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This work proposes a numerical method to solve the Radiative Transfer Equation by sequentially coupling the First-Order Scattering (FOS) and the P 1 approximations. The FOS method represents highly-anisotropic radiative intensity distributions for zero and one scattering events; the P 1 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 FOS P 1 method remains accurate as long as one of the following holds: 1) sources are not highly anisotropic (radiative cone angle, θ c > π / 4 ), 2) τ ≤ 1 or 3) ω ≤ 0.5 . For the cases covered in this study, the FOS P 1 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. |
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