Abstract
In this paper, we analyze the current state of the discrete theory of radiative transfer. One-dimensional, three-dimensional and stochastic radiative transfer models are considered. It is shown that the discrete theory provides a unique solution to the one-dimensional radiative transfer equation. All approximate solution techniques based on the discrete ordinate formalism can be derived based on the synthetic iterations, the small-angle approximation, and the matrix operator method. The possible directions for the perspective development of radiative transfer are outlined.
Highlights
Radiative transfer theory is the principal method for modeling radiation propagation in the atmosphere and the ocean in the photometric ray approximation [1,2]
The radiation field is decomposed into a coherent part, which determines the optical characteristics of the medium, and an incoherent one, which is related to the processes of multiple light scattering and satisfies the radiative transfer equation (RTE)
The Boundary Value Problem for the Radiative Transfer Equation for a Slab Let us analyze the numerical solution of the boundary value problem (BVP) in the case of the plane parallel source:
Summary
Radiative transfer theory is the principal method for modeling radiation propagation in the atmosphere and the ocean in the photometric ray approximation [1,2]. In this regard, the state of the radiative transfer theory is very similar to the state of physics by the end of the 19th century, which was analyzed by W. He reviewed the state of physics at the turn of the century but most importantly, he highlighted two clouds (problems) that “obscure the beauty and clearness of the whole theory” These clouds were (a) the independence of the speed of light on the reference frame in the wave equation resulting from Maxwell’s equations and (b) the inability to describe the dependence of blackbody radiation in the framework of classical thermodynamics. Our goal in this paper is to analyze the current state of the discrete theory of radiative transfer and find its main problems, i.e., “Thomson clouds”, which will determine its future development
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