Numerical Magnetohydrodynamic (MHD) Modeling of Coronal Mass Ejections (CMEs)

The Coronal Mass Ejection (CME) is arguably the most important discovery of solar eruptive phenomena in the 20th century. It is now also recognized that CMEs have great impact on the Earth's environment by inducing geomagnetic storms. Thus, development of simulation models to understand the physical mechanisms of CME initiation and propagation has become a challenge in the solar MHD community. In this paper we shall summarize chronologically the development of the theoretical analyses, and the successes and failures of the numerical magnetohydrodynamic (MHD) simulations of coronal mass ejections (CMEs) during the past two decades. The chronological development of numerical simulation models and the evolution of the numerical methods to treat this class of problems are presented. The most appropriate way to model CMEs is to have (i) a realistic pre-event coronal atmosphere, and (ii) realistic driving mechanisms. Details of the progress and assessment of the theoretical and modeling efforts for the understanding of the physics of the CME initiation and propagation will be presented, and the numerical methods to construct these simulation models will be discussed.