High-Order Harmonics Calculation for the Power Reconstruction of 3D Pin-Scale Whole-Core

Abstract The high-order harmonics of neutron diffusion equation is used in the reconstruction method to reconstruct the core power distribution. There are two methods available for the high-order harmonics solving: power iteration method with source correction (PIMSC) and Krylov subspace method. PIMSC was commonly used in the high-order harmonics calculation of the homogeneous assembly-scale neutron diffusion equation. However, this method cannot use the discontinuity factor theory, and the diffusion system is not equivalent to the transport system. Meanwhile, the convergence rate is influenced by the dominance ratio. In order to calculate the high-order harmonics of the 3D multigroup pin-scale whole-core neutron diffusion equation and guarantee equivalence between the neutron diffusion equation and the neutron transport equation, the 3D pin-scale generalized equivalence theory based coarse mesh finite difference (gCMFD) system is used in the high-order harmonic calculation, which is equivalent to the transport system using the discontinuity factor theory. The implicitly restart Arnoldi method (IRAM) is used to solve the 3D pin-scale gCMFD system. IRAM is a kind of Krylov subspace method which utilizes the implicit restart technology to improve the solving speed. To verify IRAM in high-order harmonics calculation, the results of C5G7 benchmark calculated by the PIMSC and IRAM are compared. The whole-core model of low-temperature heating reactor (LTHR) is used to test the calculating ability of pin-scale high-order harmonics and analyze the express ability of power. The numerical results indicate that IRAM has superior computational efficiency compared to PIMSC, being approximately 431 times faster. Additionally, for the low temperature heating reactor, the high-order harmonics solved by IRAM have good accuracy in the pin-scale power reconstruction.