One speed black sphere problem: Some benchmark results

Abstract

Benchmark numerical results for the black sphere problem (one speed, isotropic scattering) are reported by extending some previous computations on the relevant integral transport equation [Loyalka, S.K., 1975. A numerical method for solving integral equations of neutron transport. Nuclear Science and Engineering 56, 317–319]. Spheres of radii (non-dimensionalized in terms of a mean free path) in the range 10−6–106 are considered, and a transformation of the range from (R,∞) to (0,1), is used together with successively high order quadratures, and high precision in all computations. Two different quadrature sets (Gauss–Legendre and Gauss–Kronrod) are explored and convergent and accurate numerical results for the extrapolation distance as well as the density profile are obtained.