2022/03/23 by Manabu Machida, Machida, Manabu
Engineering · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Radiative Heat Transfer Studies #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.2203.12327
arxiv created 2022/03/23 · openalex publication_date 2022/03/23 · arxiv updated 2022/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In one-dimensional transport theory, the method of analytical discrete ordinates (ADO) is known to be a concise and fast numerical scheme to solve the radiative transport equation. However, the extension of ADO to three dimensions has been restricted to the case of isotropic scattering. In this paper, we extend ADO to the case of the three-dimensional radiative transport equation with anisotropic scattering. This extension is made possible by the technique of rotated reference frames. The radiative transport equation with constant absorption and scattering coefficients in the half space is solved by the extended ADO in three dimensions. Moreover, we show that even an analytical solution in the half space is obtained by extending the singular eigenfunction approach with rotated reference frames.