Hybridized Discontinuous Galerkin method for extremely anisotropic diffusion problems

In hot plasma, the ratio of the thermal conductivities parallel and perpendicular to the magnetic field can exceed 10 orders of magnitude. Numerical errors associated with the discretization of the parallel heat flux can cause it to pollute the perpendicular heat flux, leading to the underestimation of the confinement properties of a 3D configuration. A widespread approach to this problem has been to choose a coordinate system such that one of the coordinates is aligned with the flux surfaces. This method is becomes impractical in the presence of even a single island chain. Here, we show that the hybridized discontinuous Galerkin method provides a parallel and adaptive framework for solving extremely anisotropic problems. In particular, we demonstrate that it can model correctly, on a rectangular grid, the temperature flattening in neighboring magnetic islands before the onset of chaos.