A fast and accurate synthetic iteration-based algorithm for numerical simulation of radiative transfer in a turbid medium

Abstract

It has been shown that the regular part of the solution (RPS) which remains after separating the anisotropic part of the solution (APS) in the small-angle modification of the spherical harmonics method (SHM) is a smooth quasi-isotropic function with individual peaks in the angular distribution. The smooth part of the RPS without peaks can be determined in the two-streaming or diffuse approximation. The first iteration of the angular distribution of the radiance significantly refines the solution and allows one to restore the abovementioned angular peaks. The quasi-diffusion approximation—separation of the APS on the basis of the SHM, the determination of the RPS in the diffusion approximation, and the refinement of the solution on the basis of the first iteration—does not depend on the symmetry of the problem and, therefore, can be generalized to the case of an arbitrary geometry of the medium.