Representation of homogenized cross section data by Canonical-Polyadic decomposition

Abstract

In this paper, the tensor Canonical-Polyadic (CP) decomposition method is applied to represent few-group homogenized cross sections. The results of the method are analyzed when applied to two assemblies typical of VVER reactor (in Russian Vodo-Vodyanoi Energetichesky Reaktor meaning Water-Water Power Reactor). In particular, the presented analysis focuses on the 22UA assembly, represented by a dataset of 2-group assembly-homogenized cross sections, and on the 430GO assembly, represented by a dataset of 20-group pin-by-pin homogenized cross sections. Both assemblies’ specifications are taken from the X2VVER benchmark.

Errors in microscopic and macroscopic cross sections, are evaluated to assess the accuracy of the method to reproduce reference few-group homogenized cross sections. Furthermore, the reactivity error as well the error on fission-production and on absorption rate distributions are discussed by two fictive simple 3-D colorset simulations to evaluate the impact of the reconstructed cross sections on reactor core simulations. Additionally, the potential effectiveness of incorporating the CP decomposition into standard two-step neutronics schemes is studied and analyzed to effectively take into account the thermal-hydraulics feedback during core simulations. Preliminary results demonstrate the capability of the method to sensibly reduce the data storage as well as the memory usage and the computational time during cross-sections’ update.