Abstract
Hydrodynamical (HD) simulations played an important role in understanding the dynamics and shaping of Planetary Nebulae (PNe) in the past century. However, HD solutions are just a first order approach. The new millennium arrives with the generalized understanding that the effects of magnetic fields (i.e., MHD) are necessary to study the dynamics of PNe. Thus, B-fields introduce a whole new number of physical possibilities for the modeling. We here review recent advances in MHD modeling of PNe.
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