ANGULAR QUADRATURES FOR IMPROVED TRANSPORT COMPUTATIONS

Abstract

This paper introduces new octant-range angular quadrature formulas for neutron and photon transport computations. The octant-range quadratures are the three-dimensional (3-D) natural analogue of the one-dimensional (1-D) double-Gauss quadrature most suitable for slab problems with a high degree of heterogeneity. The new quadratures are applicable to a wide range of problems, and are especially suitable for problems with material discontinuities at interfaces and corners where it is advantageous to split the unit sphere of possible directions of particle motion into eight distinct octants. The octant-range quadratures are generalizations to quadruple-range quadrature formulas for two-dimensional (2-D) rectangular x–y geometries introduced by the present author in the 1970s. A mathematical restriction on the previous quadruple-range quadratures is also relaxed in the present paper. As a consequence, improved accuracy is achieved with fewer angular directions, resulting in significant savings in computing cost.