Reduction of angle splitting and computational time for the finite volume method in radiative transfer analysis via phase function normalization

The commonly implemented splitting of solid angles to ensure scattered energy conservation in the finite volume method does not exactly conserve phase function asymmetry factor after directional discretization, leading to significant changes in scattering effect for radiative transfer analysis in highly anisotropic scattering media. In addition, use of a large number of split sub-angles results in drastic increases in computational CPU time and computer memory. The phase function normalization approach considered in this study is found to guarantee accurate conservation of both scattered energy and asymmetry factor simultaneously after directional discretization as well as depress solid angle splitting, vastly reducing the computational convergence time with improved accuracy. As a test, radial and axial radiative heat flux profiles in a scattering cylinder generated both with and without the phase function normalization are compared among different levels of angle discretization and splitting as well as with the discrete-ordinates method. The effects of changes in optical thickness, angular resolution, scattering albedo, and phase function approximation are examined.