A comparative study of data-driven MHD simulations of solar coronal evolution with photospheric flows derived from two different approaches

Data-driven simulation proves to be a powerful tool in revealing the dynamic process of the solar corona, but it remains challenging to implement the driving boundary conditions in a self-consistent way and match the observables at the photosphere. Here, we test two different photospheric velocity-driven MHD simulations in studying the quasi-static evolution of solar active region NOAA 11158. The two simulations were identically initialized with an MHD equilibrium as relaxed from a non-linear force-free field extrapolation from a vector magnetogram. Then, we energized the MHD system by applying the time series of photospheric velocity at the bottom boundary as derived by two different codes, the DAVE4VM and PDFI, from the observed vector magnetograms. To mimic the small-scale flux cancellation on the photosphere, the magnetic diffusion at the bottom boundary was set to be inversely proportional to the local scale length of the magnetic field. The result shows the evolution curves of the total magnetic energy and unsigned magnetic flux generated by the PDFI velocity match the corresponding curves from the observations much better than those by the DAVE4VM one. The structure of the current layer and synthetic image in PDFI simulation also has a more reasonable consistency with SDO/AIA 131 Å observation. The only shortage of the PDFI velocity is its capability in reproducing the morphology of sunspots, as characterized by a slightly lower correlation coefficient for the bottom magnetic field in simulations and magnetograms. Overall, this study suggests the superiority of each method in the models driven by the bottom velocity, which represents a further step toward the goal of reproducing more realistically the evolution of coronal magnetic fields using data-driven modeling.