Analytical discrete ordinates for the three-dimensional radiative radiative equation in the half space

TL;DR

This paper extends the analytical discrete ordinates method to three-dimensional radiative transport equations with anisotropic scattering in the half space, using rotated reference frames to obtain analytical solutions.

Contribution

It introduces a novel extension of ADO to 3D anisotropic scattering problems using rotated reference frames, enabling analytical solutions in the half space.

Findings

Extended ADO to 3D anisotropic scattering

Achieved analytical solutions in the half space

Demonstrated effectiveness of rotated reference frames

Abstract

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.