This paper reviews some of the many 3D numerical experiments of the emergence of magnetic fields from the solar interior and the subsequent interaction with the pre-existing coronal magnetic field. The models described here are idealised, in the sense that the internal energy equation only involves the adiabatic, Ohmic and viscous shock heating terms. However, provided the main aim is to investigate the dynamical evolution, this is adequate. Many interesting observational phenomena are explained by these models in a self-consistent manner.
Hood, A. W., Archontis, V., & MacTaggart, D. (2012). 3D MHD flux emergence experiments: idealised models and coronal interactions: Solar Physics, 278(1), 3–31. https://doi.org/10.1007/s11207-011-9745-2