Abstract Ever since the magnetohydrodynamic (MHD) method for extrapolation of the solar coronal magnetic field was first developed to study the dynamic evolution of twisted magnetic flux tubes, it has proven to be efficient in the reconstruction of the solar coronal magnetic field. A recent example is the so-called data-driven simulation method (DDSM), which has been demonstrated to be valid by an application to model analytic solutions such as a force-free equilibrium given by Low and Lou. We use DDSM for the observed magnetograms to reconstruct the magnetic field above an active region. To avoid an unnecessary sensitivity to boundary conditions, we use a classical total variation diminishing Lax-Friedrichs formulation to iteratively compute the full MHD equations. In order to incorporate a magnetogram consistently and stably, the bottom boundary conditions are derived from the characteristic method. In our simulation, we change the tangential fields continually from an initial potential field to the vector magnetogram. In the relaxation, the initial potential field is changed to a nonlinear magnetic field until the MHD equilibrium state is reached. Such a stable equilibrium is expected to be able to represent the solar atmosphere at a specified time. By inputting the magnetograms before and after the X3.4 flare that occurred on 2006 December 13, we find a topological change after comparing the magnetic field before and after the flare. Some discussions are given regarding the change of magnetic configuration and current distribution. Furthermore, we compare the reconstructed field line configuration with the coronal loop observations by XRT onboard Hinode. The comparison shows a relatively good correlation.

Keywords Sun: activity — Sun: flares — Sun: corona

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