ABSTRACT
A novel numerical algorithm for the solution of nonlinear diffusion equation on the surface of a sphere and in a spherical shell is presented. The algorithm essentially employs splitting of the problem’s operator along coordinate directions; besides, the 2D lat-long problem is solved by using two different coordinate maps on the sphere. This leads to 1D finite difference problems with simple periodic boundary conditions in the latitudinal and longitudinal directions, respectively, which results in linear algebraic problems with band matrices and thus permits applying fast linear solvers, such as Sherman-Morrison formula and Thomas algorithm. The developed method is tested on several numerical experiments, including simulation of the phenomena of blow-up and temperature waves.
