Abstract

Energy discretization of the transport equation is difficult due to numerous strong, narrow cross-section (XS) resonances. The standard traditional multigroup (MG) method can be sensitive to approximations in the weighting spectrum chosen for XS averaging, which can lead to inaccurate treatment of important phenomena such as self-shielding. We generalize the concept of a group to a discontiguous range of energies to create the Finite-Element with Discontiguous-Support (FEDS) method. FEDS uses clustering algorithms from machine learning to determine optimal definitions of discontiguous groups. By combining parts of multiple resonances into the same group, FEDS can accurately treat resonance behavior even when the number of groups is orders of magnitude smaller than the number of resonances. In this paper, we introduce the theory of the FEDS method and describe the workflow needed to use FEDS, noting that ordinary MG codes can use FEDS XSs without modification, provided these codes can handle upscattering. This allows existing MG codes to produce FEDS solutions. In the context of light water reactors, we investigate properties of FEDS XSs compared to MG XSs and compare $k$-eigenvalue and reaction rate quantities of interest to continuous-energy Monte Carlo, showing that FEDS provides higher accuracy and less cancellation of error than MG with expert-chosen group structures.

摘要

由于许多强、窄截面 (XS) 共振，传输方程的能量离散化很困难。标准的传统多群 (MG) 方法可能对为 XS 平均选择的加权谱中的近似值敏感，这可能导致对自屏蔽等重要现象的处理不准确。我们将群的概念推广到不连续的能量范围，以创建具有不连续支持的有限元 (FEDS) 方法。FEDS 使用机器学习中的聚类算法来确定不连续组的最佳定义。通过将多个共振的部分组合到同一组中，即使组数比共振数小几个数量级，FEDS 也可以准确地处理共振行为。在本文中，我们介绍了 FEDS 方法的理论并描述了使用 FEDS 所需的工作流程，注意到普通 MG 代码可以不加修改地使用 FEDS XS，只要这些代码可以处理上散射。这允许现有的 MG 代码生成 FEDS 解决方案。在轻水反应堆的背景下，我们研究了 FEDS XS 与 MG XS 相比的特性并比较$克$- 对连续能量蒙特卡罗感兴趣的特征值和反应速率量，表明与具有专家选择的组结构的 MG 相比，FEDS 提供更高的准确性和更少的误差消除。