ON FINITE-DIFFERENCE SOLUTIONS OF THE HEAT EQUATION IN SPHERICAL COORDINATES
Jules Thibault, Simon Bergeron, Hugues W. Bonin · Numerical Heat Transfer · 1987
The finite-difference solution for the temperature distribution within a sphere exposed to a nonuniform surface heat flux involves special difficulties because of the presence of mathematical singularities. For this reason, the adequacy of some finite-difference representations of the heat diffusion equation is examined. In particular, neglecting the contribution from the term causing the singularity is shown as an accurate and efficient method of treating a singularity in spherical coordinates. A method based on the superposition principle is investigated and found quite suitable for this kind of problem in spherical coordinates.