A Fast and Stable Solution Method for the Radiative Transfer Problem

Abstract

Radiative transfer theory considers radiation in turbid media and is used in a wide range of applications. This paper outlines a problem formulation and a solution method for the radiative transfer problem in multilayer scattering and absorbing media using discrete ordinate model geometry. A selection of different steps is brought together. The main contribution here is the synthesis of these steps, all of which have been used in different areas, but never all together in one method. First, all necessary steps to get a numerically stable solution procedure are treated, and then methods are introduced to increase the speed by a factor of several thousand. This includes methods for handling strongly forward-scattering media. The method is shown to be unconditionally stable, though the problem was previously considered numerically intractable.