  It is well known that magnetic fields dominate the dynamics in the solar
corona, and new generation of numerical modelling of the evolution of coronal
magnetic fields, as featured with boundary conditions driven directly by
observation data, are being developed. This paper describes a new approach of
data-driven magnetohydrodynamic (MHD) simulation of solar active region (AR)
magnetic field evolution, which is for the first time that a data-driven
full-MHD model utilizes directly the photospheric velocity field from DAVE4VM.
We constructed a well-established MHD equilibrium based on a single vector
magnetogram by employing an MHD-relaxation approach with sufficiently small
kinetic viscosity, and used this MHD equilibrium as the initial conditions for
subsequent data-driven evolution. Then we derived the photospheric surface
flows from a time series of observed magentograms based on the DAVE4VM method.
The surface flows are finally inputted in time sequence to the bottom boundary
of the MHD model to self-consistently update the magnetic field at every time
step by solving directly the magnetic induction equation at the bottom
boundary. We applied this data-driven model to study the magnetic field
evolution of AR 12158 with SDO/HMI vector magnetograms. Our model reproduced a
quasi-static stress of the field lines through mainly the rotational flow of
the AR's leading sunspot, which makes the core field lines to form a coherent S
shape consistent with the sigmoid structure as seen in the SDO/AIA images. The
total magnetic energy obtained in the simulation matches closely the
accumulated magnetic energy as calculated directly from the original vector
magnetogram with the DAVE4VM derived flow field. Such a data-driven model will
be used to study how the coronal field, as driven by the slow photospheric
motions, reaches a unstable state and runs into eruptions.
