Accurate spherical harmonics solutions for neutron transport problems in multi-region spherical geometry

Abstract

A stable spherical harmonics (PN) method for solving the problem of a multi-region sphere with internal sources subject to an externally incident angular flux is developed. The method consists in solving the problem locally (region by region) and using an iterative sweep technique to connect and update the solutions for the different regions until global convergence is attained. A post-processing step which is very effective in improving the PN solutions is also developed. Since calculating the current from its definition in terms of the angular flux is prone to loss of precision in spherical geometry, an alternative scheme for computing accurate post-processed currents is devised.Because the developed method does not rely on space and angle discretizations, it can achieve very accurate results even for problems with solutions that display strong flux gradients. This kind of problem is challenging for methods built on discretization schemes. An example of such a problem is solved and the results obtained demonstrate the good performance of the method. Accurate numerical results are also given for two variants of the example problem that involve changes in the driving term and in the scattering law.