Reduced-order modeling of neutron transport separated in energy by Proper Generalized Decomposition with applications to nuclear reactor physics

Abstract

In this article, we formulate and implement an a priori Reduced-Order Model (ROM) of neutron transport separated in energy by Proper Generalized Decomposition (PGD). Numerical experiments characterize efficacy compared to the full-order model in approximating the neutron flux, multigroup cross sections, and coarse-group flux. Problems consider representative light water reactor pins of UO2 or Mixed Oxide fuel with CASMO-70, XMAS-172, and SHEM-361 energy meshes. We demonstrate the ROM can estimate the angular flux within roughly 0.36% L2 error—or 0.05% with update of the energy basis—given 50 modes, or enrichment iterations, even for the finest mesh, SHEM-361. The corresponding scalar flux errors round to 0.2% and 0.01%. Further, collapsing from SHEM-361 to (an aligned analogue of) CASMO-70, we find few (1–3) modes yield multigroup cross sections comparable to those of an infinite medium approximation, while 30 produces values practically indistinguishable from those of the full-order model, as assessed by the error of the coarse-group solution. This holds true with both Consistent-P and Inconsistent-P transport corrections. Comparing the coarse-group solutions, we observe the L2 error of the ROM with 10 modes (0.5%) is comparable to that introduced by cross section condensation. Given additional (20, 30) modes, the ROM is able to converge below this threshold (to 0.11–0.16%, 0.06–0.09%, respectively). Ultimately, we expect this PGD ROM may achieve considerable savings in computing multigroup cross sections. Moreover, the ROM provides an alternative means of approximation to cross section condensation, preferable in that it introduces neither a loss of resolution nor irrecoverable error.