Abstract
The outmost layer of solar atmosphere, corona, has many activities, such as flares, coronal mass ejections, solar prominences, and coronal rains. In order to fully understand the nonlinear physical process of these activities, one of the most popular approaches is to construct multidimensional numerical models via radiative magnetohydrodynamic numerical simulations. To simulate macroscopic coronal physics, we need to numerically solve magnetohydrodynamic equations coupled with radiative cooling, thermal conduction, and heating. The mainstream numerical methods to numerically solve these problems are introduced. The numerical scheme to solve the magnetohydrodynamic equations is composed of reconstruction to cell-interface values, approximate Riemann solver, methods to control divergence of magnetic field, and time integrator. We then review on the state of art in numerical studies on solar active region, flares, prominences, and coronal rains.
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