Recent advances in solar data-driven MHD simulations of the formation and evolution of CME flux ropes

Filament eruptions and coronal mass ejections are physical phenomena related to magnetic flux ropes carrying electric current. A magnetic flux rope is a key structure for solar eruptions, and when it carries a southward magnetic field component when propagating to the Earth. It is the primary driver of strong geomagnetic storms. As a result, developing a numerical model capable of capturing the entire progression of a flux rope, from its inception to its eruptive phase, is crucial for forecasting adverse space weather. The existence of such flux ropes is revealed by the presence of sigmoids or hot channels in active regions and filaments or prominences by observations from space and ground instruments. After proposing cartoons in 2D, potential, linear, non-linear-force-free-field (NLFFF) and non-force-free-field (NFFF) magnetic extrapolations, 3D numerical magnetohydrodynamic (MHD) simulation models were developed, first in a static configuration and later dynamic data-driven MHD models using high resolution observed vector magnetograms. This paper reviews a few recent developments in data-driven models, such as the time-dependent magneto-frictional (TMF) and thermodynamic magnetohydrodynamic (MHD) models. Hereafter, to demonstrate the capacity of these models to reveal the physics of observations, we present the results for three events explored in our group: 1. the eruptive X1.0 flare on 28 October 2021; 2. the filament eruption on 18 August 2022; and 3. the confined X2.2 flare on 6 September 2017. These case studies validate the ability of data-driven models to retrieve observations, including the formation and eruption of flux ropes, 3D magnetic reconnection, CME three-part structures and the failed eruption. Based on these results, we provide some arguments for the formation mechanisms of flux ropes, the physical nature of the CME leading front, and the constraints of failed eruptions.