Title and Abstract
Title: Past and Future of Data-Constrained/Driven MHD simulations of Solar Eruptions
Abstract: Three-dimensional (3D) magnetohydrodynamic (MHD) simulation is a powerful tool for understanding the 3D dynamics of the coronal magnetic fields and plasmas in solar eruptions. Since the mid of 2000s, the recent solar satellites, such as Hinode and Solar Dynamics Observatory have provided high resolution photospheric magnetic field data, both in space and time. These data have given us an opportunity to conduct data-constrained or -driven MHD simulations of solar eruptions that brought lots of new insights of them. In this talk, first I will review our works on data-constrained and -driven MHD simulations and mention the remaining issues that will be addressed in the next few years. Second, I will further discuss the nonlinear force-free field and non-force-free field (magnetohydrostatic field) extrapolation codes that will be developed in next 1-2 years to apply the high-resolved photospheric data obtained with Goode Solar Telescope of the Big Bear Solar Observatory and Daniel K. Inouye Solar Telescope.