A generalization to octant-range quadrature is also introduced in order to allow for discontinuities at material interfaces for two-and three-dimensional transport problems which can be modeled with 60-degree triangular or hexagonal mesh subdivisions in the x-y plane. 1. IntroductionThe discrete ordinates method, which is the basis for major production transport programs, approximates integrals of the scattering term of the particle transport equation over all (infinitely many) possible directions of particle motion, by an angular quadrature summation over a finite set of discrete angular directions. As a consequence, the number of angular directions chosen, as well as their distribution over the unit sphere, governs overall accuracy. In addition, for where Q, is the direction cosine measured with respect to the r-axis. Explicit dependence on the three direction cosines in three-dimensional geometry is still as expressed in Eq. (3) y/(Q) =y(Qx, Qy, Qz).The functional dependence on direction cosines as expressed in Eqs. (5) The octant-range quadrature for r-z and x-y-z problems can be extended to the unit sphere in a similar manner. Details will be omitted for brevity.

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