Semi-analytic benchmark for multi-group free-gas Legendre moments and the application of Gauss quadrature in generating thermal scattering Legendre moments

摘要

As high-fidelity simulations become routine and computational modelers begin to ask questions about uncertainty in calculations, the understanding of uncertainties in nuclear data, including multigroup cross-sections to high scattering orders, is also becoming important. In this paper we look at how a widely-used data processing code, NJOY, processes thermal cross-section data. Using an alternative integration scheme, Gauss quadrature, for angular integration to generate thermal scattering cross sections from the thermal scattering laws for graphite and ZrHx, we observed discrepancies between these results and NJOY's results using equal-probable cosines on high order Legendre moments. In order to find a reliable comparison between the methods in NJOY and alternatives, we derived novel analytical expressions for high order Legendre moments of the free gas scattering model. Such expressions are analytically tractable but complicated. Using these expressions we construct a semi-analytic benchmark for multigroup Legendre moments. By comparing the results among the benchmark, Gauss quadrature and NJOY, we found that Gauss quadrature can preserve comparable accuracy as NJOY for lower order Legendre moments for free gas scattering and outperforms NJOY in generating high order moments. Our findings indicate that for high-scattering moments, multigroup data could be an source of uncertainty in thermal reactor calculations. (C) 2015 Elsevier Ltd. All rights reserved.