Reduced Computational Cost, Totally Symmetric Angular Quadrature Sets forDiscrete Ordinates Radiation Transport

摘要

Several new quadrature sets for use in the discrete ordinates method of solvingthe Boltzmann neutral particle transport equation are derived. These symmetric quadratures extend the traditional symmetric quadratures by allowing ordinates perpendicular to one or two of the coordinate axes. Comparable accuracy with fewer required ordinates is obtained. Quadratures up to seventh order are presented. The validity and efficiency of the quadratures is then tested and compared with the Sn level symmetric quadratures relative to a Monte Carlo benchmark solution. The criteria for comparison include current through the surface, scalar flux at the surface, volume average scalar flux, and time required for convergence. Appreciable computational cost was saved when used in an unstructured tetrahedral cell code using highly accurate characteristic methods. However, no appreciable savings in computation time was found using the new quadratures compared with traditional Sn methods on a regular Cartesian mesh using the standard diamond difference method. These quadratures are recommended for use in three-dimensional calculations on an unstructured mesh.