Phase-Function Normalization in the 3-D Discrete-Ordinates Solution of Radiative Transfer—PART I: Conservation of Scattered Energy and Asymmetry Factor

Abstract

The conditions for which conversation of scattered energy and phase-function asymmetry factor after discrete-ordinates methods (DOM) directional discretization for 3-D radiative transfer in anisotropic scattering media breaks down are examined. Directional discretization in anisotropic scattering media is found to alter the scattering asymmetry factor—a second-type of “false scattering.” Phase-function normalization which conserves scattered energy alone cannot correct this problem, and conservation of the asymmetry factor is simultaneously required. A normalization technique developed by the authors, which was successfully tested in 2-D asymmetric cylindrical-coordinate radiative transfer analysis, is intensively examined and validated with benchmark problems in 3-D Cartesian coordinates. In Part I of this study, the degree of anisotropy for which normalization is necessary to conserve these inherent quantities is presented for various phase-function approximations and discrete quadrature sets.