一种基于本征正交分解的并群方法

A Group Condensation Method Based on Proper Orthogonal Decomposition

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 interference calculation can ensure that the eigenvalue deviation is less than 37 pcm at the seventh order,while the deviation of traditional group condensation is 1359 pcm.The relative deviation of the reconstructed cell energy spectrum with the biggest interference effect is less than 0.5%,while the difference between the energy spectrum used by the traditional group method and the 44-group energy spectrum is more than 14%.These results prove that the multi-group method based on the proper orthogonal decomposition can effectively improve the accuracy of the energy spectrum in the minority group structure and has great development prospects.