![Sample our Engineering & Technology journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5933/TOC-Subject-Sample-2021-Engineering-Tech.jpg"})
Abstract
The long-standing problem of implementing the method effectively for spherical geometry is revisited in this work. It is shown that a least-squares approach to the method resolves to a great extent the numerical instability reported for the first time by Aronson in 1984. In the proposed version of the method, a small loss of accuracy is still observed for intermediate orders of the approximation, but in high order (typically
), full accuracy is recovered, and the method can be used with confidence even for extremely high orders of the approximation. Numerical results of benchmark quality are tabulated for the quantities of interest for two basic transport problems in spherical geometry: the albedo problem for a sphere and the critical-sphere problem, both including cases that show the effects of scattering anisotropy described by the binomial law.
Acknowledgment
The work of RDMG was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) of Brazil under grant 306231/2014-0.