Diagonalization of diffusion equations in two and three dimensions - Albert, J.M. (Journal of atmospheric and solar-terrestrial physics, 2018)
Multidimensional diffusion is central to radiation belt and ring current dynamics, but obtaining numerical solutions reliably is subject to difficulties related to “cross terms” in the diffusion equation. Eliminating them, by constructing new coordinates which diagonalize the diffusion matrix, has been found to be effective in two dimensions. Here this approach is reformulated to be both clearer and more robust, with analytical expressions replacing numerical solutions of differential equations. An approach to extending the method to three dimensions is presented and discussed. •Multidimensional diffusion occurs in the ring current and radiation belts.•Cross terms, which can cause numerical problems, can be eliminated in 2D.•This technique is generalized, and extension to 3D is discussed.