Improved Treatment of Anisotropic Scattering in Radiation Transfer Analysis Using the Finite Volume Method

Abstract

Discretization of the integral anisotropic-scattering term in the equation of radiative transfer will result in two kinds of numerical errors -alterations in scattered energy and asymmetry factor. Though quadrature flexibility with large angular directions and further solid-angle splitting in the finite volume method (FVM) allow for reductionminimization of these errors, computational efficiency is adversely impacted. A phase-function normalization technique to get rid of these errors is simpler and is applied to the 3-D FVM for the first time to improve anisotropic radiation transfer computation accuracy and efficiency. FVM results are compared to Monte Carlo and discrete-ordinates method predictions of radiative heat transfer in a cubic enclosure housing a highly-anisotropic participating medium. It is found that the FVM results generated using the normalization technique conform accurately to the results of the other two methods with little impact on computational efficiency.

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

“…(11) and (12), and directional symmetry e U l 0 l ¼ e U ll 0 simultaneously. DOM radiation transfer results generated using this normalization technique have been shown to eliminate angular false scattering errors, resulting in accurate conformity to both FVM and Monte Carlo (MC) predictions [40,44].…”

“…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.…”

“…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].…”

“…All calculations are based on a spatial grid of Dx ⁄ = Dy ⁄ = Dz ⁄ = 0.077 and M = 72 discrete directions. For all optical thicknesses, angular false scattering errors are negligible for g 6 0.50, due to the fact that alterations in both discretized g and total scattering effect (1 À g) r s are minimal for weakly forward-scattering media [44].…”

FVM for Solving Three Phase Percolation Model of Unsaturated-saturated Zone

“…A new generation of numerical algorithm belongs to the Finite Volume Method (FVM) [Hunter, B. et al 2016, Shewchuk, J.R. 2002, & Hejazi, H. et al 2014 . Its processes are that divide the solving area into a series of discrete non-overlapping control volume, and make sure each node has a control volume around; integral the differential equation to be solved at each little control volume to derive a set of discrete equations.…”