1
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The improved odCMFD method based on the 2D/1D Fourier analysis. ANN NUCL ENERGY 2023. [DOI: 10.1016/j.anucene.2023.109775] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/06/2023]
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2
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Comprehensive investigation of the Ronen method in slab geometry. NUCLEAR ENGINEERING AND TECHNOLOGY 2022. [DOI: 10.1016/j.net.2022.09.026] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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3
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Zhou X, Liu Z, Cao L, Wu H. Convergence analysis for the CMFD accelerated 2D/1D neutron transport calculation method based on Fourier analysis. ANN NUCL ENERGY 2022. [DOI: 10.1016/j.anucene.2022.108982] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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4
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Ferrer RM, Park H. Analysis of Corner Balance Nonlinear Diffusion Acceleration and Moment-Based, Spatially Linear Transport Discretizations. NUCL SCI ENG 2022. [DOI: 10.1080/00295639.2021.2011668] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Rodolfo M. Ferrer
- Studsvik Scandpower, Inc., 1070 Riverwalk Drive, Suite 150, Idaho Falls, Idaho 83402
| | - HyeongKae Park
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545
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5
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7
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Oshima Y, Endo T, Yamamoto A. Impact of Angular and Spatial Source Distribution Approximations on Convergence Performance of Nonlinear Acceleration Methods for MOC in Slab Geometry. NUCL SCI ENG 2021. [DOI: 10.1080/00295639.2021.1982549] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Yoshiki Oshima
- Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
| | - Tomohiro Endo
- Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
| | - Akio Yamamoto
- Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
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8
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Shen Q, Choi S, Kochunas B. A Robust, Relaxation-Free Multiphysics Iteration Scheme for CMFD-Accelerated Neutron Transport k-Eigenvalue Calculations—II: Numerical Results. NUCL SCI ENG 2021. [DOI: 10.1080/00295639.2021.1906586] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Qicang Shen
- University of Michigan, Department of Nuclear Engineering and Radiological Sciences, Ann Arbor, Michigan 48109-2104
| | - Sooyoung Choi
- University of Michigan, Department of Nuclear Engineering and Radiological Sciences, Ann Arbor, Michigan 48109-2104
| | - Brendan Kochunas
- University of Michigan, Department of Nuclear Engineering and Radiological Sciences, Ann Arbor, Michigan 48109-2104
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9
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Shen Q, Kochunas B. A Robust, Relaxation–Free Multiphysics Iteration Scheme for CMFD–Accelerated Neutron Transport k–Eigenvalue Calculations–I: Theory. NUCL SCI ENG 2021. [DOI: 10.1080/00295639.2021.1906585] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Qicang Shen
- University of Michigan, Department of Nuclear Engineering and Radiological Sciences, Ann Arbor, Michigan 48109-2104
| | - Brendan Kochunas
- University of Michigan, Department of Nuclear Engineering and Radiological Sciences, Ann Arbor, Michigan 48109-2104
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10
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Fine Mesh Finite Difference acceleration method based on the Generalized Equivalence Theory for the 2-D MOC transport calculation. ANN NUCL ENERGY 2021. [DOI: 10.1016/j.anucene.2021.108450] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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11
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Jain L, Mohanakrishnan P, Karthikeyan R, Kannan U. Convergence study of CMFD based acceleration schemes for multi-group transport calculations with fission source using fourier analysis. ANN NUCL ENERGY 2021. [DOI: 10.1016/j.anucene.2021.108314] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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12
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Ferrer RM. Stability analysis of coarse-mesh finite difference acceleration schemes and moment-based, spatially-linear discretizations. ANN NUCL ENERGY 2021. [DOI: 10.1016/j.anucene.2021.108280] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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13
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Comparative studies of iterative methods for solving the “optimally diffusive” coarse mesh finite difference accelerated transport equation. ANN NUCL ENERGY 2021. [DOI: 10.1016/j.anucene.2021.108211] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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14
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A linear prolongation CMFD acceleration for two-dimensional discrete ordinate k-eigenvalue neutron transport calculation with pin-resolved mesh using discontinuous Galerkin finite element method. ANN NUCL ENERGY 2021. [DOI: 10.1016/j.anucene.2020.108103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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15
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Numerical stability analysis of lp-CMFD acceleration for the discrete ordinates neutron transport calculation discretized with discontinuous Galerkin Finite Element Method. ANN NUCL ENERGY 2021. [DOI: 10.1016/j.anucene.2020.108036] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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16
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Convergence analysis of the non-linear CMFD schemes for acceleration of multi-group fixed source neutron transport calculations. ANN NUCL ENERGY 2021. [DOI: 10.1016/j.anucene.2020.108041] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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17
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A linearized coarse mesh finite difference preconditioner for the within-group Krylov subspace iteration based on two-dimensional method of characteristics. ANN NUCL ENERGY 2021. [DOI: 10.1016/j.anucene.2020.107889] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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18
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Abstract
The coarse-mesh finite difference (CMFD) scheme is a very effective nonlinear diffusion acceleration method for neutron transport calculations. CMFD can become unstable and fail to converge when the computational cell optical thickness is relatively large in k-eigenvalue problems or diffusive fixed-source problems. Some variants and fixups have been developed to enhance the stability of CMFD, including the partial current-based CMFD (pCMFD), optimally diffusive CMFD (odCMFD), and linear prolongation-based CMFD (lpCMFD). Linearized Fourier analysis has proven to be a very reliable and accurate tool to investigate the convergence rate and stability of such coupled high-order transport/low-order diffusion iterative schemes. It is shown in this paper that the use of different transport solvers in Fourier analysis may have some potential implications on the development of stabilizing techniques, which is exemplified by the odCMFD scheme. A modification to the artificial diffusion coefficients of odCMFD is proposed to improve its stability. In addition, two explicit expressions are presented to calculate local optimal successive overrelaxation (SOR) factors for lpCMFD to further enhance its acceleration performance for fixed-source problems and k-eigenvalue problems, respectively.
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19
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Zhang G, Yang WS. Quadratic axial expansion function with sub-plane acceleration scheme for the high-fidelity transport code PROTEUS-MOC. ANN NUCL ENERGY 2020. [DOI: 10.1016/j.anucene.2020.107713] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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20
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Wu W, Giudicelli G, Smith K, Forget B, Yao D, Yu Y, Luo Q. Improvements of the CMFD acceleration capability of OpenMOC. NUCLEAR ENGINEERING AND TECHNOLOGY 2020. [DOI: 10.1016/j.net.2020.04.001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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21
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Wang D. Enhancing lpCMFD Acceleration with Successive Overrelaxation for Neutron Transport Source Iteration. NUCL SCI ENG 2020. [DOI: 10.1080/00295639.2020.1785190] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Dean Wang
- The Ohio State University, 201 West 19th Avenue, Columbus, Ohio 43210
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22
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Implementation and performance study of lpCMFD acceleration method for multi-energy group k-eigenvalue neutron transport problem in hexagonal geometry. ANN NUCL ENERGY 2020. [DOI: 10.1016/j.anucene.2019.107220] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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23
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Oshima Y, Endo T, Yamamoto A, Kodama Y, Ohoka Y, Nagano H. Impact of Various Parameters on Convergence Performance of CMFD Acceleration for MOC in Multigroup Heterogeneous Geometry. NUCL SCI ENG 2020. [DOI: 10.1080/00295639.2020.1722512] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Yoshiki Oshima
- Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan
| | - Tomohiro Endo
- Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan
| | - Akio Yamamoto
- Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan
| | - Yasuhiro Kodama
- Nuclear Fuel Industries, Ltd., 1-950 AsashiroNishi, Kumatori-cho, Sennan-gun, Osaka, 590-0481, Japan
| | - Yasunori Ohoka
- Nuclear Fuel Industries, Ltd., 1-950 AsashiroNishi, Kumatori-cho, Sennan-gun, Osaka, 590-0481, Japan
| | - Hiroaki Nagano
- Nuclear Fuel Industries, Ltd., 1-950 AsashiroNishi, Kumatori-cho, Sennan-gun, Osaka, 590-0481, Japan
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24
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Xu Z, Zheng Y, Wang Y, Wu H. IFDF acceleration method with adaptive diffusion coefficients for SN nodal calculation in SARAX code system. ANN NUCL ENERGY 2020. [DOI: 10.1016/j.anucene.2019.107056] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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25
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Convergence study of variants of CMFD acceleration schemes for fixed source neutron transport problems in 2D Cartesian geometry with Fourier analysis. ANN NUCL ENERGY 2019. [DOI: 10.1016/j.anucene.2019.06.021] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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26
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Chan Y, Xiao S. Convergence study of CMFD and lpCMFD acceleration schemes for k-eigenvalue neutron transport problems in 2-D Cartesian geometry with Fourier analysis. ANN NUCL ENERGY 2019. [DOI: 10.1016/j.anucene.2019.05.035] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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27
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28
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Yamamoto A, Endo T, Giho A. Transport consistent diffusion coefficient for CMFD acceleration and comparison of convergence properties. J NUCL SCI TECHNOL 2019. [DOI: 10.1080/00223131.2019.1618405] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Akio Yamamoto
- Graduate School of Engineering, Nagoya Univeristy, Nagoya, Japan
| | - Tomohiro Endo
- Graduate School of Engineering, Nagoya Univeristy, Nagoya, Japan
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29
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Zhang G, Hsieh A, Yang WS, Jung YS. Consistent pCMFD Acceleration Schemes of the Three-Dimensional Transport Code PROTEUS-MOC. NUCL SCI ENG 2019. [DOI: 10.1080/00295639.2018.1560854] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Guangchun Zhang
- University of Michigan, Department of Nuclear Engineering and Radiological Science, Ann Arbor, Michigan 48105
| | - Albert Hsieh
- University of Michigan, Department of Nuclear Engineering and Radiological Science, Ann Arbor, Michigan 48105
| | - Won Sik Yang
- University of Michigan, Department of Nuclear Engineering and Radiological Science, Ann Arbor, Michigan 48105
| | - Yeon Sang Jung
- Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, Illinois 60439
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30
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Affiliation(s)
- Dean Wang
- University of Massachusetts Lowell, 1 University Avenue, Lowell, Massachusetts 01854
| | - Sicong Xiao
- University of Massachusetts Lowell, 1 University Avenue, Lowell, Massachusetts 01854
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31
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Accelerated polynomial axial expansions for full 3D neutron transport MOC in the APOLLO3® code system as applied to the ASTRID fast breeder reactor. ANN NUCL ENERGY 2018. [DOI: 10.1016/j.anucene.2017.11.010] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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32
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Xiao S, Ren K, Wang D. A Local Adaptive Coarse-Mesh Nonlinear Diffusion Acceleration Scheme for Neutron Transport Calculations. NUCL SCI ENG 2017. [DOI: 10.1080/00295639.2017.1394088] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Sicong Xiao
- University of Massachusetts Lowell, 1 University Avenue, Lowell, Massachusetts 01854
| | - Kangyu Ren
- University of Massachusetts Lowell, 1 University Avenue, Lowell, Massachusetts 01854
| | - Dean Wang
- University of Massachusetts Lowell, 1 University Avenue, Lowell, Massachusetts 01854
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33
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Yamamoto A, Giho A, Endo T. Recent developments in the GENESIS code based on the Legendre polynomial expansion of angular flux method. NUCLEAR ENGINEERING AND TECHNOLOGY 2017. [DOI: 10.1016/j.net.2017.06.016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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34
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Yuk S, Cho NZ. Two-Level Convergence Speedup Schemes for p-CMFD Acceleration in Neutron Transport Calculation. NUCL SCI ENG 2017. [DOI: 10.1080/00295639.2017.1332891] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Seungsu Yuk
- Korea Advanced Institute of Science and Technology (KAIST), Department of Nuclear and Quantum Engineering, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Korea
| | - Nam Zin Cho
- Korea Advanced Institute of Science and Technology (KAIST), Department of Nuclear and Quantum Engineering, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Korea
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35
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Zhu A, Kochunas B, Xu Y, Jarrett M, Larsen E, Downar T. Theoretical Convergence Rate Lower Bounds for Variants of Coarse Mesh Finite Difference to Accelerate Neutron Transport Calculations. NUCL SCI ENG 2017. [DOI: 10.1080/00295639.2017.1293408] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Ang Zhu
- University of Michigan, Department of Nuclear Engineering and Radiological Sciences, Ann Arbor, Michigan 48109
| | - Brendan Kochunas
- University of Michigan, Department of Nuclear Engineering and Radiological Sciences, Ann Arbor, Michigan 48109
| | - Yunlin Xu
- University of Michigan, Department of Nuclear Engineering and Radiological Sciences, Ann Arbor, Michigan 48109
| | - Michael Jarrett
- University of Michigan, Department of Nuclear Engineering and Radiological Sciences, Ann Arbor, Michigan 48109
| | - Edward Larsen
- University of Michigan, Department of Nuclear Engineering and Radiological Sciences, Ann Arbor, Michigan 48109
| | - Thomas Downar
- University of Michigan, Department of Nuclear Engineering and Radiological Sciences, Ann Arbor, Michigan 48109
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