressible MHD code has been used to numerically study the asymmetric driven reconnection processes in the vicinity of the magnetopause. The initial magnetic field configuration is assumed to be in a mechanical equilibrium state. The cases with identical temperatures (Tm0/Ts0=1.0) and four different ratios of magnetic field strength (Q=Bm0/Bs0=1.0, 1.5, 2.0, 2.5), and the case with Tm0/Ts0=2.0 and Q=1.5 are investigated (Bm0, Tm0 and Bs0, Ts0 are the initial magnetic strength and temperature outside the current sheet on the magnetosphere and the magnetosheath, respectively ). When the magnetic field on the magnetosheath side is set as southward, a recurrent formation of multiple magnetic bubbles with various scales occurs under the action of the inward plasma flow imposed at the left and right boundaries. In the simulation, some bubbles coalesce into a bigger one and then it is convected out of the simulation domain; the others are convected through the top boundary all alone. Thus, the plasmoid events with different scales and different time intervals take place intermittently and the impulsive features of magnetic reconnection are clearly shown. The multiple magnetic islands are all high-temperature and large-density regions in comparison with the ambient environment. The bipolar signatures or fluctuant variations of normal magnetic field component are generated by the formation of multiple magnetic islands. This result is similar to the FTEs signature.