Three-Dimensional Variational Nodal Transport Methods for Cartesian, Triangular, and Hexagonal Criticality Calculations

The variational nodal transport method is generalized for the effective treatment of multigroup criticality problems in two and three dimensions. A symbolic manipulation procedure is developed to achieve the fully automated generation of nodal response matrices in three-dimensional and non-Cartesian geometries. A red-black partitioned matrix algorithm for accelerating the solutions of the resulting within-group equations is presented, and its efficacy demonstrated. The methods are implemented as an option of the Argonne National Laboratory code DIF3D and applied to a series of five benchmark problems in x-y-z and hexagonal-z geometries. For reactors with large transport effects, the variational P₃ calculations agree with accurate Monte Carlo eigenvalues to within a few hundredths to a few tenths of a percent while requiring Cray X-MP computing times ranging from tens to hundreds of seconds.