A collocation method for radiative transfer in a linearly anisotropically-scattering slab media with internal sources, space-dependent albedo and reflecting boundaries

1990 ◽  
Vol 173 (2) ◽  
pp. 299-308 ◽  
Author(s):  
S. J. Wilson ◽  
T. R. Nanda
Keyword(s):  
Radiative Transfer ◽  
Collocation Method ◽  
Reflecting Boundaries ◽  
Internal Sources

Discrete space theory of radiative transfer I. Fundamentals

1969 ◽  
Vol 313 (1513) ◽  
pp. 183-197 ◽  
Keyword(s):  
Radiative Transfer ◽  
Star Product ◽  
Formal Theory ◽  
Space Theory ◽  
Scattering Media ◽  
One Dimensional ◽  
Infinitesimal Generators ◽  
Arbitrary Thickness ◽  
Internal Sources ◽  
Physical Constitution

This paper sets out a formal theory of radiative transfer in one-dimensional scattering media of arbitrary physical constitution. The theory is based on an extension of the treatment of Redheffer, in which the response of a layer of arbitrary thickness to fluxes incident on its boundaries is described by a certain linear operator. Juxtaposition of two such layers gives a third layer, whose operator can be related to those of its constituents by an operation designated as the star product. It is shown that this set of operators constitutes a semigroup under the star product, and that the infinitesimal generators of the semigroup can be computed in term s of the physical properties of the medium , point by point. This makes it possible to write equivalent discrete and differential equations from both of which transmission and reflexion operators, the emission due to internal sources, and the internal fluxes at prescribed levels in the medium can be obtained.

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