Applicability of phase-function normalization techniques for radiation transfer computation

The applicability of recently developed four phase-function (PF) normalization techniques for modeling radiation transfer in strongly anisotropic scattering media is intensively examined using the discrete-ordinates method. The three simple techniques via normalization of only the forward- and/or backward-scattering directions have been shown to reduce normalization complexity while retaining diffuse radiation computation accuracy for Henyey-Greenstein (HG) PFs. For Legendre PFs, however, such simple techniques are found to result in unphysical negative PF values at one or a few correction directions in some cases. Additionally, negative PF values can occur with these simple techniques for ballistic radiation transfer for both HG and Legendre PF types. If negative-intensity correction is applied, however, radiative heat transfer calculation can still converge regardless of the appearance of negative PF values. The relatively complex Hunter and Guo (2012) technique, in which normalization is realized through a correction matrix covering all discrete directions, is shown to be applicable for diffuse and ballistic radiation for both PF types.