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An Accurate SUPG-stabilized Continuous Galerkin Discretization for Anisotropic Heat Flux in Magnetic Confinement Fusion
Golo A. Wimmer1; Ben S. Southworth1; Koki Sagiyama2; Xian-Zhu Tang1
1 Los Alamos National Laboratory
2 Imperial College London
The SMAI Journal of computational mathematics, Volume 11 (2025), pp. 473-496.

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.

Published online:
DOI: 10.5802/smai-jcm.131
Classification: 65M60, 80M10
Keywords: Anisotropic heat conduction, anisotropic diffusion, auxiliary operator, continuous Galerkin, SUPG

Golo A. Wimmer 1; Ben S. Southworth 1; Koki Sagiyama 2; Xian-Zhu Tang 1

1 Los Alamos National Laboratory
2 Imperial College London 
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     journal = {The SMAI Journal of computational mathematics},
     pages = {473--496},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
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Golo A. Wimmer; Ben S. Southworth; Koki Sagiyama; Xian-Zhu Tang. An Accurate SUPG-stabilized Continuous Galerkin Discretization for Anisotropic Heat Flux in Magnetic Confinement Fusion. The SMAI Journal of computational mathematics, Volume 11 (2025), pp. 473-496. doi : 10.5802/smai-jcm.131. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.131/

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