The first-Order scattering [formula omitted] method

Abstract

This work proposes a numerical method to solve the Radiative Transfer Equation by sequentially coupling the First-Order Scattering (FOS) and the P1 approximations. The FOS method represents highly-anisotropic radiative intensity distributions for zero and one scattering events; the P1 approximation considers the smoother distributions obtained in subsequent scattering events. As long as the phase function is not highly anisotropic (|g|<0.6), the numerical method proposed proved accurate (averaged local errors below 10%) practically for any source, albedo (ω), and domain optical thickness (τ). Moreover, in the highly forward scattering range (0.6<g<0.9), the FOSP1 method remains accurate as long as one of the following holds: 1) sources are not highly anisotropic (radiative cone angle, θc>π/4), 2) τ≤1 or 3) ω≤0.5. For the cases covered in this study, the FOSP1 method achieves 10 to 100-fold speed up (w.r.t. Monte Carlo simulations with a similar accuracy). The method is free of a directional mesh and statistical noise, providing an interesting combination between accuracy, computational efficiency, and ease of implementation in arbitrary domains.