  We apply a data-driven MHD model to investigate the three-dimensional (3D)
magnetic field of NOAA active region (AR) 11117 around the time of a C-class
confined flare occurred on 2010 October 25. The MHD model, based on the
spacetime conservation-element and solution-element (CESE) scheme, is designed
to focus on the magnetic-field evolution and to consider a simplified solar
atomsphere with finite plasma $\beta$. Magnetic vector-field data derived from
the observations at the photoshpere is inputted directly to constrain the
model. Assuming that the dynamic evolution of the coronal magnetic field can be
approximated by successive equilibria, we solve a time sequence of MHD
equilibria basing on a set of vector magnetograms for AR 11117 taken by the
Helioseismic and Magnetic Imager (HMI) on board the {\it Solar Dynamic
Observatory (SDO)} around the time of flare. The model qualitatively reproduces
the basic structures of the 3D magnetic field, as supported by the visual
similarity between the field lines and the coronal loops observed by the
Atmospheric Imaging Assembly (AIA), which shows that the coronal field can
indeed be well characterized by the MHD equilibrium in most time. The magnetic
configuration changes very limited during the studied time interval of two
hours. A topological analysis reveals that the small flare is correlated with a
bald patch (BP, where the magnetic field is tangent to the photoshpere),
suggesting that the energy release of the flare can be understood by magnetic
reconnection associated with the BP separatrices. The total magnetic flux and
energy keep increasing slightly in spite of the flare, while the computed
magnetic free energy drops during the flare with an amount of $\sim 10^{30}$
erg, which seems to be adequate to provide the energy budget of the minor
C-class confined flare.

Solar and Stellar Astrophysics