Three-Dimensional Radiative Transfer in an Anisotropically Scattering, Semi-Infinite Medium
Generalized reflection function
Three-dimensional radiative transfer in an anisotropic scattering medium exposed to spatially varying, collimated radiation is studied. The generalized reflection function for a semi-infinite medium with a very general scattering phase function is the focus of this investigation. An integral transform is used to reduced the three-dimensional transport equation to a one-dimensional form, and a modified Ambarzumian's method is applied to formulate a nonlinear integral equation for the generalized reflection function. The integration is over both the polar and azimuthal angles; hence, the integral equation is said to be in the double-integral form. The double-integral, reflection function formulation can handle a variety of anisotropic phase functions and does not require an expansion of the phase function in a Legendre polynomial series. Complicated kernel transformations of previous single-integral studies are eliminated. Single and double scattering approximations are developed. Numerical results are presented for a Rayleigh phase function to illustrate the computational characteristics of the method and are compared to results obtained with the single-integral method. Agreement between the two approaches is excellent; however, as the transform variable increases beyond five the number of quadrature points required for the double-integral method to produce accurate solutions significantly increases. A new interpolation scheme produces accurate results when the transform variable is large. © 2002 Elsevier Science Ltd. All rights reserved.
D. W. Mueller and A. L. Crosbie, "Three-Dimensional Radiative Transfer in an Anisotropically Scattering, Semi-Infinite Medium," Journal of Quantitative Spectroscopy and Radiative Transfer, Elsevier, Jan 2002.
The definitive version is available at https://doi.org/10.1016/S0022-4073(01)00191-1
Mechanical and Aerospace Engineering
Article - Journal
© 2002 Elsevier, All rights reserved.