Curved Mesh and Adaptive Mesh Refinement Strategies for Strong Magnetic Anisotropy

Transport in magnetized edge plasma along the magnetic field lines is many orders of magnitude stronger than transport perpendicular to the field lines. As a result, the drift-reduced (extended) magnetohydrodynamics approach used to model the plasma results in operators that are highly anisotropic and in sharp boundary layers where the magnetic field topology changes, such as at the magnetic separatrix in a tokamak. Approximation theory results show that mesh elements must be smaller than the boundary layer width to properly resolve the solution in the layer, regardless of the order of finite element function space used. Thus, uniform mesh approaches quickly become unusable for the sharp layers in realistic anisotropy regimes. Instead, this work leverages the high-order curved mesh and adaptive mesh refinement capabilities of the MFEM finite element library to make simulating edge plasma in realistic anisotropy regimes more tractable. Curved meshes can conform the mesh edges to magnetic field lines in realistic tokamak geometry, enabling elements thin enough in the perpendicular direction to resolve the layer yet elongated enough in the parallel direction to reduce the problem size. Adaptive mesh refinement can systematically improve accuracy within and around boundary layers, especially when the location of layers is not predictable. The significant improvement in accuracy, given a fixed computational cost, provided by both curved meshes and adaptive mesh refinement is presented for simplified tokamak magnetic field geometries.