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

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.