Angular Quadrature Sets for the Streaming Ray Method in x-y Geometry

Abstract

Streaming ray (SR) computations normally employ a set of specially selected ray directions. For x-y geometry, these directions are not uniformly spaced in the azimuthal angle nor do they conform to any of the standard quadrature sets in current use. For simplicity in all previous SR computations uniform angular weights were used. This Note investigates two methods, a bisection scheme and a Fourier scheme, for selecting more appropriate azimuthal angular weights. In the bisection scheme the azimuthal weight assigned to an SR direction is half the angular spread (in the x-y plane) between its two adjacent ray directions. In the Fourier method, the weights are chosen such that the number of terms in a Fourier series exactly integrable on the interval (0,2π) is maximized.Several sample calculations have been performed. While both the Fourier and bisection weights showed significant advantage over the uniform weights used previously, the Fourier scheme appears to be the best method. Lists of bisection and Fourier weights are given for quadrature sets containing 4, 8, 12, …, 60 azimuthal SR directions.