On MHD modeling of coronal mass ejections

We give at first a brief overview of the motivation for magnetohydrodynamic simulations of coronal mass ejections that can be classified as principal, local, and global, and discuss some of the present problems with the modeling. Besides the initiation, acceleration, evolution, and interactions of CMEs with the background solar wind, with each other and with planetary magnetospheres, we identify the need for large-scale MHD and multi-fluid models that explicitly incorporate effects of kinetic processes occurring on micro- or meso-scales. Concentrating on the acceleration and heating of the solar wind and CMEs by plasma waves, we describe an alternative route to this goal. Subsequently, we present CWENO-based local CME simulations and relate them to observations with the ACE spacecraft near 1 AU.