Effectiveness of the discrete generalized multigroup method based on truncated, POD-driven basis sets

Abstract

Presented is the evaluation of the discrete generalized multigroup (DGM) method using a truncated basis constructed from proper orthogonal decomposition (POD). The DGM method uses an orthogonal basis to collapse fine-group fluxes and cross sections to a coarse-group structure with higher order modes in each coarse-group. By solving the course-group equation, an approximation to the fine-group flux can be reconstructed from the course-group flux. This approximation is used to recollapse the cross sections, which leads to an improved approximation. Past development of the DGM method used the discrete Legendre polynomials (DLPs), which do not perform well under truncation, for approximating the spectral shape of the flux. In this work, basis sets constructed using POD were used for the DGM method for several fine-group structures. The POD basis incorporates spectral information from small, representative problems, which are designed to capture spectral information from the full problem. The most effective, practical POD basis approximated the fission density with an error of less than 0.01% relative to a reference problem using approximately 6 degrees of freedom per coarse-group for all fine-group structures. The reference chosen was a 1-D, repeating lattice of 10 pins of UO2 fuel cells adjacent to 10 pins of 7.0% MOX fuel pins. The DGM method when subject to truncation performed far better using POD basis sets than when used with the DLP basis.