Geospace Environment Modeling (GEM) magnetic reconnection challenge: MHD and Hall MHD - constant and current dependent resistivity models

The work is part of several papers investigating two-dimensional magnetic reconnection in the same initial configuration with different plasma approximations. The present work compares the results of magnetic reconnection in this configuration using constant and current dependent resistivity models in the framework of traditional MHD and Hall MHD. The results can be summarized as follows. For constant resistivity the effects of diffusion or the formation of a long thin current layer limit the reconnection rate. Current dependent resistivity models result in enhanced reconnection rates in all considered cases. In these cases, reconnection is faster by a factor of 2 in the Hall MHD approximation compared to the traditional MHD. The maximum reconnection rate for the Hall MHD for all current dependent resistivities is similar to 0.2 and appears largely independent of the model specifics and the initial perturbation.