On conservation of scattered energy and angle in radiative transfer computations

Abstract

Paper presented to the 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Florida, 14-16 July 2014.

To compute accurately radiative transfer in anisotropicallyscattering media, conservation of both scattered energy and angle after discretization is required. Alteration of asymmetry factor (i.e., average cosine of scattering angles) due to angular discretization leads to a third type of numerical error, named as angular false scattering. The error that was known as “false scattering” is actually caused by spatial discretization and has nothing to do with scattering; and thus, it is more appropriate to be called “numerical smearing”. Five phase-function normalization techniques, designed to attempt to conserve scattered energy, angle, or both, are analyzed here using DOM and FVM for both diffuse and ballistic radiation, to determine their capability to mitigate errors and produce accurate radiative transfer. Comparisons with Monte Carlo benchmark predictions are used to gauge accuracy. The two normalization techniques that conserve both scattered energy and asymmetry factor simultaneously are found to result in substantial improvements in radiative transfer accuracy with respect to MC predictions and comparison to each other. Normalization for ballistic radiation situations is shown to be crucial. Normalization impacts FVM and DOM in similar manners, as the accuracy of both is equal. In terms of computational efficiency, it is found that the DOM is more efficient than the FVM when both have the same number of angular directions.