Extending the Spectral Difference Method with Divergence Cleaning (SDDC) to the Hall MHD Equations

The Hall Magnetohydrodynamic (MHD) equations are an extension of the standard MHD that include “Hall” term from general Ohm’s law. decouples ion and electron motion physically on inertial length scales. Implementing in a numerical solver allows more physical simulations for plasma dynamics scales less than scale but greater length. present effort is important step towards producing correct results to problems, such as Geospace Environmental Modeling (GEM) Magnetic Reconnection problem. being modified currently capable solving resistive unstructured grids using spectral difference scheme which arbitrarily high-order method relatively simple parallelize. GEM problem used evaluate whether have been correctly implemented with divergence cleaning (SDDC) algorithm by comparing against reconnection rates reported literature.