  We performed a magnetohydrodynamic (MHD) simulation using a nonlinear
force-free field (NLFFF) in solar active region 11158 to clarify the dynamics
of an X2.2-class solar flare. We found that the NLFFF never shows the drastic
dynamics seen in observations, i.e., it is in stable state against the
perturbations. On the other hand, the MHD simulation shows that when the
strongly twisted lines are formed at close to the neutral line, which are
produced via tether-cutting reconnection in the twisted lines of the NLFFF,
consequently they erupt away from the solar surface via the complicated
reconnection. This result supports the argument that the strongly twisted lines
formed in NLFFF via tether-cutting reconnection are responsible for breaking
the force balance condition of the magnetic fields in the lower solar corona.
In addition to this the dynamical evolution of these field lines reveals that
at the initial stage the spatial pattern of the footpoints caused by the
reconnection of the twisted lines appropriately maps the distribution of the
observed two-ribbon flares. Interestingly, after the flare the reconnected
field lines convert into the structure like the post flare loops, which is
analogous to EUV image taken by SDO. Eventually, we found that the twisted
lines exceed a critical height at which the flux tube becomes unstable to the
torus instability. These results illustrate the reliability of our simulation
and also provide an important relationship between flare-CME dynamics.
