Uniform Gauss-Weight Quadratures for Discrete Ordinate Transport Calculations

Recently, a uniform equal-weight quadrature set, UE_n, and a uniform Gauss-weight quadrature set, UG_n, have been derived. These quadratures have the advantage over the standard level-symmetric LQ_n quadrature sets in that the weights are positive for all orders,and the transport solution may be systematically converged by increasing the order of the quadrature set. As the order of the quadrature is increased,the points approach a uniform continuous distribution on the unit sphere,and the quadrature is invariant with respect to spatial rotations. The numerical integrals converge for continuous functions as the order of the quadrature is increased.

The numerical characteristics of the UE_n quadrature set have been investigated previously. In this paper, numerical calculations are performed to evaluate the application of the UG_n quadrature set in typical transport analyses. A series of DORT transport calculations of the >1-MeV neutron flux have been performed for a set of pressure-vessel fluence benchmark problems. These calculations employed the UG_n (n = 8, 12, 16, 24, and 32) quadratures and indicate that the UG_n solutions have converged to within ~0.25%. The converged UG_n solutions are found to be comparable to the UE_n results and are more accurate than the level-symmetric S₁₆ predictions.