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

Wimmer, Golo Albert; Southworth, Ben Scott; Sagiyama, Koki; Tang, Xian-Zhu

doi:10.5802/smai-jcm.131

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

Journal Article · Mon Aug 25 00:00:00 EDT 2025 · The SMAI Journal of computational mathematics

DOI:https://doi.org/10.5802/smai-jcm.131· OSTI ID:2589851

^[1]; ^[1]; Sagiyama, Koki ^[2]; ^[1]

Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Imperial College, London (United Kingdom)

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.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: Engineering and Physical Sciences Research Council; USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities (SUF); USDOE Office of Science (SC), Fusion Energy Sciences (FES)

Grant/Contract Number:: 89233218CNA000001; AC02-05CH11231

OSTI ID:: 2589851

Report Number(s):: LA-UR--24-33208; 10.5802/smai-jcm.131; 2426-8399

Journal Information:: The SMAI Journal of computational mathematics, Journal Name: The SMAI Journal of computational mathematics Vol. 11; ISSN 2426-8399

Publisher:: Cellule MathDoc/Centre MersenneCopyright Statement

Country of Publication:: United States

Language:: English

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Anisotropic heat conduction
SUPG
anisotropic diffusion
auxiliary operator
continuous Galerkin

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