| It is well known that the discrete-ordinates method (DOM) suffers from two shortcomings: 1) numerical smearing (or false scattering) error due to spatial discretization, and 2) ray effect error due to limited number of discrete angular directions. It is less aware that all numerical methods based on the discretization solution of the integral-differential equation of radiation transfer (ERT), such as the finite volume method (FVM), experience similar issues. In this dissertation, the existence of a third type of numerical error, termed "angular false scattering" for anisotropic scattering media, is revealed and presented for both DOM and FVM. In all practical applications, radiation scattering is anisotropic in nature. Angular discretization of anisotropy may not preserve the scattering phase-function asymmetry factor, resulting in an artificial alteration of medium scattering properties - angular false scattering.;Phase-function normalization was the prevailing approach in DOM to numerically conserve scattered energy. In this dissertation, this technique is employed, for the first time, to simultaneously conserve both scattered energy and asymmetry factor for both DOM and FVM. Traditionally, the solid-angle splitting approach was implemented to conserve scattered energy for FVM. It is found, however, that extremely high splitting levels are required to preserve asymmetry factor for strongly scattering media, substantially increasing computational cost. Here, two novel phase-function normalization techniques are developed for FVM and DOM radiation transfer analysis to specifically mitigate angular false scattering errors by simultaneously conserving scattered energy and asymmetry factor. Normalization approaches are formulated for both diffuse and ballistic radiation transfer. Radiation transfer predictions generated using both the DOM and FVM with the normalization approaches are compared with statistical Monte Carlo predictions to gauge their accuracy and efficiency. Proper phase-function normalization is shown to greatly improve radiation transfer accuracy, while concurrently improving computational efficiency by allowing for substantial reduction in both discrete direction number and solid-angle splitting density. Application of phase-function normalization for ballistic radiation transfer is found to be crucial. Additionally, phase-function normalization allows for accurate conformity between DOM and FVM solutions of the ERT. |
