Analytical methods for computational modeling of fixed-source slab-geometry discrete ordinates transport problems: Response matrix and hybrid SN

Presented here are two analytical methods for computational modeling of fixed-source slab-geometry discrete ordinates (S-N) transport problems for shielding and nuclear reactor fuel-moderator lattice calculations. For shielding calculations a response matrix method is described, which generates numerical solutions completely free from spatial truncation errors. Therefore, the offered response matrix method with the one-region block inversion (RBI) iterative scheme converges numerical results for the region-edge angular fluxes, that coincide with the numerical values generated from the S-N analytical solution, apart from computational finite arithmetic considerations. As with lattice cell calculations in nuclear reactor physics, we describe an analytical direct method for hybrid S-N calculations. The basic idea is to use higher order angular quadrature set in the highly absorbing fuel region (S-N,) and lower order angular quadrature set in the diffusive moderator region (S-NM), i.e., N-F > N-M. Special continuity conditions for the fuel exiting fluxes that constitute the incoming fluxes for the moderation region, and conversely, for the moderator exiting fluxes that constitute the incoming fluxes for the fuel region are applied in the present hybrid numerical scheme. These special continuity conditions are based on the equivalence of the multigroup S-N and P-N (- 1) equations in slab geometry. A spatial reconstruction scheme is added to yield detailed profile of the solution within each homogenized region of the slab, starting from the coarse-mesh results. Test problems are given to illustrate the methods' accuracy. (C) 2013 Elsevier Ltd. All rights reserved.