Three-dimensional Resistive Magnetohydrodynamics in Hydra

The Magnetohydrodynamics package in the ALE radiation-hydrodynamics code Hydra implements the three-dimensional resistive magnetic diffusion equations in the small Hall limit. The diffusion equations are discretized, on semi-structured grids, using a vector finite element method with H(curl), H(div) and H(grad) conforming spaces, resulting in a method that is second order accurate in space and fully implicit in time. Coupling of the MHD forces and Joule heating to the hydrodynamics package is accomplished through a split scheme. The package includes a second-order accurate advection method utilizing an exact DeRham complex to preserve the divergence free magnetic induction. Several improvements to the package have been applied, including matrix monotonicity constraints, a scalable iterative solution method and an arbitrary linear circuit source. This work is proceeding to create an MHD package that incorporates the full Ohm's law.