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It is well known that magnetic fields dominate the dynamics in the solarcorona, and new generation of numerical modelling of the evolution of coronalmagnetic fields, as featured with boundary conditions driven directly byobservation data, are being developed. This paper describes a new approach ofdata-driven magnetohydrodynamic (MHD) simulation of solar active region (AR)magnetic field evolution, which is for the first time that a data-drivenfull-MHD model utilizes directly the photospheric velocity field from DAVE4VM.We constructed a well-established MHD equilibrium based on a single vectormagnetogram by employing an MHD-relaxation approach with sufficiently smallkinetic viscosity, and used this MHD equilibrium as the initial conditions forsubsequent data-driven evolution. Then we derived the photospheric surfaceflows from a time series of observed magentograms based on the DAVE4VM method.The surface flows are finally inputted in time sequence to the bottom boundaryof the MHD model to self-consistently update the magnetic field at every timestep by solving directly the magnetic induction equation at the bottomboundary. We applied this data-driven model to study the magnetic fieldevolution of AR 12158 with SDO/HMI vector magnetograms. Our model reproduced aquasi-static stress of the field lines through mainly the rotational flow ofthe AR's leading sunspot, which makes the core field lines to form a coherent Sshape consistent with the sigmoid structure as seen in the SDO/AIA images. Thetotal magnetic energy obtained in the simulation matches closely theaccumulated magnetic energy as calculated directly from the original vectormagnetogram with the DAVE4VM derived flow field. Such a data-driven model willbe used to study how the coronal field, as driven by the slow photosphericmotions, reaches a unstable state and runs into eruptions.

MHD Modeling of Solar Coronal Magnetic Evolution Driven by Photospheric Flow