一种基于本征正交分解的并群方法  

A Group Condensation Method Based on Proper Orthogonal Decomposition

作　　者：武世伏 张乾 张晋超 赵强 WU Shifu;ZHANG Qian;ZHANG Jinchao;ZHAO Qiang(Fundamental Science on Nuclear Safety and Simulation Technology Laboratory,Harbin Engineering University,Harbin 150001,China;Laboratory for Advanced Nuclear Energy Theory and Applications,Zhejiang Institute of Modern Physics,Department of Physics,Zhejiang University,Zhejiang 310058,China)

机构地区：[1]哈尔滨工程大学,核安全与仿真技术国防重点学科实验室,黑龙江哈尔滨150001 [2]浙江大学物理学系,浙江近代物理中心,先进核能理论与应用实验室,浙江杭州310058

出　　处：《原子能科学技术》2023年第8期1575-1583,共9页Atomic Energy Science and Technology

基　　金：国家自然科学基金(12105063);核反应堆系统设计技术重点实验室运行基金(HT-KFKT-24-2021011);核数据重点实验室稳定支持基金(JCKY2021201C154);中核集团“青年英才”项目。

摘　　要：传统两步法的少群近似是导致功率分布误差的重要来源。离散广义并群理论是一种新的并群方法,可以通过离散正交基函数在少群结构中恢复精细能谱,一方面降低并群误差,另一方面可以提高中子学计算在能量上的分辨率,同时保持少群输运计算的效率优势。本文采用本征正交分解方法,对一系列UO 2和MOX燃料栅元的典型44群能谱所构成的样本空间进行正交展开,获得代表能谱特征的正交基函数。基于并群理论,对一维UO 2和MOX栅元混合组件问题进行了4群的输运计算,并重构出特定位置的44群能谱。同时,对截断阶数对不同少群结构重构精度的影响进行了分析。在4群的少群结构下,选取干涉效应最明显的组件结合处的UO 2和MOX栅元进行44群输运计算获得的能谱作为样本快照进行本征正交分解生成的正交基函数,在7阶便可以保证特征值偏差小于37 pcm,而传统并群方法的偏差为1359 pcm;恢复干涉效应的栅元能谱相对偏差小于0.5%,而传统并群方法使用的能谱与真实能谱差别在14%以上。基于本征正交分解的并群方法在改善两步法能群归并误差中有着很大的应用前景。The group condensation is a key process of the two-step method and is the guarantee of efficiency of the two-step method.However,the group condensation of the two-step method also reduces the energy resolution and leads to the calculation errors.The proper orthogonal decomposition can use the small sample snapshot of the problem to produce a set of generate orthonormal basis functions containing the characteristic information of the snapshot through the singular value decomposition.This discrete orthonormal basis can reconstruct the fine energy spectrum in the minority group structure.It can reduce the error of group condensation and improve accuracy while maintaining the efficiency advantages of minority-group transport calculation.This method can improve the disadvantage of the original discrete general multigroup method that needs the complete expanded discrete Legendre polynomials to reconstruct the fine energy spectrum,leads to higher memory costs and a larger computational burden than the equivalent multigroup formulation of a given problem.In this paper,the proper orthogonal decomposition method was used to orthogonally expand the sample space composed of the typical 44-group energy spectrum of a series of UO 2 and MOX fuel cells to obtain the orthogonal basis functions representing the characteristic information of the energy spectrum of the UO 2 and MOX fuel cells.Based on the generalized multi-group theory,the 4-group transport calculation of the one-dimensional UO 2 and MOX cells hybrid array problem was carried out,and the 44-group energy spectrum of the whole problem and the positions with the most obvious interference was reconstructed with the proper orthogonal basis functions.Besides,the influence of the truncation order on the reconstruction accuracy of different minority group structures was analyzed.Under the 4-group structure,the basis functions generated by the proper orthogonal decomposition of the energy spectrum snapshots of the UO 2 and MOX cells 44-group with the most obvious interferenc

关 键 词：能群归并 能谱重构 本征正交分解 干涉效应 

分 类 号：TL327[核科学技术—核技术及应用]