Angular quadratures for improved transport computations Page: 3 of 72
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Angular Quadratures for Improved Transport Computations
I. K. Abu-Shumays
This paper introduces new octant-range, composite-type Gauss and mid-point rule 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 octant-range 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 composite-type Gauss and mid-point rule angular quadratures are designed for
shielding problems dominated by particle streaming gaps, as well as certain shielding problems
dominated by voids, such as dry cell storage problems.
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 result, improved accuracy is achieved with fewer angular directions,
which leads to significant savings in computing cost. The octant-range quadratures presented
include new quadruple-range quadratures for cylindrical geometries.
A generalization to octant-range quadratures 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.
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Abu-Shumays, I.K. Angular quadratures for improved transport computations, article, July 22, 1999; West Mifflin, Pennsylvania. (digital.library.unt.edu/ark:/67531/metadc709988/m1/3/: accessed August 16, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.