An efficient method for the anisotropic diffusion equation in magnetic fields
DOI:
https://doi.org/10.21914/anziamj.v64.17966Keywords:
Summation by parts, Computational methods, Plasma PhysicsAbstract
We solve the anisotropic diffusion equation in 2D, where the dominant direction of diffusion is defined by a vector field which does not conform to a Cartesian grid. Our method uses operator splitting to separate the diffusion perpendicular and parallel to the vector field. The slow time scale is solved using a provably stable finite difference formulation in the perpendicular to the vector field, and an integral operator for the diffusion parallel to it. Energy estimates are shown to for the continuous and semi-discrete cases. Numerical experiments are performed showing convergence of the method, and examples is given to demonstrate the capabilities of the method.
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Published
2023-10-23
Issue
Section
Proceedings Computational Techniques and Applications Conference