Abstract

A Resonance calculation using energy Spectrum Expansion (RSE) method is newly proposed in this paper. In this method, ultra-fine-group (UFG) spectra appearing in a resonance calculation are expanded by orthogonal bases on energy, which are extracted from the UFG spectra obtained in homogeneous geometry with various background cross sections using singular value decomposition and low-rank approximation. Namely, this method is based on the concept of a reduced order model. A neutron transport equation for flux moments (expansion coefficients) similar to the conventional one is derived and is numerically solved. This method applies to two benchmark problems in which a resonance interference effect and spatial self-shielding effect can appear. The results indicate that this method accurately predicts the reference effective cross sections and reaction rates obtained from direct UFG calculation in heterogeneous geometry.

摘要

本文新提出了一种使用能谱扩展（RSE）方法的共振计算。在该方法中，共振计算中出现的超细群 (UFG) 光谱通过基于能量的正交基础进行扩展，这些能量是从使用奇异值分解和低秩的具有各种背景横截面的均匀几何中获得的 UFG 光谱中提取的近似。即，该方法基于降阶模型的概念。导出了与常规方程类似的通量矩（膨胀系数）的中子输运方程，并对其进行了数值求解。该方法适用于可能出现共振干扰效应和空间自屏蔽效应的两个基准问题。