The importance of the Hall term in plasma physics has been well known since the early work of James Lighthill in the 1960s. On the other hand, since the early 2000s, there has been a stream of analytical, computational, and experimental evidence establishing that Resistive and Hall terms incorporate the “minimal amount of physics” required to reproduce magnetic reconnection rates observed in practice.

In this talk, I present a structure-preserving method for the compressible Resistive Hall magnetohydrodynamics model. The differential operator is split into two parts: a hydrodynamic part consisting of the compressible Euler equations and a magnetic part consisting of a system that couples the Lorentz force to the induction equation. The method uses continuous Lagrange elements for the Euler part and a curl-conforming finite element space for the magnetic part. The hydrodynamic part preserves the positivity of the density and internal energy, the conservation of total energy, and the minimum principle for the specific entropy. Owing to the choice of finite elements, the magnetic part preserves the divergence involution constraint. The magnetic part of the system is solved by the Crank-Nicolson method, which requires using Newton's method. Coercivity estimates for the Jacobian of the corresponding Newton iteration are presented. We introduce a high-order artificial resistivity to improve the conditioning of the nonlinear residual and the invertibility of the corresponding Jacobian. Several challenging benchmarks, including a smooth whistler wave, the Orszag–Tang vortex for comparing resistive MHD with resistive Hall-MHD, and a magnetic reconnection problem, are solved to validate the method's robustness and accuracy.

This presentation is archived in the Mediasite catalog and available at the following url ...

mediacast.ttu.edu/Mediasite/Play/da582ce4ae0a4c9988d3f7e1ff937ecf1d