Convergence study of traditional 2D/1D coupling method for k-eigenvalue neutron transport problems with Fourier analysis
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초록
2D/1D coupling method is an important neutron transport calculation method due to its high accuracy and relatively low computation cost. However, 2D/1D coupling method may diverge especially in small axial mesh size. To analyze the convergence behavior of 2D/1D coupling method, a Fourier analysis for k-eigenvalue neutron transport problems is implemented. The analysis results present the divergence problem of 2D/1D coupling method in small axial mesh size. Several common attempts are made to solve the divergence problem, which are to increase the number of inner iterations of the 2D or 1D calculation, and two times 1D calculations per outer iteration. However, these attempts only could improve the convergence rate but cannot deal with the divergence problem of 2D/1D coupling method thoroughly. Moreover, the choice of axial solvers, such as DGFEM SN and traditional SN, and its effect on the convergence behavior are also discussed. The results show that the choice of axial solver is a key point for the convergence of 2D/1D method. The DGFEM SN based 2D/1D method could converge within a wide range of optical thickness region, which is superior to that of traditional SN method.
Abstract
2D/1D coupling method is an important neutron transport calculation method due to its high accuracy and relatively low computation cost. However, 2D/1D coupling method may diverge especially in small axial mesh size. To analyze the convergence behavior of 2D/1D coupling method, a Fourier analysis for k-eigenvalue neutron transport problems is implemented. The analysis results present the divergence problem of 2D/1D coupling method in small axial mesh size. Several common attempts are made to solve the divergence problem, which are to increase the number of inner iterations of the 2D or 1D calculation, and two times 1D calculations per outer iteration. However, these attempts only could improve the convergence rate but cannot deal with the divergence problem of 2D/1D coupling method thoroughly. Moreover, the choice of axial solvers, such as DGFEM SN and traditional SN, and its effect on the convergence behavior are also discussed. The results show that the choice of axial solver is a key point for the convergence of 2D/1D method. The DGFEM SN based 2D/1D method could converge within a wide range of optical thickness region, which is superior to that of traditional SN method.
참고문헌 (29)
- J. Y. Cho, "Three-dimensional heterogeneous whole core transport calculation employing planar MOC solutions", Trans. Am. Nucl. Soc, 87, pp.234~236 (2002)
- N. Z. Cho, "Refinement of the 2D", 1D fusion method for 3D whole core transport calculation, 2002, pp.87, 417~420
- H. G. Joo, "Methods and Performance of a Three-Dimensional Whole Core Transport Code DeCART", Proc. PHYSPR, American Nuclear Society (2004)
- G. S. Lee, "2D", 1D fusion method solutions of the three-dimensional transport OECD benchmark problems C5G7 MOX, 2006, pp.48, 410~423
- J. Y. Cho, "Axial SPN and radial MOC coupled whole core transport calculation", J. Nucl. Sci. Technol. (Tokyo, Jpn.), 44, pp.1156~1171 (2007)
- Y. Jung, "Decoupled Planar MOC Solution for Dynamic Group Constant Generation in Direct Three-Dimensional Core Calculations", Proc. M&C, 44 (2009)
- Q. Shen, "Transient analysis of C5G7-TD benchmark with MPACT", Ann. Nucl. Energy, 125, pp.107~120 (2018)
- B. Wang, "A modified predictor-corrector quasi-static method in NECP-X for reactor transient analysis based on the 2D", 1D transport method, 2018, pp.108, 122~135
- J. Ma, "Perturbation theory-based whole-core eigenvalue sensitivity and uncertainty (SU) analysis via a 2D", 1D transport code, 2020, pp.2020, 13~
- B.W. Kelly, "2D", 1D Approximations to the 3D Neutron Transport Equation I: Theory, 2013, ~
- M. Jarrett, "Progress in Characterizing 2D", 1D Accuracy in MPACT, 2017, ~
- S. G. Hong, "Fourier convergence analysis of the rebalance methods for discrete ordinates transport equations in eigenvalue problems", Nucl. Sci. Eng, 164(1), pp.33~52 (2010)
- A. Zhu, "An optimally diffusive coarse mesh finite difference method to accelerate neutron transport calculations", Ann. Nucl. Energy, 95, pp.116~124 (2016)
- B. W. Kelly, "A consistent 2D", 1D approximation to the 3D neutron transport equation, 2015, pp.295, 598~614
- K.P. Keady, "Stability of SN k-eigenvalue iterations using CMFD acceleration", Proc. Int. Conf. On Mathematics and Computation (M&C), Supercomputing in Nuclear Applications (SNA) and the Monte Carlo (MC)Method (2015), American Nuclear society
- Y. Chan, "Convergence study of variants of CMFD acceleration schemes for fixed source neutron transport problems in 2D cartesian geometry with Fourier analysis", Ann. Nucl. Energy, 134, pp.273~283 (2019)
- Y. Chan, "Convergence study of CMFD and lpCMFD acceleration schemes for k-eigenvalue neutron transport problems in 2D cartesian geometry with Fourier analysis", Ann. Nucl. Energy, 133, pp.327~337 (2019)
- L. Jain, "Convergence study of CMFD based acceleration schemes for multi-group transport calculations with fission source using Fourier analysis", Ann. Nucl. Energy, 160, pp.108314~ (2021)
- L. Jain, "Comparative studies of iterative methods for solving the optimally diffusive coarse mesh finite difference accelerated transport equation", Ann. Nucl. Energy, 157, pp.108211~ (2021)
- B. Kong, "A discontinuous Galerkin finite element method based axial SN for the 2D", 1D transport method, 2022, pp.152, 104391~
- X. Zhou, "Convergence analysis for the CMFD accelerated 2D", 1D neutron transport method based on Fourier analysis, 2022, pp.17, 108982~
- Y. Chan, "A linear prolongation CMFD acceleration for two-dimensional discrete ordinate k-eigenvalue neutron transport calculation with pinresolved mesh using discontinuous Galerkin finite element method", Ann. Nucl. Energy, 154, pp.108103~ (2021)
- D. Wang, "A linear prolongation approach to stabilizing CMFD", Nucl. Sci. Eng, 190(1), pp.45~55 (2018)
- D. Wang, "Stabilizing CMFD with Linear Prolongation", PHYSOR (2018)
- K. Paul, "OpenMC : a state-of-the-art Monte Carlo code for research and development", Ann. Nucl. Eng, 82, pp.90~97 (2015)
- J. J. Klingensmith, "Tort solutions to the threedimensional MOX benchmark, 3D extension C5G7MOX", Prog. Nucl. Energy, 48(5), pp.445~455 (2006)
- M. A. Smith, "Benchmark on Deterministic Transport Calculations without Homogenization" (2003), Nuclear energy agency organization for economic cooperation and development (NEA-OECD)
- B. Kong, "Convergence study of DGFEM SN based 2D", 1D coupling method for solving neutron transport k-eigenvalue problems with Fourier analysis, 2022, pp.177, 109327~
- Hyun Chul Lee, "Fourier convergence analysis of two-dimensional", onedimensional coupling methods for the three-dimensional neutron diffusion eigenvalue problems, 2014, pp.156(1), 74~85