Erlangen 2018 – scientific programme
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P: Fachverband Plasmaphysik
P 1: Helmholtz Graduate School I - Theory
P 1.5: Talk
Monday, March 5, 2018, 12:10–12:35, A 0.112
An aligned discontinuous Galerkin method for anisotropic diffusion and variants — •Benedict Dingfelder1,3, Florian Hindenlang1, Ralf Kleiber2, Axel Könies2, and Eric Sonnendrücker1,3 — 1Max-Planck-Institut für Plasmaphysik, Garching, Germany — 2May-Planck-Institut für Plasmaphysik, Greifswald, Gearmany — 3Technische Universität München, Garching, Germany
In magnetized plasmas of fusion devices the strong magnetic field leads to highly anisotropic physics. If only diffusion processes are considered, the diffusion along the magnetic field is dominating. In the limit of vanishing perpendicular diffusion, we obtain the anisotropic diffusion equation with a semidefinite diffusion tensor whose associated eigenvalue problem reads -∇·( b b ·∇φ) = ω^2 φ in Ω⊂R^2 for the two-dimensional fully periodic domain Ω and direction of the magnetic field b. This eigenvalue problem is difficult to solve due to the non-coercivity of the differential operator. We propose a discontinuous Galerkin (DG) method on a non-conforming mesh with locally aligned cells which allows us to coarsen the resolution parallel to the magnetic field. The resulting distribution of resolution is particularly suited for calculating small eigenvalues.