This paper reviews our recent progress in the numerical study of coronal mass ejections (CMEs) based on flux rope model, which shows that when the reconnection-favored emerging flux appears either within or ABSTRACT on the outer edge of the filament channel, the flux rope would lose its equilibrium, and be ejected, while a current sheet is formed below the flux rope. For the case with emergence within the filament channel, even small flux is enough to trigger the loss of equilibrium, however, there is a threshold for the emerging flux on the outer edge of the filament channel. Given that anomalous resistivity sets in (e.g. when the current density exceeds a critical value), fast reconnection is resulted in, leading to fast eruption of the flux rope and localized flare (either impulsive-type or LDE-type depending on the height of the reconnection point) near the solar surface. The numerical results can well explain why CMEs are not centered on flares and provide hints for CME-flare spatial and emporal relationships.

A class of pseudo-reconnection caused by a shifted mesh in MHD simulations is reported. In term of this mesh system, some non-physical results may be obtained in certain circumstances, e.g., magnetic reconnection occurs without resistivity. After comparison, another kind of mesh system is strongly recommended.