Asymptotically-preserving semi-implicit finite volume scheme for Extended Magnetohydrodynamics (MHD) equations

Accurate and efficient modeling of plasmas across density regimes remains a challenge in understanding systems like Z-pinch experiments. While resistive MHD (RMHD) applies for high-density plasmas, it omits critical physics that become increasingly important as plasma density decreases. These missing terms naturally limit current growth in low-density regions, whereas RMHD simulations must compensate through artificial modifications that may jeopardize accuracy.

Extended MHD (XMHD) addresses these limitations by incorporating Hall, electron inertia, and pressure terms via a generalized Ohm's law. XMHD naturally captures the density-dependent physics without artificial parameters, however existing XMHD implementations often sacrifice computational efficiency and fail to recover ideal MHD behavior in appropriate limits. A new XMHD algorithm is thus proposed and implemented on Artemis, a multifluid radiation hydrodynamics code built on top of Parthenon for HPC and AMR support. This new algorithm retains most of ideal MHD framework to ensure it is asymptotically preserved in ideal MHD limits. This is verified against published test problems for both ideal and extended MHD.