This work describes efforts in the development of a gas-kinetic method (GKM) enhanced with resistive and Hall magnetohydrodynamics (MHD) effects. This method, known as MGKM (for MHD-GKM), has previously been validated as a hybrid-type method using finite-difference schemes to incorporate the electromagnetic effects onto an underlying hydrodynamic gas-kinetic scheme. The current state-of-the-art has been improved with a finite-volume scheme for calculation of ideal and Hall MHD physics. In addition, a second-order temporal integration scheme as well as a method of controlling the divergence of the magnetic field have been implemented. A short discussion of the importance of each addition is presented, along with validating numerical results.
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