A fully‐implicit numerical algorithm of two‐fluid two‐phase flow model using Jacobian‐free Newton–Krylov method

Fan, Jie; Gou, Junli; Huang, Jun; Shan, Jianqiang

doi:10.1002/fld.5155

Cited by 5 publications

(5 citation statements)

References 38 publications

(54 reference statements)

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“…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%

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

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“…After that, JFNK was used for solving nonlinear equations in different fields. [42][43][44][45] The successful application of the JFNK method to any given problem requires an efficient preconditioner because Krylov methods generally do not function well without a suitable preconditioner. Various preconditioning techniques are available in the literature; however, none are unique or generalized.…”

Section: Introductionmentioning

confidence: 99%

“…Later, Knoll et al 41 published a survey paper on the approaches and applications of the matrix‐free Newton method and referred to it as a Jacobian‐free Newton–Krylov (JFNK) method. After that, JFNK was used for solving nonlinear equations in different fields 42–45 …”

Section: Introductionmentioning

confidence: 99%

Physics‐based preconditioning of Jacobian‐free Newton–Krylov solver for Navier–Stokes equations using nodal integral method

Ahmed,

Singh,

Kumar

2023

Numerical Methods in Fluids

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The nodal integral methods (NIMs) have found widespread use in the nuclear industry for neutron transport problems due to their high accuracy. However, despite considerable development, these methods have limited acceptability among the fluid flow community. One major drawback of these methods is the lack of robust and efficient nonlinear solvers for the algebraic equations resulting from discretization. Since its inception, several modifications have been made to make NIMs more agile, efficient, and accurate. Modified nodal integral method (MNIM) and modified MNIM (M2NIM) are the two most recent and efficient versions of the NIM for fluid flow problems. M2NIM modifies the MNIM by replacing the current time convective velocity with the previous time convective velocity, leading to faster convergence albeit with reduced accuracy. This work proposes a preconditioned Jacobian‐free Newton–Krylov approach for solving the Navier–Stokes equation using MNIM. The Krylov solvers do not generally work well without an appropriate preconditioner. Therefore, M2NIM is used here as a preconditioner to accelerate the solution of MNIM. Due to pressure–velocity coupling in the Navier–Stokes equation, developing a quality preconditioner for these equations needs significant effort. The momentum equation is solved using the time‐splitting alternate direction implicit method. The velocities obtained from the solution are then used to solve the pressure Poisson equation. The computational results for the Navier–Stokes equation are presented to underscore the advantages of the developed algorithm.

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“…Compared with the widely-used traditional coupling methods, such as operator splitting method and Picard iteration method [4][5][6] , Jacobian-free Newton-Krylov (JFNK) algorithm [7] is well-known due to its low storage and high-order convergence rate. JFNK algorithm has been widely used in the latest nuclear engineering simulation codes [8][9][10][11] . Based on the JFNK algorithm, a Multi-physics Object Oriented Simulation Environment (MOOSE) has been developed by Idaho National Laboratory (INL) targeted at the solution of coupled nonlinear PDEs [12] .…”

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.

show abstract

A fully‐implicit numerical algorithm of two‐fluid two‐phase flow model using Jacobian‐free Newton–Krylov method

Cited by 5 publications

References 38 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

Physics‐based preconditioning of Jacobian‐free Newton–Krylov solver for Navier–Stokes equations using nodal integral method

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

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