On Numerical Solution of Strongly Anisotropic Diffusion Equation on Misaligned Grids

Problems with extremely high-transport anisotropy often arise in strongly magnetized plasmas. The numerical solution of the highly anisotropic transport equations becomes quite difficult when the computational grid is not aligned with the strong transport direction, since this can cause large numerical errors. Constructing a finite-difference scheme for a strongly anisotropic diffusion equation on a misaligned grid is discussed, and quantitative assessment of the numerical error is made for a set of example problems.