A New and Simple Technique to Normalize the HG Phase Function for Conserving Scattered Energy and Asymmetry Factor

Abstract

A new, yet simple, technique is formulated for normalizing the Henyey-Greenstein (HG) phase function by ensuring conservation of both scattered energy and asymmetry factor simultaneously, and is analyzed for use in determining accurate radiative transfer predictions in strongly anisotropic scattering media using the discrete ordinates method (DOM). Two recently published simple normalization techniques are able to conserve either scattered energy or asymmetry factor after discretization solely by normalization of the forward-scattering HG phase-function value. However, normalization of only the forward-scattering term cannot conserve two quantities simultaneously. The present technique normalizes both the forward-scattering and backward-scattering terms in order to conserve both scattered energy and asymmetry factor simultaneously and maintain most of the phase-function shape while retaining simplicity and efficiency. Analysis of radiative transfer predictions shows that results generated using the present technique conform accurately to finite-volume method (FVM) and Monte Carlo (MC) predictions, as well as to those generated using the authors' previously developed matrix normalization technique, validating its accuracy.

Notes

^a Convergence time estimated using number of iterations and time per iteration.