Understanding the transport of heat in magnetized plasmas is imperative to furthering efforts towards controlled thermonuclear fusion. This work analyzes various numerical algorithms that are useful in studying temperature equilibration due to anisotropic heat transport. The study includes two numerical approaches to the standard Braginskii closure, the more accurate using a mixed auxiliary scalar in the finite-element formulation. The physically correct kinetic closure for heat flow parallel to the magnetic field is also tested. These approaches were used to study the benchmark case for anisotropic thermal conduction presented in the original NIMROD [C.R. Sovinec et al. “Journal of Computational Physics” 195 (2004) 355–386] paper. The results demonstrate that the mixed auxiliary scalar implementation of the Braginskii closure, and the kinetic closure achieve far more accuracy with less spatial resolution than the standard implementation of the Braginskii closure.
Adair, Brett, "Numerical Methods for Anisotropic Thermal Conduction" (2018). Physics Capstone Projects. Paper 67.