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 th at CMEs have great impact on the Earth's environment by inducing geomagneti c 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 ejectio ns (CMEs) during the past two decades. The chronological development of num erical simulation models and the evolution of the numerical methods to trea t this class of problems are presented. The most appropriate way to model C MEs is to have (i) a realistic pre-event coronal atmosphere, and (ii) reali stic driving mechanisms. Details of the progress and assessment of the theo retical and modeling efforts for the understanding of the physics of the CM E initiation and propagation will be presented, and the numerical methods t o construct these simulation models will be discussed.