Phase-Function Normalization in the 3-D Discrete-Ordinates Solution of Radiative Transfer—PART II: Benchmark Comparisons

Abstract

Radiative transfer in a cubic enclosure, subject to varying conditions, is determined using the discrete-ordinates method (DOM) with the two normalization techniques introduced in Part I of this study. Their predictions are compared with Monte Carlo simulations. For all cases, false scattering due to directional discretization cannot be corrected when the old technique, which solely conserves scattered energy, is implemented; and thus, significant discrepancies exist when compared to Monte Carlo results. The new technique, which conserves both scattered energy and the asymmetry factor, is able to retain original scattering properties after directional discretization, leading to improved accuracy when compared to Monte Carlo. In addition, a parametric study is presented to gauge the impact of asymmetry-factor conservation on media with various optical properties. Finally, the impact of normalization is investigated for both ultrafast radiative transfer and ballistic incidence with varying incident angle.

Numerical smearing, ray effect, and angular false scattering in radiation transfer computation

“…This condition becomes greatly violated as scattering becomes increasingly anisotropic [43], leading to extreme discrepancies in radiation transfer prediction and, in some cases, ERT solution divergence.…”

“…In order to ensure mitigation of angular false scattering in approximate methods, such as the DOM and FVM, it is critical that scattered energy and asymmetry factor are simultaneously conserved after directional discretization. A new phase-function normalization approach developed by the current authors [40] is able to achieve such concurrent conservation, leading to accurate conformity of both DOM [42,43] and FVM [44] ERT solutions with benchmark Monte Carlo predictions.…”

“…Errors of this type are a third type of numerical error, termed recently as ''angular false scattering'' [43]. Numerical smearing has also been referred to as ''false scattering'' in the literature, as errors of this type appear to emulate unrealistic and nonphysical scattering behavior due to spatial discretization.…”

“…A lack of conservation of asymmetry factor after angular discretization can dramatically change the scattering properties of the medium, which can lead to substantial radiation transfer errors [40][41][42][43][44]. Errors of this type are a third type of numerical error, termed recently as ''angular false scattering'' [43].…”

“…Non-conservation of asymmetry factor after angular discretization results in alteration of medium scattering properties, which certainly changes ERT solution. Errors of this type are a third type of numerical error, termed as ''angular false scattering'' [42][43]. In order to ensure mitigation of angular false scattering in approximate methods, such as the DOM and FVM, it is critical that scattered energy and asymmetry factor are simultaneously conserved after directional discretization.…”