  The relationship between solar eruption and sunspot rotation has been widely
reported, and the underlying mechanism requires to be studied. Here we
performed a full 3D MHD simulation of data-constrained approach to study the
mechanism of flare eruptions in active region (AR) NOAA 10930, which is
characterized by continuous sunspot rotation and homologous eruptions. We
reconstructed the potential magnetic field from the magnetogram of Hinode/SOT
as the initial condition and drove the MHD system by applying continuous
sunspot rotation at the bottom boundary. The key magnetic structure before the
major eruptions and the pre-formed current sheet were derived, which is
responsible for the complex MHD evolution with multiple stages. The major
eruptions were triggered directly by fast reconnection in the pre-formed
current sheet above the main polarity inversion line between the two major
magnetic polarities of the AR. Furthermore, our simulation shows the homologous
eruption successfully. It has reasonable consistence with observations in
relative strength, energy release, X-ray and H{\alpha} features and time
interval of eruptions. In addition, the rotation angle of the sunspot before
the first eruption in the simulation is also close to the observed value. Our
simulation offers a scenario different from many previous studies based on
ideal instabilities of twisted magnetic flux rope, and shows the importance of
sunspot rotation and magnetic reconnection in efficiently producing homologous
eruptions by continuous energy injection and impulsive energy release in a
recurrent way.
