Stable and Accurate Method for Simulating the Anisotropic Diffusion in Toroidally Confined Magnetic Fields
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In magnetic toroidal confinement fusion, transport of particles or temperature happens primarily along magnetic field lines, with the ratio of diffusion parallel and perpendicular to the field lines sometimes exceeding the order of 10^8. A simple model for the transport is the anisotropic diffusion equation, however it can be difficult to solve numerically due to the ratio of diffusion coefficients, since the numerical error can quickly overwhelm the diffusion perpendicular to field lines. In this presentation we will discuss a novel approach to solving the anisotropic diffusion equation in a periodic slab using summation by parts finite difference methods. The diffusion parallel to the magnetic field lines is computed by interpolation and then added to the perpendicular diffusion solution by a parallel penalty term. The method is efficient, provably energy stable and asymptotic-preserving. We will present numerical experiments verifying the numerical accuracy and stability of the method. We further demonstrate the usefulness of the method by comparison of the solutions with existing theory in plasma physics.
