Development and Evaluation of High-Fidelity Product and Evenly Spaced Angular Quadratures for Three-Dimensional Discrete Ordinates Calculations with Large Air Regions

Using two different methods, angular quadrature sets are developed with greater than about 1000 angles per octant to reduce ray effects in three-dimensional (3-D), discrete ordinates radiation transport calculations with large air or void regions. Quadrature sets from both methods are evaluated in two distinct 3-D models sensitive to quadrature details and are shown to behave reasonably well. The first method is a previously described method that is examined here in 3-D. The second method produces quadrature sets that have quadrature directions approximately evenly spaced over the entire surface of the unit sphere.