Abstract
Coronal mass ejections (CMEs) play a key role in space weather. The mathematical modelling of these violent solar phenomena can contribute to a better understanding of their origin and evolution and as such improve space weather predictions. We review the state-of-the-art in CME simulations, including a brief overview of current models for the background solar wind as it has been shown that the background solar wind affects the onset and initial evolution of CMEs quite substantially. We mainly focus on the attempt to retrieve the initiation and propagation of CMEs in the framework of computational magnetofluid dynamics (CMFD). Advanced numerical techniques and large computer resources are indispensable when attempting to reconstruct an event from Sun to Earth. Especially the simulations developed in dedicated event studies yield very realistic results, comparable with the observations. However, there are still a lot of free parameters in these models and ad hoc source terms are often added to the equations, mimicking the physics that is not really understood yet in detail.
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