GET-based time-dependent lattice homogenization using a global-local approach

Abstract

To reduce computational effort, production-type full-core neutronic calculations are usually performed using few-group diffusion theory and a node-homogenized core model, whereby each homogenized node is assumed to have uniform neutronic properties. Homogenized-node properties are determined such that the flux and reaction rates obtained from few-group diffusion calculations using the node-homogenized model are as close as possible to their counterparts obtained using a detailed-geometry, many-group, full-core transport calculation; what constitutes the heterogeneous, reference results. Generalized Equivalence Theory (GET) is widely used to determine the node-homogenized neutronic properties, namely macroscopic cross sections and discontinuity factors. For time-independent calculations, if the reference results are available, then GET provides a way to generate node-homogenized few-group macroscopic cross sections and discontinuity factors such that the node-homogenized diffusion model produces node fluxes and reaction rates identical to the reference node-integrated fluxes and reaction rates. Since full-core reference results are not usually available, node-homogenized parameters are usually generated from single-node detailed-geometry many-group transport calculations using reflective boundary conditions. The corresponding (approximate) discontinuity factors are known as “assembly” discontinuity factors (ADFs). Methods have also been proposed to account for the true node-boundary conditions without resorting to full-core reference calculations. This work extends the equivalence between the heterogeneous model and the node-homogenized model to time-dependent problems and investigates, specifically, the effect of accounting for the time dependence of discontinuity factors compared to the case of using ADFs. A simple, one-dimensional, two-group diffusion model is used for this preliminary investigation. The heterogeneous reference solution is found using fine-mesh finite differences, whereas the node-homogenized solution is found using coarse-mesh (one mesh per node) finite differences. Results show that accounting for the time dependence of the discontinuity factors can reduce node-flux errors from ∼30% to ∼0.025%.