Yuanzineng kexue jishu (Aug 2023)
A Group Condensation Method Based on Proper Orthogonal Decomposition
Abstract
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 UO2 and MOX fuel cells to obtain the orthogonal basis functions representing the characteristic information of the energy spectrum of the UO2 and MOX fuel cells. Based on the generalized multi-group theory, the 4-group transport calculation of the one-dimensional UO2 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 UO2 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 1 359 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.
