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.
