On Conservation of Scattered Energy and Angle in Radiative Transfer Computations

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. INTRODUCTION In engineering problems where radiation is the dominant mode of heat transfer, such as high-temperature combustion and material processing [1-11], fire [12-15] and atmospheric radiation [16-19], renewable solar energy [20-22], space exploration [23-25], microwave and laser applications [26-38], accurate and complete solutions of the governing equation of radiative transfer (ERT) are desired. The integro-differential nature of the ERT makes analytical solution difficult [4, 5], and thus numerical methods, such as the finite volume method (FVM) [39-45] and discrete-ordinates method (DOM) [45-49], are preferred. Numerical methods have garnered increasing attention in the field of radiation heat transfer, as they provide cost-effective alternatives to costly experimentation and their efficiency and accuracy has been improved with the advance of computational technology.