Physics
Scientific paper
Sep 1990
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990jqsrt..44..317p&link_type=abstract
Journal of Quantitative Spectroscopy and Radiative Transfer (ISSN 0022-4073), vol. 44, Sept. 1990, p. 317-338. Research supporte
Physics
9
Anisotropy, Diffusion Theory, Perturbation Theory, Radiative Transfer, Boundary Conditions, Diffusion Coefficient, Transport Theory
Scientific paper
This paper considers certain aspects of the asymptotic derivation of the diffusion (differential) approximation to the equation of transfer. It is argued that it is not necessary to assume small absorption as has been traditional in the classic asymptotic derivation of the diffusion approximation. As part of these considerations, a family of asymptotic scalings in the equation of transfer is considered, each yielding a diffusion equation but with different diffusion coefficients if the scattering phase function is anisotropic. A preferred scaling is obtained by appealing to the local infinite medium solution of the equation of transfer. In a related development, consideration of an entirely different scaling, which corresponds to a perturbation about the local infinite solution, gives a slightly different diffusion equation for an anisotropic source. Applying these considerations to the multigroup equation of transfer establishes, for linearly anisotropic scattering, the multigroup diffusion approximation as an asymptotic limit of transport theory, a result heretofore not available.
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