Symposium on Advanced Sensors and Modeling Techniques for Nuclear Reactor Safety

Enhancements to the Discrete Generalized Multigroup Method

This work seeks to improve the practicality of the discrete generalized multigroup (DGM) method. The DGM method divides a fine-group energy domain into a set of coarse groups. Fine-group fluxes within each coarse group are expanded in an orthogonal basis, and cross section moments are defined to preserve the reaction rates of the fine-group solution. Previous implementations of DGM suffered from large memory requirements, so this work work explores options to reduce the memory footprint by (a) homogenizing cross-section moments over coarse regions and (b) representing discrete-angle dependence through truncated Legendre expansions. Tests were performed using a 1-D, discrete ordinates implementation to analyze a 10-pin assembly consisting of UO$_2$ and MOX. For full, fine-group calculations, conventional spatial homogenization leads to pin-power errors of up to about 1\% for this particular problem. Truncation of the angular dependence using zeroth-order flux moments leads to errors of approximately 2\% in pin powers. An increase to first-order expansions reduces the errors by about one order of magnitude. With spatial homogenization and a linear angular approximation, DGM with a truncated basis yields an eigenvalue error below 1\% and pin-power errors of up to approximately 1.5\%, about three times larger than the corresponding case without a truncated expansion. Use of these techniques represents a step toward a practical implementation of DGM, which provides a framework for generation and use of broad-group cross sections that can incorporate higher-order information for on-the-fly spectral corrections.