Spectral spherical harmonics discrete ordinate method

A new method for modeling the radiative transfer in inhomogeneous three-dimensional media illuminated by a Gaussian beam is described. This approach, called the Spectral Spherical Harmonics Discrete Ordinate Method (SSHDOM), uses the Fourier expansion method to transform the three-dimensional radiative transfer into an one-dimensional equation in the spectral domain, and the Spherical Harmonics Discrete Ordinate Method (SHDOM) for its solution. Specifically, (i) the source function is represented in the spectral domain through a spherical harmonic expansion, (ii) the spectral one-dimensional radiative transfer equation is integrated along discrete ordinates through a spatial grid, and (iii) the solution method is based on the Picard iteration. Both SSHDOM and SHDOM algorithms are implemented in a common computer code. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

The new method described in the study uses the Spectral Spherical Harmonics Discrete Ordinate Method (SSHDOM) to model radiative transfer in inhomogeneous three-dimensional media illuminated by a Gaussian beam. It transforms the radiative transfer into an one-dimensional equation in the spectral domain using the Fourier expansion method and solves it using the Spherical Harmonics Discrete Ordinate Method (SHDOM). The solution process involves representing the source function in the spectral domain, integrating the spectral one-dimensional radiative transfer equation along discrete ordinates, and implementing a solution method based on Picard iteration.