A multi-level nonlinear elimination-based JFNK method for multi-scale multi-physics coupling problem in pebble-bed HTR

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

doi:10.1016/j.anucene.2022.109281

Cited by 4 publications

(2 citation statements)

References 32 publications

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“…Due to the inherently featured multi-scale and multi-physics effects in nuclear reactor systems [1,2], a reactor simulation is a coupled problem including several phenomena. Nonlinear partial differential equations (PDEs) are usually used to describe this coupled system behavior.…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

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

Wu,

Zhang,

Liu

et al. 2024

Energies

Self Cite

View full text Add to dashboard Cite

show abstract

“…Due to the inherently featured of multi-scale and multi-physical in the reactor systems, the nuclear reactor simulation is a multi-physics coupling calculation [1][2] , where a nonlinear coupled partial differential equation system is used to describe the physical behavior at different scales and physics fields. The steady-state neutron diffusion k-eigenvalue problem is the fundamental component of the multi-physics system.…”

Section: Introductionmentioning

confidence: 99%

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

Wu,

ZHANG,

Liu

et al. 2023

Preprint

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Jacobian-free Newton Krylov (JFNK) is an attractive method to solve nonlinear equations in nuclear engineering systems, 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 JFNK algorithm, significantly affecting 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. An efficient 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 construct an efficient preconditioning matrix with low computational cost automatically. Furthermore, the reordering algorithm is employed for the ILU(k) to reduce the additional non-zero elements and pursue robust computational performance. A two-dimensional LRA neutron steady-state benchmark problem is used to evaluate the performance of the proposed preconditioning technique, and steady-state neutron diffusion problem with thermal-hydraulic feedback is also utilized as a supplement. The results show that coloring algorithms can efficiently and automatically construct the preconditioning matrix. The reordering-based ILU(k) preconditioner shows excellent robustness, avoiding the effect of fill-in levels k choice in incomplete LU factorization.

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A modified JFNK with line search method for solving k-eigenvalue neutronics problems with thermal-hydraulics feedback

Liu

Han

et al. 2023

Nuclear Engineering and Technology

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A multi-level nonlinear elimination-based JFNK method for multi-scale multi-physics coupling problem in pebble-bed HTR

Cited by 4 publications

References 32 publications

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

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

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

A modified JFNK with line search method for solving k-eigenvalue neutronics problems with thermal-hydraulics feedback

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