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Technical Papers

Consistent pCMFD Acceleration Schemes of the Three-Dimensional Transport Code PROTEUS-MOC

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Pages 828-853 | Received 14 Sep 2018, Accepted 17 Dec 2018, Published online: 07 Feb 2019

References

  • K. T. CLARNO et al., “High Fidelity Core Simulator for Analysis of Pellet Clad Interaction,” Proc. ANS MC2015, Nashville, Tennessee, April 19–23, 2015.
  • B. KENDRICK et al., “CASL Multiphysics Modeling of CRUD Deposition in PWRs,” Proc. LWR Fuel Performance Mtg. TopFuel 2013, Charlotte, North Carolina, September 15–19, 2013.
  • N. Z. CHO, G. S. LEE, and C. J. PARK, “Refinement of the 2-D/1-D Fusion Method for 3-D Whole Core Transport Calculation,” Trans. Am. Nucl. Soc., 87, 417 (2002).
  • J. Y. CHO et al., “Three-Dimensional Heterogeneous Whole Core Transport Calculation Employing Planar MOC Solutions,” Trans. Am. Nucl. Soc., 87, 234 (2002).
  • H. G. JOO et al., “Methods and Performance of a Three-Dimensional Whole-Core Transport Code DeCART,” Proc. Physics of Fuel Cycles and Advanced Nuclear Systems: Global Developments (PHYSOR-2004), Chicago, Illinois, April 25–29, 2004, American Nuclear Society (2004) (CD-ROM).
  • G. S. LEE and N. Z. CHO, “2D/1D Fusion Method Solutions of the Three-Dimensional Transport OECD Benchmark Problem C5G7 MOX,” Prog. Nucl. Energy, 48, 410 (2006); https://doi.org/10.1016/j.pnucene.2006.01.010.
  • J. CHO et al., “Axial SPN and Radial MOC Coupled Whole Core Transport Calculations,” J. Nucl. Sci. Technol., 44, 1156 (2007); https://doi.org/10.1080/18811248.2007.9711359.
  • Y. S. JUNG et al., “Practical Numerical Reactor Employing Direct Whole Core Neutron Transport and Subchannel Thermal/Hydraulic Solver,” Ann. Nucl. Energy, 62, 357 (2013); https://doi.org/10.1016/j.anucene.2013.06.031.
  • B. KOCHUNAS et al., “MPACT: Michigan Parallel Advanced Characteristics Transport,” Proc. M&C 2013, Sun Valley, Idaho, May 5–9, 2013.
  • B. COLLINS et al., “Stability and Accuracy of 3D Neutron Transport Simulations Using the 2D/1D Method in MPACT,” J. Comp. Phy., 326, 612 (2016); https://doi.org/10.1016/j.jcp.2016.08.022.
  • Z. LIU et al., “Development and Verification of the High-Fidelity Neutronics and Thermal-Hydraulic Coupling Code System NECP-X/SUBSC,” Prog. Nucl. Energy, 103, 114 (2018); https://doi.org/10.1016/j.pnucene.2017.11.010.
  • M. A. SMITH et al., “New Neutronics Analysis Tool Development at Argonne National Laboratory,” Proc. Int. Conf. Fast Reactors and Related Fuel Cycles (FR09), Kyoto, Japan, December 7–11, 2009.
  • G. GUNOW et al., “Reducing 3D MOC Storage with Axial on the Fly Ray Tracing,” Proc. PHYSOR 2016, Sun Valley, Idaho, May 1–5, 2016, American Nuclear Society (2016).
  • A. M. LAFLECHE, M. A. SMITH, and C. LEE, “PROTEUS-MOC: A 3D Deterministic Solver Incorporating 2D Method of Characteristics,” Proc. Mathematics and Computation (M&C 2013), Sun Valley, Idaho, May 5–9, 2013.
  • M. HURSIN, “Full Core, Heterogeneous, Time Dependent Neutron Transport Calculations with the 3D Code DeCart,” PhD Thesis, University of California, Department of Nuclear Engineering, Berkeley (2010).
  • B. W. KELLY and E. W. LARSEN, “2D/1D Approximations to the 3D Neutron Transport Equation. I: Theory,” Proc. Mathematics and Computation (M&C 2013), Sun Valley, Idaho, May 5–9, 2013.
  • G. GUNOW et al., “Accuracy and Performance of 3D MOC for Full-Core PWR Problems,” Proc. M&C 2017, Jeju, Korea, April 16–20, 2017 (2017).
  • “OpenMP Application Program Interface Version 3.0,” OpenMP Architecture Review Board (2008).
  • S. SANTANDREA et al., “A Neutron Transport Characteristics Method for 3D Axially Extruded Geometries Coupled with A Fine Group Self-Shielding Environment,” Nucl. Sci. Eng., 186, 239 (2017); https://doi.org/10.1080/00295639.2016.1273634.
  • E. R. SHEMON et al., “NEAMS Neutronics: Development and Validation Status,” Proc. ICAPP 2014, Charlotte, North Carolina, April 6–9, 2014.
  • A. HSIEH and W. S. YANG, “Implementation of CMFD Acceleration Scheme in PROTEUS-MOC,” Trans. Am. Nucl. Soc., 117, 1140 (2017).
  • E. W. LARSEN and J. E. MOREL, “Advances in Discrete-Ordinates Methodology,” Nuclear Computational Science: A Century in Review, pp. 1–84, Springer (2010).
  • J. S. WARSA, T. A. WAREING, and J. E. MOREL, “Krylov Iterative Methods and the Degraded Effectiveness of Diffusion Synthetic Acceleration for Multidimensional SN Calculations in Problems with Material Discontinuities,” Nucl. Sci. Eng., 147, 218 (2004); https://doi.org/10.13182/NSE02-14.
  • B. W. PATTON and J. P. HOLLOWAY, “Application of Preconditioned GMRES to the Numerical Solution of the Neutron Transport Equation,” Ann. Nucl. Energy, 29, 109 (2002); https://doi.org/10.1016/S0306-4549(01)00034-2.
  • K. S. SMITH and J. D. RHODES III, “Full-Core, 2-D, LWR Core Calculations with CASMO-4E,” Proc. PHYSOR 2002, Seoul, Korea, October 7–10, 2002; https://doi.org/10.1044/1059-0889(2002/er01).
  • Y. SAAD, Numerical Methods for Large Eigenvalue Problems, Halstead Press, New York (1992).
  • Y. SAAD, “Chebyshev Acceleration Techniques for Solving Nonsymmetric Eigenvalue Problems,” Math. Comput., 42, 166, 567 (1984); https://doi.org/10.1090/S0025-5718-1984-0736453-8.
  • B. C. YEE et al., “Space-Dependent Wielandt Shifts for Multigroup Diffusion Eigenvalue Problems,” Nucl. Sci. Eng., 188, 140 (2017); https://doi.org/10.1080/00295639.2017.1350001.
  • D. F. GILL et al., “Newton’s Method for the Computations of k-Eigenvalues in Sn Transport Applications,” Nucl. Sci. Eng., 168, 37 (2011); https://doi.org/10.13182/NSE10-01.
  • M. T. CALEF et al., “Nonlinear Krylov Acceleration Applied to a Discrete Ordinates Formulation of the k-Eigenvalue Problem,” J. Comput. Phy., 238, 188 (2013); https://doi.org/10.1016/j.jcp.2012.12.024.
  • E. D. FICHTL, J. S. WARSA, and M. T. CALEF, “Nonlinear Acceleration of Sn Transport Calculations,” Proc. Mathematics and Computation (M&C 2011), Rio de Janeiro, Brazil, May 8–12, 2011.
  • D. A. KNOLL, H. PARK, and C. NEWMAN, “Acceleration of k-Eigenvalue/Criticality Calculations Using the Jacobian-Free Newton-Krylov Method,” Nucl. Sci. Eng., 167, 133 (2011); https://doi.org/10.13182/NSE09-89.
  • S. P. HAMILTON, “Numerical Solution of the k-Eigenvalue Problem,” PhD Thesis, Emory University, Department of Mathematics and Computer Science (2010).
  • H. PARK, D. A. KNOLL, and C. K. NEWMAN, “Nonlinear Acceleration of Transport Criticality Problems,” Nucl. Sci. Eng., 172, 52 (2012); https://doi.org/10.13182/NSE11-81.
  • J. WILLERT, H. PARK, and D. A. KNOLL, “A Comparison of Acceleration Methods for Solving the Neutron Transport k-Eigenvalue Problem,” J. Comp. Phy., 274, 681 (2014); https://doi.org/10.1016/j.jcp.2014.06.044.
  • Y. S. JUNG and W. S. YANG, “A Consistent CMFD Formulation for Acceleration of Neutron Transport Calculations Based on Finite Element Method,” Nucl. Sci. Eng., 185, 307 (2017); https://doi.org/10.1080/00295639.2016.1272369.
  • N. Z. CHO and C. J. PARK, “A Comparison of Coarse Mesh Rebalance and Coarse Mesh Finite Difference Accelerations for the Neutron Transport Calculations,” Proc. Mathematics and Computation (M&C 2003), Gatlinburg, Tennessee, April 7–10, 2003, American Nuclear Society (2003).
  • M. JARRETT et al., “Analysis of Stabilization Techniques for CMFD Acceleration of Neutron Transport Problems,” Nucl. Sci. Eng., 184, 208 (2016); https://doi.org/10.13182/NSE16-51.
  • N. Z. CHO, G. S. LEE, and C. J. PARK, “Partial Current-Based CMFD Acceleration of the 2D/1D Fusion Method for 3D Whole-Core Transport Calculations,” Trans. Am. Nucl. Soc., 88, 594 (2003).
  • Y. SAAD and M. H. SCHUTLZ, “GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems,” SIAM J. Sci. Stat. Comput., 7, 856 (1986); https://doi.org/10.1137/0907058.
  • S. YUK and N. Z. CHO, “Two-Level Convergence Speedup Schemes for p-CMFD Acceleration in Neutron Transport Calculation,” Nucl. Sci. Eng., 188, 1 (2017); https://doi.org/10.1080/00295639.2017.1332891.
  • D. Y. ANISTRATOV, “Multilevel NDA Methods for Solving Multigroup Eigenvalue Neutron Transport Problems,” Nucl. Sci. Eng., 174, 150 (2013); https://doi.org/10.13182/NSE12-28.
  • L. R. CORNEJO and D. Y. ANISTRATOV, “Nonlinear Diffusion Acceleration Method with Multigrid in Energy for k-Eigenvalue Neutron Transport Problems,” Nucl. Sci. Eng., 184, 514 (2016); https://doi.org/10.13182/NSE16-78.
  • B. C. YEE, B. KOCHUNAS, and E. W. LARSEN, “A Multilevel in Space and Energy Solver for Multigroup Diffusion Eigenvalue Problems,” Nucl. Eng. Technol., 49, 1125 (2017); https://doi.org/10.1016/j.net.2017.07.014.
  • B. C. YEE, “MSED: A Multilevel in Space and Energy Solver for Multigroup Diffusion and CMFD Eigenvalue Problems,” PhD Thesis, University of Michigan, Department of Nuclear Engineering and Radiological Sciences (2018).
  • N. ORDY et al., “Coarse Mesh Rebalance Acceleration Applied to an Iterative Domain Decomposition Method on Unstructured Mesh,” Nucl. Sci. Eng., 187, 240 (2017); https://doi.org/10.1080/00295639.2017.1320891.
  • W. A. RHOADES and R. L. CHILDS, “The TORT Three-Dimensional Discrete Ordinates Neutron/Photon Transport Code,” ORNL-6268, Oak Ridge National Laboratory (1987).
  • S. RAY and R. S. MODAK, “On the Method of the External Source Problem in a Slightly Subcritical Reactor,” Nucl. Sci. Eng., 170, 75 (2012); https://doi.org/10.13182/NSE10-87TN.
  • J. PLANCHARD, “On the Calculation of Flux in Slightly Subcritical Reactors with External Neutron Sources,” Prog. Nucl. Energy, 23, 181 (1990); https://doi.org/10.1016/0149-1970(90)90001-L.
  • M. A. SMITH, E. E. LEWIS, and B.-C. NA, “Benchmark on Deterministic Transport Calculations Without Spatial Homogenization: A 2-D/3-D MOX Fuel Assembly 3-D Benchmark,” NEA/NSC/DOC(2003)16, Organization for Economic Co-operation and Development/Nuclear Energy Agency (2003).
  • C. H. LEE et al., “Simulation of TREAT Cores Using High-Fidelity Neutronics Code PROTEUS,” Proc. of M&C 2017, Jeju, Korea, April 16–20, 2017.
  • G. A. FREUND et al., “Design Summary Report on the Transient Reactor Test Facility (TREAT),” ANL-6034, Argonne National Laboratory (1960).
  • J. HOU et al., “OECD/NEA Benchmark for Time-Dependent Neutron Transport Calculations Without Spatial Homogenization,” Nucl. Eng. Des., 317, 177 (2017); https://doi.org/10.1016/j.nucengdes.2017.02.008.
  • E. LEWIS and J. W. F. MILLER, Computational Methods of Neutron Transport, American Nuclear Society, Inc., LaGrange Park, Illinois (1993).
  • P. ALFELD, “Fixed Point Iteration with Inexact Function Values,” Math. Comp., 38, 87 (1982); https://doi.org/10.1090/S0025-5718-1982-0637288-5.
  • B. KOCHUNAS et al., “Application of the SDD-CMFD Acceleration Method to Parallel 3-D MOC Transport,” PHYSOR 2014—The Role of Reactor Physics Toward a Sustainable Future, Kyoto, Japan, September 28–October 3, 2014.
  • M. A. SMITH and E. R. SHEMON, “User Manual for the PROTEUS Mesh Tools,” ANL/NE-15/17 Rev. 1.0, Argonne National Laboratory (Jun. 2015).
  • CUBIT web page; https://cubit.sandia.gov (current as of Sep. 14, 2018).
  • J. LEPPANEN, “Serpent—A Continuous-Energy Monte Carlo Reactor Physics Burnup Calculation Code,” VTT Technical Research Centre of Finland, June 18, 2015.

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