Asymptotic analysis of radiative transfer problems

Details Asymptotic analysis of radiative transfer problems Asymptotic analysis of radiative transfer problems

Apr 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983jqsrt..29..285l&link_type=abstract

Journal of Quantitative Spectroscopy and Radiative Transfer (ISSN 0022-4073), vol. 29, April 1983, p. 285-310. Research sponsore

Computer Science

24

Asymptotic Methods, Diffusion Theory, Radiative Transfer, Boundary Conditions, Boundary Layer Equations, Equilibrium, Integral Equations, Variational Principles

Scientific paper

The equations of radiative transfer are systematically analyzed by asymptotic methods. To lowest order, the classical equilibrium diffusion approximation is recovered. The next order analysis leads to the equilibrium diffusion differential equations and initial condition, but with a boundary condition containing a linear extrapolation distance alpha. This quantity is related to the solution of a canonical halfspace problem and is computed by deriving an appropriate variational principle. For the case of no scattering, an exact Wiener-Hopf solution is available. The F(N) solution technique is also applied to the problem of obtaining alpha with good results. Higher order asymptotic radiative transfer descriptions are discussed and, while not immediately constituting practical calculational techniques, do have implications for computing the parameters in the multiband treatment of the frequency variable.

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