Statistics – Computation
Scientific paper
Apr 1985
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985jqsrt..33..347w&link_type=abstract
Journal of Quantitative Spectroscopy and Radiative Transfer (ISSN 0022-4073), vol. 33, April 1985, p. 347-363. Navy-supported re
Statistics
Computation
1
Boundary Value Problems, Legendre Functions, Light Scattering, Radiative Transfer, Scattering Functions, Spherical Harmonics, Boundary Conditions, Collimation, Light Beams, Radiance, Slabs
Scientific paper
Spherical harmonics may be used to solve radiative transfer problems with extreme forward scattering, provided that the PN approximation is truncated with a quantity that depends on the angle of incidence, and harmonics of high degree are summed separately. In slab geometry this method is compatible with Marshak's boundary conditions and with an extra integration using a formal solution. Acceptable accuracy is obtainable using approximations as low as P(3)-P(7). Analytic schemes improve the convergence of high harmonics and assist in selection of PN(m) approximation that matches the angle of incidence for best accuracy. As computational aids, roots of PN(m) and useful sums and integrals that may be regarded as Legendre transforms and their inverse are tabulated.
Sidorowich John J.
Wells Willard H.
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