Variational nodal perturbation theory with anisotropic scattering

摘要

The variational nodal perturbation method previously developed in two- and three-dimensional Cartesian and hexagonal geometries using the diffusion and full or simplified spherical harmonics transport approximations, is extended to treat problems with anisotropic scattering. The requisite solution to the adjoint transport equation with anisotropic scattering in formulated and incorporated into the VARIANT (VARIational Anisotropic Nodal Transport) option of the Argonne National Laboratory DIF3D production code. The method, which calculates changes in the critical eigenvalue due to perturbations arising from changes in the material cross sections, is demonstrated by applying perturbations to an anisotropic hexagonal benchmark. Exact and first order perturbation theory are used to calculate changes in the critical eigenvalue and compared to the change obtained by direct calculation in VARIANT. The time savings obtained by using perturbation theory is substantial; times for base forward and adjoint calculations are much greater than the times for perturbation calculations.