A modified JFNK method for solving the fundamental eigenmode in k-eigenvalue problem

Liu, Lixun; Wu, Yingjie; Liu, Baokun; Han, Zhang; Guo, Jiong; Li, Fu

doi:10.1016/j.anucene.2021.108823

Cited by 8 publications

(7 citation statements)

References 20 publications

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“…However, the physical models considered in this paper were relatively simple, such as the condenser and deaerator, which could be further developed and compared with the validated model in the future. Moreover, the neutronics and thermal-hydraulics coupling model based on JFNK had been developed in our existing works [1,[7][8][9]. In the future, we plan to further couple the primary circuit and secondary circuit based on the JFNK method.…”

Section: Discussionmentioning

confidence: 99%

“…The JFNK (Jacobian-free Newton-Krylov) method is a promising method to solve this challenging issue, which could realize all the physical field synchronization convergence and has a higher convergence rate and stronger stability than the traditional methods [5]. Therefore, many scholars study the JFNK method to solve complex coupling problems, such as H. Park [6], H. Zhang [7][8][9], and M. Fratoni [10]. However, most existing JFNK research mainly focuses on the reactor core and primary circuit problem.…”

Section: Introductionmentioning

confidence: 99%

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A Modified JFNK for Solving the HTR Steady State Secondary Circuit Problem

Jiang

Zhang

et al. 2023

Energies

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A nuclear power plant is a complex coupling system, which features multi-physics coupling between reactor physics and thermal-hydraulics in the reactor core, as well as the multi-circuit coupling between the primary circuit and the secondary circuit by the shared steam generator (SG). Especially in the pebble-bed modular HTR nuclear power plant, different nuclear steam supply modules are further coupled together through the shared main steam pipes and the related equipment in the secondary circuit, since the special configuration of multiple reactor modules connects to a steam turbine. The JFNK (Jacobian-Free Newton–Krylov) method provides a promising coupling framework to solve the whole HTR nuclear power plant problem, due to its excellent convergence rate and strong robustness. In this work, the JFNK method was modified and applied to the steady-state calculation of the HTR secondary circuit, which plays an important role in simultaneous solutions for the whole HTR nuclear power plant. The main components in the secondary circuit included SG, steam turbine, condenser, feed pump, high/low-pressure heat exchanger, deaerator, as well as the extraction steam from the steam turbine. The results showed that the JFNK method can effectively solve the steady state issue of the HTR secondary circuit. Moreover, the JFNK method could converge well within a wide range of initial values, indicating its strong robustness.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Modified JFNK for Solving the HTR Steady State Secondary Circuit Problem

Jiang

Zhang

et al. 2023

Energies

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“…Here, the reordering algorithms are used for ILU(k) factorization, and the fill-in levels of k = 10 are considered in this work. Compared with the ILU (10) under the natural ordering, the number of non-zeros after factorizations under reordering algorithms is reduced, as shown in Table 3. Therefore, compared with the natural ordering, the total computational time of ILU (10) under reordering algorithms is relatively robust.…”

Section: Preconditioning Matrix Factorization Techniquesmentioning

confidence: 99%

“…Compared with the ILU (10) under the natural ordering, the number of non-zeros after factorizations under reordering algorithms is reduced, as shown in Table 3. Therefore, compared with the natural ordering, the total computational time of ILU (10) under reordering algorithms is relatively robust. In order to further analyze the performance of the reordering-based ILU(k) preconditioner, a steady-state neutron diffusion k-eigenvalue problem with thermal-hydraulic feedback is also utilized as a supplement.…”

Section: Preconditioning Matrix Factorization Techniquesmentioning

confidence: 99%

“…Compared with the traditional methods, such as the operator splitting method and Picard iteration method [4][5][6], the Jacobian-free Newton-Krylov (JFNK) algorithm [7] is a powerful solver for the nonlinear equations due to its high-order convergence rate. The JFNK algorithm has been widely used in the newly developed nuclear reactor simulator [8][9][10][11], such as the MOOSE platform [12] and LIME platform [13,14]. In detail, several nuclear engineering programs have been made by Idaho National Laboratory based on the MOOSE platform, such as the reactor physics code MAMOTH [15], the advanced thermal-hydraulic code Pronghorn [16], and the two-phase flow code RELAP-7 [17].…”

Section: Introductionmentioning

confidence: 99%

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An Efficient and Robust ILU(k) Preconditioner for Steady-State Neutron Diffusion Problem Based on MOOSE

Wu,

Zhang,

Liu

et al. 2024

Energies

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Jacobian-free Newton Krylov (JFNK) is an attractive method to solve nonlinear equations in the nuclear engineering community, and has been successfully applied to steady-state neutron diffusion k-eigenvalue problems and multi-physics coupling problems. Preconditioning technique plays an important role in the JFNK algorithm, significantly affecting its computational efficiency. The key point is how to automatically construct a high-quality preconditioning matrix that can improve the convergence rate and perform the preconditioning matrix factorization efficiently and robustly. A reordering-based ILU(k) preconditioner is proposed to achieve the above objectives. In detail, the finite difference technique combined with the coloring algorithm is utilized to automatically construct a preconditioning matrix with low computational cost. Furthermore, the reordering algorithm is employed for the ILU(k) to reduce the additional non-zero elements and pursue robust computational performance. A 2D LRA neutron steady-state benchmark problem is used to evaluate the performance of the proposed preconditioning technique, and a steady-state neutron diffusion k-eigenvalue problem with thermal-hydraulic feedback is also utilized as a supplement. The results show that coloring algorithms can automatically and efficiently construct the preconditioning matrix. The computational efficiency of the FDP with coloring could be about 60 times higher than that of the preconditioner without the coloring algorithm. The reordering-based ILU(k) preconditioner shows excellent robustness, avoiding the effect of the fill-in level k choice in incomplete LU factorization. Moreover, its performances under different fill-in levels are comparable to the optimal computational cost with natural ordering.

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A movable boundary model for helical coiled once-through steam generator using preconditioned JFNK method

Liu

Han

et al. 2022

International Journal of Advanced Nuclear Reactor Design and Te

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A modified JFNK method for solving the fundamental eigenmode in k-eigenvalue problem

Cited by 8 publications

References 20 publications

A Modified JFNK for Solving the HTR Steady State Secondary Circuit Problem

A Modified JFNK for Solving the HTR Steady State Secondary Circuit Problem

An Efficient and Robust ILU(k) Preconditioner for Steady-State Neutron Diffusion Problem Based on MOOSE

A movable boundary model for helical coiled once-through steam generator using preconditioned JFNK method

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