The Discrete Ordinates Method For Solving The Transport Equation In Cylindrical Geometry Quadrature Group Selection And Application

Exact analytic solution of neutron transport equations can be obtained on extremely few occasions, so people have to search for numerical solutions, practically. It is an important work that how to construct and select angular quadrature. Presently, most of research and work on neutron transport and quadrature are for the three dimensional problems, rather than for the two dimensional ones. Most of the known quadrature is, however, more suitable for three-dimensional problems than for two-dimensional ones. The main reason is that inherent symmetries in two-dimensional problems have not been fully considered. On the other hand, most paper concerning neutron transportion were discussed in the plane x-y, but many problems have to be discussed in cylindrical systems practically.Based on the neutron transport theory; the features of this paper are the utilization of inherent two-dimensional symmetries and the development of accurate angular quadrature. The most appropriate quadrature for polar angle is double-Gauss and for azimuthal angle is Chebyshev-Gauss in two-dimensional cylindrical geometry. Using author's own program, numerical comparisons of the various quadrature for two standard problems, the source problem and the critical problem, are summarized. The results suggest that the new quadrature proves competitive for transport problems in reducing ray effects and improving accuracy.