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

• Published in: Atmospheric and oceanic optics 2017, Vol.30 (1), p.70-78
• Main Authors: Budak, V. P., Zheltov, V. S., Lubenchenko, A. V., Freidlin, K. S., Shagalov, O. V.
• Format: Article
• Language: English
• Subjects: Alliances; Angular distribution; Approximation; Computer simulation; Diffusion; Dye dispersion; Iterative methods; Lasers; Mathematical analysis; Mathematical models; Optical Devices; Optical Models and Databases; Optics; Photonics; Physics; Physics and Astronomy; Radiance; Radiative transfer; Spherical harmonics
• ISSN: 1024-8560; 2070-0393
• DOI: 10.1134/S1024856017010031

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.