An accurate SUPG-stabilized continuous Galerkin discretization for anisotropic heat flux in magnetic confinement fusion
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909430846586880 |
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| author | Wimmer, Golo A. Southworth, Ben S. Sagiyama, Koki Tang, Xian-Zhu |
| author_facet | Wimmer, Golo A. Southworth, Ben S. Sagiyama, Koki Tang, Xian-Zhu |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_12396 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An accurate SUPG-stabilized continuous Galerkin discretization for anisotropic heat flux in magnetic confinement fusion Wimmer, Golo A. Southworth, Ben S. Sagiyama, Koki Tang, Xian-Zhu Numerical Analysis 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. |
| title | An accurate SUPG-stabilized continuous Galerkin discretization for anisotropic heat flux in magnetic confinement fusion |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2412.12396 |