Comparing Contiguous and Discontiguous Energy Grids and Propogating Uncertainties for Radiation Transport Finite Element Methods

Abstract

The purpose of this study is to quantitatively compare the accuracy of radiation transport finite element methods which use a contiguous support to those which use a discontiguous support of the energy domain. The finite-element-with-discontiguous-support method (FEDS) is a generalized finite element framework for discretizing the energy domain of radiation transport simulations. FEDS first decomposes the energy domain into coarse groups and then further partitions the coarse groups into discontiguous energy elements within each coarse group. A minimization problem is solved in order to optimally cluster portions of the energy domain into FEDS elements.

This document presents a procedure for propagating uncertainties for FEDS, and afterwards presents four benchmark problems that test the efficacy of FEDS, compared to Multigroup, for different radiation transport problems. The results from these benchmark problems suggest that we are accurately generating FEDS cross sections, correctly propating uncertainties from the nuclear data libraries, and that FEDS converges faster than Multigroup to an energy-resolved solution. The absolute error in the verification problems were 6 x 10^-8 and 5 x 10^-8, respectively, and the absolute error in the validation problems were 2 x 10^-4, and 4 x 10^-3, respectively.