An Accurate SUPG-stabilized Continuous Galerkin Discretization for Anisotropic Heat Flux in Magnetic Confinement Fusion

We present a novel spatial discretization for the anisotropic heat conduction equation, aimed at improved accuracy at the high levels of anisotropy seen in a magnetized plasma, for example, for magnetic confinement fusion. The new discretization is based on a mixed formulation, introducing a form of the directional derivative along the magnetic field as an auxiliary variable and discretizing both the temperature and auxiliary fields in a continuous Galerkin (CG) space. Both the temperature and auxiliary variable equations are stabilized using the streamline upwind Petrov–Galerkin (SUPG) method, ensuring a better representation of the directional derivatives and therefore an overall more accurate solution. This approach can be seen as the CG-based version of our previous work (Wimmer, Southworth, Gregory, Tang, 2024), where we considered a mixed discontinuous Galerkin (DG) spatial discretization including DG-upwind stabilization. We prove consistency of the novel discretization, and demonstrate its improved accuracy over existing CG-based methods in test cases relevant to magnetic confinement fusion. This includes a long-run tokamak equilibrium sustainment scenario, demonstrating a 35% and 32% spurious heat loss for existing primal and mixed CG-based formulations versus 4% for our novel SUPG-stabilized discretization.. Authors: Wimmer, Golo Albert [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000278711748); Southworth, Ben Scott [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000202834928); Sagiyama, Koki [Imperial College, London (United Kingdom)]; Tang, Xian-Zhu [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000240366643). DOE Contract: 89233218CNA000001; AC02-05CH11231. Subjects: 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 97 MATHEMATICS AND COMPUTING; Anisotropic heat conduction; SUPG; anisotropic diffusion; auxiliary operator; continuous Galerkin