CN-121997648-A - Self-adaptive source iteration acceleration method based on physical-data driving

CN121997648ACN 121997648 ACN121997648 ACN 121997648ACN-121997648-A

Abstract

The invention provides a self-adaptive source iteration acceleration method based on physical-data driving, which belongs to the field of reactor physical calculation, and comprises the steps of firstly setting an initial threshold value and a convergence standard, dispersing a steady neutron diffusion equation by adopting a coarse mesh finite difference method, and establishing an equation set; and determining whether to execute the acceleration strategy by judging the relation between the maximum relative error of the flux and the threshold value. And when the conditions are met, calculating acceleration parameters, constructing a flux error snapshot matrix, adopting incremental orthogonalization analysis to calculate residual ratio, judging whether to carry out flux prediction correction according to the residual ratio, continuously calculating an equation set twice after correction, and adaptively updating a threshold value. And (5) iterating circularly until convergence conditions are met. The invention integrates the advantages of physical constraint and data driving, adaptively adjusts parameters and strategies, greatly reduces iteration times on the premise of ensuring calculation accuracy, and remarkably improves the solving efficiency of steady-state multidimensional multi-group neutron diffusion equations.

Inventors

ZHANG BINHANG
ZHANG YIHAN
YUAN XIANBAO
ZHANG YONGHONG
GONG HANYUAN
SUN YUQING

Assignees

三峡大学

Dates

Publication Date: 20260508
Application Date: 20260116

Claims (3)

1. The self-adaptive source iterative acceleration method based on physical-data driving is characterized by comprising the following steps of: S1, setting a flux maximum relative error threshold value Noise threshold Initial value of (2), flux maximum relative error And Discretizing a steady neutron diffusion equation by adopting a coarse net finite difference method to establish a coarse net finite difference equation set; S2, calculating a coarse mesh finite difference equation set; S3, judging Whether or not to be smaller than : If it is Greater than or equal to S2 is entered; If it is Less than S4 is entered; S4, will Assignment to ; S5, saving the flux of the nth step, calculating flux errors of two adjacent steps, and constructing a snapshot matrix; S6, calculating flux error modal attenuation condition, namely residual ratio r in real time by adopting an incremental orthogonalization analysis method, and combining the residual ratio r with the flux error modal attenuation condition Comparison: If r is greater than or equal to S2 is entered; If r is smaller than S7, entering into S7; S7, snapshot matrix information is extracted, flux error items of the n+1th step and the n th step are calculated, and the flux of the n+1th step is updated by the flux of the n th step and the flux error items; S8, entering S2 to calculate a twice coarse net finite difference equation set, and updating And compare And To update : If it is Greater than or equal to Will be Assignment to ; If it is Less than Will be Assignment to ; S8, judging the calculation after the calculation of S2 is finished And Whether the convergence criterion is reached: If it is present Or (b) If the convergence criterion is not met, S2 is entered; If it is present And If the convergence criterion is met, S9 is entered; and S9, ending the iterative computation.
2. The method for iterative acceleration of adaptive sources based on physical-data driving according to claim 1, wherein in S5, the snapshot matrix comprises the steps of: S501 when Less than When the flux is stored in sequence, calculating flux errors of two adjacent steps: ;(1) ;(2) Wherein: for the column vectors formed by two adjacent flux errors of different areas and different energy groups, For the flux of the m-th group to be preserved, For the flux of the m +1 group, A set of vectors for m sets of flux errors; S502, will be M sets of column vectors of Gram-Schmidt orthogonalization: ;(3) Wherein: is the m-th column vector after orthogonalization; S503, calculating the residual ratio r after orthogonalization: ;(4) S504 when r is greater than or equal to And continuing to calculate a coarse net finite difference equation set, and repeating the steps S501 to S503 until r is smaller than When the storage flux is finished; S505, constructing a snapshot matrix: ;(5) Where a total of n groups of fluxes are saved from the beginning to the end, A snapshot matrix is constructed for all the saved two-step flux errors.
3. The method as claimed in claim 1, wherein in S7, the flux error terms of the n+1th step and the n-th step are calculated, and the n+1th step flux is updated by the n-th step flux and the flux error term, and the method comprises the following steps: S701 is to Divided into sub-matrices And The following are provided: ;(6) ;(7) s702, constructing the relation between the formula (6) and the formula (7) as follows: ;(8) Wherein: Is that And (3) with Is a relationship matrix of (a); S703 pair Performing polar decomposition: ;(9) Wherein: Is a matrix of orthogonality which is a set of orthogonal matrices, A semi-positive definite matrix; s704, constructing the relation between the formula (8) and the formula (9) as follows: ;(10) s705 left-hand multiplication of (10) Right multiplication The method comprises the following steps: ;(11) In which let K be equal to ; S706, the iteration format of the steady-state multidimensional multi-group neutron diffusion equation is as follows: ;(12) wherein L is vanishing term coefficient matrix, S is generating term coefficient matrix, Q is exogenous term vector; s707 formula (12) may be written as: ;(13) Wherein B is the product of the inverse of the matrix L and the matrix S, and B is the product of the inverse of the matrix L and the exogenous term vector Q; S708 when n tends to infinity: ;(14) S709, constructing the relation between the formula (13) and the formula (14) as follows: ;(15) Wherein: Is at present A flux convergence value below; S710 introducing flux error term : ;(16) Wherein: Is at present The difference between the flux convergence value and the stored nth step flux; s711 the relation between the construction formula (15) and the formula (16) is as follows: ;(17) S712 introduction of : ;(18) Wherein: Is that At the position of Projection below; s713, constructing the relationship between the formula (11), the formula (17) and the formula (18) as follows: ;(19) s714, obtaining a flux error term by the formula (18) and the formula (19): ;(20) s715, updating the n+1 step flux by the formula (16) and the formula (20): ;(21)。

Description

Self-adaptive source iteration acceleration method based on physical-data driving Technical Field The invention belongs to the field of reactor physical computing, and particularly relates to a self-adaptive source iteration acceleration method based on physical-data driving. Background In the process of reactor physical numerical calculation, calculation accuracy and solving efficiency are core factors for determining the reliability of numerical simulation results and engineering practicability. At present, along with the increasing complexity of the core geometry, the number of energy groups is continuously increased, so that the solving scale of the multidimensional multi-group neutron diffusion equation is rapidly increased. When the traditional source iteration solves the neutron diffusion problem of the large-scale reactor core, the convergence speed is limited by the scattering ratio of the required solution problem, the closer the scattering ratio is to 1, the slower the convergence speed is, a large number of iteration steps are required to be consumed to reach the preset convergence standard, and the overall calculation cost is obviously increased. Therefore, it is necessary to develop a self-adaptive source iterative acceleration method based on physical-data driving, and under different iteration conditions, the self-adaptive adjustment is performed through an incremental orthogonalization analysis method with physical constraint、And constructing a flux error snapshot matrix, calculating flux error items of the n+1 step and the n step, and updating the flux of the n+1 step by using the flux of the n step and the error item, so that the updated flux is fast approximate to a convergence value. Finally, on the premise of ensuring the calculation accuracy, the iteration times are greatly reduced, and the calculation efficiency is remarkably improved. Disclosure of Invention The invention aims to solve the technical problem that when the traditional source iteration is used for solving the neutron diffusion problem of a large-scale reactor core, a discrete equation set is required to be solved for many times no matter a node method or a finite difference method is adopted, so that the relative errors of flux before and after iteration are continuously reduced. The problem of slow convergence easily occurs in the later iteration stage, a large number of iteration steps are required to be consumed to reach the preset convergence standard, and the overall calculation cost is obviously increased. Therefore, the invention provides a self-adaptive source iteration acceleration method based on physical-data driving according to the change of flux errors of two adjacent steps. The method saves a great amount of calculation time and cost on the premise of ensuring calculation accuracy. In order to achieve the above object, the present invention provides a physical-data driving-based adaptive source iterative acceleration method, comprising the steps of: S1, setting a flux maximum relative error threshold value Noise thresholdInitial value of (2), flux maximum relative errorAndDiscretizing a steady neutron diffusion equation by adopting a coarse net finite difference method to establish a coarse net finite difference equation set; S2, calculating a coarse mesh finite difference equation set; S3, judging Whether or not to be smaller than: If it isGreater than or equal toS2 is entered; If it is Less thanS4 is entered; S4, will Assignment to; S5, saving the flux of the nth step, calculating flux errors of two adjacent steps, and constructing a snapshot matrix; S6, calculating flux error modal attenuation condition, namely residual ratio r in real time by adopting an incremental orthogonalization analysis method, and combining the residual ratio r with the flux error modal attenuation condition Comparison: If r is greater than or equal to S2 is entered; If r is smaller than S7, entering into S7; S7, snapshot matrix information is extracted, flux error items of the n+1th step and the n th step are calculated, and the flux of the n+1th step is updated by the flux of the n th step and the flux error items; S8, entering S2 to calculate a twice coarse net finite difference equation set, and updating And compareAndTo update: If it isGreater than or equal toWill beAssignment to; If it isLess thanWill beAssignment to; S8, judging the calculation after the calculation of S2 is finishedAndWhether the convergence criterion is reached: If it is present Or (b)If the convergence criterion is not met, S2 is entered; If it is present AndIf the convergence criterion is met, S9 is entered; and S9, ending the iterative computation. Preferably, in S5, the snapshot matrix comprises the following steps: S501 when Less thanWhen the flux is stored in sequence, calculating flux errors of two adjacent steps: ;(1) ;(2) Wherein: for the column vectors formed by two adjacent flux errors of different areas and different energy groups, For th