Group Structure Optimization Using the PyGroup Code

Abstract

Group constants are used as coefficients in the energy domain discretized Linear Boltzmann Equation (LBE), in which the Continuous-Energy (CE) fluxes are also integrated over energy bins and transformed into group fluxes. This procedure, based on the Multi-Group (MG) theory, is widely applied in radiation transport and diffusion simulations Careful preparation of MG cross section data, or group constants, is thus a prerequisite for success in acquiring high-fidelity LBE solutions. Generation of MG cross section data itself is a complicated multi-step task, since group constants are indispensably coupled with the solution of the LBE, i.e. the flux spectrum in the problem to be solved. Theoretically, a MG cross section library is only valid for the problem that it is built upon. Nevertheless, in practice MG cross section libraries are prepared for similar type of problems, such as thermal reactors, fast reactors, etc., to facilitate the neutronic simulations. Generally, CE point-wise cross section data set, generated by both theoretical models and experimental data, is first converted to Fine-Group (FG) libraries using a pre-defined or precalculated flux spectra, then, Broad-Group (BG) libraries are collapsed from the fine-group libraries using problem-dependent flux spectra. Proper treatments of energy and spatial self-shielding and resonance cross section are required in the CE-to-MG converting process Previously, we have developed a computer code, YGROUP, for fine-to-broad group cross section collapsing. To maintain high accuracy of the resulting BG libraries, YGROUP provides users several options on collapsing strategies and weighting schemes for group binning and evaluation of BG cross section data in users' specific problems.. An approach based on Particle Swarm Optimization was applied to automatically determine the optimal group structure. We also developed a hybrid weighting scheme to further improve BG library performance for Special Nuclear Materials (SNM) detection applications. In this work, a new computer code, PyGroup, has been developed to implement the PSO approach with an improved simulation-driven fitness function design that includes both response and forward/adjoint flux errors. Together with YGROUP, and deterministic transport code TITAN/PENMSHXP, the PyGroup code package is tested on a Dual Range Coincident Counter (DRCC) model. In this paper, we demonstrated the capability of the PyGroup code for group structure optimization using the DRCC detector model. In the future, an iteration scheme can be implemented to determine the number of broad groups based on a user-defined tolerance. we will also apply PyGroup to more complicated reactor models, and investigate physics-based fitness function designs to further reduce computational cost. (authors)