A Neutron Transport Characteristics Method for 3D Axially Extruded Geometries Coupled with a Fine Group Self-Shielding Environment

References

• J. ASKEW, “A Characteristics Formulation of the Neutron Transport Equation in Complicated Geometries,” AEEW-M-1108, United Kingdom Atomic Energy Establishment (1972).
   Google Scholar
• M. HALSALL, “CACTUS, a Characteristics Solution to the Neutron Transport Equations in Complicated Geometries,” AEEW-R-1291, United Kingdom Atomic Energy Establishment (1980).
   Google Scholar
• R. M. FERRER and J. D. RHODES III, “A Linear Source Approximation for the Method of Characteristics,” Nucl. Sci. Eng., 182, 151 (2016); http://dx.doi.org/10.13182/NSE15-6.
   Google Scholar
• W. BOYD et al., “The OpenMOC Method of Characteristics Neutral Particle Transport Code,” Ann. Nucl. Energy, 68, 43 (2014); http://dx.doi.org/10.1016/j.anucene.2013.12.012.
   Google Scholar
• R. ROY, “The Cyclic Characteristic Method,” Proc. Int. Conf. Physics of Nuclear Science and Technology, Long Island, New York, October 5–8, 1998.
   Google Scholar
• J. Y. CHO and H. G. JOO, “Solution of the C5G7MOX Benchmark Three Dimensional Extension Problems by the Decart Direct Whole Core Calculation Code,” Prog. Nucl. Energy, 48, 5, 456 (2006); http://dx.doi.org/10.1016/j.pnucene.2006.01.006.
   Google Scholar
• J. CHO et al., “Axial SPN and Radial MOC Coupled Whole Core Transport Calculation,” J. Nucl. Sci. Technol., 44, 1156 (2007); http://dx.doi.org/10.1080/18811248.2007.9711359.
   Google Scholar
• Y. S. JUNG et al., “Practical Numerical Reactor Employing Direct Whole Core Neutron Transport and Sub-Channel Thermal/Hydraulic Solver,” Ann. Nucl. Energy, 62, 357 (2013); http://dx.doi.org/10.1016/j.anucene.2013.06.031.
   Google Scholar
• N. Z. CHO, G. S. LEE, and C. J. PARK, “Fusion of Method of Characteristics and Nodal Method for 3-D Whole-Core Transport Calculation,” Trans. Am. Nucl. Soc., 87, 322 (2002).
   Google Scholar
• 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); http://dx.doi.org/10.1016/j.pnucene.2006.01.010.
   Google Scholar
• B. KOCHUNAS et al., “Overview of Development and Design of MPACT: Michigan Parallel Characteristics Transport Code,” Proc. Int. Conf. M&C 2013, Sun Valley, Idaho, May 5–9, 2013, American Nuclear Society (2013).
   Google Scholar
• B. W. KELLEY and E. W. LARSEN, “2D/1D Approximations to the 3D Neutron Transport Equation. I: Theory,” Proc. Int. Conf. M&C 2013, Sun Valley, Idaho, May 5–9, 2013, American Nuclear Society (2013).
   Google Scholar
• B. W. KELLEY, B. COLLINS, and E. W. LARSEN, “2D/1D Approximations to the 3D Neutron Transport Equation. II: Numerical Comparisons,” Proc. Int. Conf. M&C 2013, Sun Valley, Idaho, May 5–9, 2013, American Nuclear Society (2013).
   Google Scholar
• S. XIAO, “Hardware Accelerated High Performance Neutron Transport Computation Based on AGENT Methodology,” PhD Dissertation, Purdue University (2009).
   Google Scholar
• H. ZHANG et al., “A 2D/1D Coupling Neutron Transport Method Based on the Matrix MOC and NEM Methods,” Proc. Int. Conf. M&C 2013, Sun Valley, Idaho, May 5–9, 2013, American Nuclear Society (2013).
   Google Scholar
• F. FEVOTTE and B. LATHUILIERE, “Micado: Parallel Implementation of a 2D-1D Iterative Algorithm for the 3D Neutron Transport Problem in Prismatic Geometries,” Proc. Int. Conf. M&C 2013, Sun Valley, Idaho, May 5–9, 2013, American Nuclear Society (2013).
   Google Scholar
• I. ZMIJAREVIC, “Résolution de l’équation de transport par des méthodes nodales et des caractéristiques dans les domaines a trois dimensions,” PhD Thesis, Université de Provence Aix-Marseille I (1998).
   Google Scholar
• R. LENAIN et al., “Domain-Decomposition Method for 2D and 3D Transport Calculations Using Hybrid MPI/OpenMP Parallelism,” Proc. M&C+SNA+MC 2015, Nashville, Tennessee, April 19–23, 2015.
   Google Scholar
• E. MASIELLO, R. SANCHEZ, and I. ZMIJAREVIC, “New Numerical Solution with the Method of Short Characteristics for 2-D Heterogeneous Cartesian Cells in the APOLLO2 Code: Numerical Analysis and Tests,” Nucl. Sci. Eng., 161, 3, 257 (2009); http://dx.doi.org/10.13182/NSE161-257.
   Google Scholar
• I. R. SUSLOV, “MCCG3D—3D Discrete-Ordinates Transport Code for Unstructured Grid. State of the Art and Future Development,” Proc. Seminar “Neutronics-96,” Obninsk, Russia, 1998, p. 162.
   Google Scholar
• G. WU and R. ROY, “A New Characteristics Algorithm for 3D Transport Calculations,” Ann. Nucl. Energy, 30, 1, 1 (2003); http://dx.doi.org/10.1016/S0306-4549(02)00046-4.
   Google Scholar
• A. HEBERT, “High Order Diamond Differencing Along Finite Characteristics,” Nucl. Sci. Eng., 169, 81 (2011); http://dx.doi.org/10.13182/NSE10-39.
   Google Scholar
• H. PRABHA, G. MARLEAU, and A. HEBERT, “Tracking Algorithms for Multi-Hexagonal Assemblies (2D and 3D),” Ann. Nucl. Energy, 69, 174 (2014); http://dx.doi.org/10.1016/j.anucene.2014.01.018.
   Google Scholar
• Z. LIU et al., “A New Three-Dimensional Method of Characteristics for the Neutron Transport Calculation,” Ann. Nucl. Energy, 38, 447 (2011); http://dx.doi.org/10.1016/j.anucene.2010.09.021.
   Google Scholar
• B. TAYLOR, D. KNOTT, and A. J. BARATTA, “A Method of Characteristics Solution to the OECD/NEA 3D Neutron Transport Benchmark Problem,” Proc. M&C+SNA 2007, Monterey, California, April 15–19, 2007.
   Google Scholar
• B. M. KOCHUNAS, Z. LIU, and T. DOWNAR: “Parallel 3-D Method of Characteristics in MPACT,” Proc. Int. Conf. M&C 2013, Sun Valley, Idaho, May 5–9, 2013, American Nuclear Society (2013).
   Google Scholar
• S. KOSAKA and E. SAJI, “Transport Theory Calculation for a Heterogeneous Multi-Assembly Problem by Characteristics Method with the Direct Neutron Path Linking Technique,” J. Nucl. Sci. Technol., 37, 1015 (2000); http://dx.doi.org/10.1080/18811248.2000.9714987.
   Google Scholar
• S. KOSAKA and T. TAKEDA, “Verification of 3D Heterogeneous Core Transport Calculation Utilizing Non-Linear Iteration Technique,” J. Nucl. Sci. Technol., 41, 6, 645 (2004); http://dx.doi.org/10.1080/18811248.2004.9715529.
   Google Scholar
• S. YUK and N. Z. CHO, “Whole-Core Transport Solutions with 2-D/1-D Fusion Kernel via p-CMFD Acceleration and p-CMFD Embedding of Nonoverlapping Local/Global Iterations,” Nucl. Sci. Eng., 181, 1, 1 (2015); http://dx.doi.org/10.13182/NSE14-88.
   Google Scholar
• R. SANCHEZ, “Prospects in Deterministic Three-Dimensional Whole-Core Transport Calculations,” Nucl. Eng. Des., 44, 2, 113 (2012); http://dx.doi.org/10.5516/NET.01.2012.501.
   Google Scholar
• A. GIHO et al., “Development of Axially Simplified Method of Characteristics in Three-Dimensional Geometry,” J. Nucl. Sci. Technol., 45, 10, 985 (2008); http://dx.doi.org/10.1080/18811248.2008.9711884.
   Google Scholar
• M. DAHMANI and R. ROY, “Parallel Solver Based on the Three-Dimensional Characteristics Method: Design and Performance Analysis,” Nucl. Sci. Eng., 150, 155 (2005); http://dx.doi.org/10.13182/NSE150-155.
   Google Scholar
• M. DAHMANI and R. ROY, “Solving Three-Dimensional Large Scale Neutron Transport Problems Using Hybrid Shared-Distributed Parallelism and Characteristics Method,” Nucl. Sci. Eng., 155, 236 (2007); http://dx.doi.org/10.13182/NSE155-236.
   Google Scholar
• D. SCIANNANDRONE, S. SANTANDREA, and R. SANCHEZ, “Optimized Tracking Strategies for Step MOC Calculations in Extruded 3D Axial Geometries,” Ann. Nucl. Energy, 87, 49 (2016); http://dx.doi.org/10.1016/j.anucene.2015.05.014.
   Google Scholar
• OPENMP ARCHITECTURE REVIEW BOARD, “OpenMP Application Program Interface Version 3.0” (2008).
   Google Scholar
• T. JEVREMOCIC, J. VUJIC, and K. TSUDA, “ANEMONA—A Neutron Transport Code for General Geometry Reactor Assembly Based on the Method of Characteristics and R-Function Solid Modeler,” Ann. Nucl. Energy, 28, 125 (2001); http://dx.doi.org/10.1016/S0306-4549(00)00038-4.
   Google Scholar
• M. A. SMITH et al., “Method of Characteristics Development Targeting the High Performance Blue Gene/P Computer at Argonne National Laboratory,” Proc. M&C 2011, Rio de Janeiro, Brazil, May 8–12, 2011.
   Google Scholar
• X. YANG and N. SATVAT, “MOCUM: A Two-Dimensional Method of Characteristics Code Based on Constructive Solid Geometry and Unstructured Meshing for General Geometries,” Ann. Nucl. Energy, 46, 20 (2012); http://dx.doi.org/10.1016/j.anucene.2012.03.009.
   Google Scholar
• K. YAMAJI et al., “Simple and Efficient Parallelization Method for MOC Calculation,” J. Nucl. Sci. Technol., 47, 1, 90 (2010); http://dx.doi.org/10.1080/18811248.2010.9711931.
   Google Scholar
• K.-S. KIM and M. D. DeHART, “Unstructured Partial- and Net-Current Based Coarse Mesh Finite Difference Acceleration Applied to the Extended Step Characteristics Method in NEWT,” Ann. Nucl. Energy, 38, 2–3, 527 (2011); http://dx.doi.org/10.1016/j.anucene.2010.09.011.
   Google Scholar
• A. HEBERT, Applied Reactor Physics, 2nd ed., Presses Internationales Polytechnique, Montreal, Canada, ISBN 978-2-553-01698-1 (2016).
   Google Scholar
• K. S. SMITH and J. D. RHODES III, “Full Core, 2D LWR Core Calculation with CASMO-4E,” Proc. PHYSOR 2002, Seoul, Korea, October 7–10, 2002.
   Google Scholar
• R. SANCHEZ et al., “APOLLO2 Year2010,” Nucl. Eng. Technol., 42, 5, 474 (2010).
   Web of Science ®Google Scholar
• H. GOLFIER et al., “APOLLO3: A Common Project of CEA, AREVA and EDF for the Development of a New Deterministic Multi-Purpose Code for Core Physics Analysis,” Proc. M&C 2009, Saratoga Springs, New York, May 3–7, 2009.
   Google Scholar
• D. SCHNEIDER et al., “APOLLO3®: CEA/DEN Deterministic MultiPurpose Code for Reactor Physics Analysis,” Proc. PHYSOR 2016, Sun Valley, Idaho, May 1–5, 2016, American Nuclear Society (2016).
   Google Scholar
• E. BRUN et al., “TRIPOLI-4®, CEA, EDF and AREVA Reference Monte Carlo Code,” Ann. Nucl. Energy, 82, 151 (2015); http://dx.doi.org/10.1016/j.anucene.2014.07.053.
   Google Scholar
• S. SANTANDREA and R. SANCHEZ, “Analysis and Improvements of the DPN Acceleration Technique for the Method of Characteristics in Unstructured Meshes,” Ann. Nucl. Energy, 32, 163 (2005); http://dx.doi.org/10.1016/j.anucene.2004.08.011.
   Google Scholar
• S. SANTANDREA et al., “Improvements and Validation of the Linear Characteristics Scheme,” Ann. Nucl. Energy, 36, 1, 46 (2009); http://dx.doi.org/10.1016/j.anucene.2008.10.007.
   Google Scholar
• G. GUNOW et al., “Reducing 3D MOC Storage with Axial on the Fly Ray Tracing,” Proc. PHYSOR 2016, May 1–5, 2016, Sun Valley, Idaho, American Nuclear Society (2016).
   Google Scholar
• R. SANCHEZ, L. MAO, and S. SANTANDREA, “Treatment of Boundary Conditions in Trajectory Based Deterministic Transport Methods,” Nucl. Sci. Eng., 140, 23 (2002); http://dx.doi.org/10.13182/NSE140-23.
   Google Scholar
• W. BOYD et al., “Parallel Performance Results for the OpenMOC Neutron Transport Code on Multicore Platforms,” Int. J. High Perform. Comput. Appl., 30, 360 (2016); http://dx.doi.org/10.1177/1094342016630388.
   Google Scholar
• S. MOUSTAFA et al., “Vectorization of a 2D–1D Iterative Algorithm for the 3D Neutron Transport Problem in Prismatic Geometries,” Proc. Joint Int. Conf. Supercomputing in Nuclear Applications and Monte Carlo 2013 (SNA+MC 2013), Paris, France, October 27–31, 2013.
   Google Scholar
• L. ADAMS and E. LARSEN, “Fast Iterative Methods for Discrete Ordinates Particle Transport Calculations,” Prog. Nucl. Energy, 40, 1, 3 (2002); http://dx.doi.org/10.1016/S0149-1970(01)00023-3.
   Google Scholar
• S. SANTANDREA, “An Integral Multi-Domain DPN Operator as Acceleration Tool for the Method of Characteristics in Unstructured Meshes,” Nucl. Sci. Eng., 155, 2, 223 (2007); http://dx.doi.org/10.13182/NSE155-223.
   Google Scholar
• Y. SAAD, Iterative Methods for Sparse Linear Systems, PWS Publishing Company, Boston, Massachusetts (1996).
   Google Scholar
• M. L. ADAMS and W. R. MARTIN, “Boundary Projection Acceleration: A New Approach to Synthetic Acceleration of Transport Calculations,” Nucl. Sci. Eng., 100, 3, 177 (1988); http://dx.doi.org/10.13182/NSE100-177.
   Google Scholar
• A. PREVITI, “Fast and Accurate Numerical Solutions in Some Problems of Particle and Radiation Transport: Synthetic Acceleration for the Method of Short Characteristics, Doppler-Broadened Scattering Kernel, Remote Sensing of the Cryosphere,” PhD Thesis, Università di Bologna (2014).
   Google Scholar
• G. RIMPAULT et al., “Algorithmic Features of the ECCO Cell Code for Treating Heterogeneous Fast Reactor Subassemblies,” Int. Topl. Mtg. Reactor Physics and Computations, Portland, Oregon, May 1–5, 1995.
   Google Scholar
• M. N. NIKOLAEV, “Comments on the Probability Table Method,” Nucl. Sci. Eng., 61, 286 (1976); http://dx.doi.org/10.13182/NSE61-286.
   Google Scholar
• L. MAO, “Subgroup Method in the APOLLO3® Self-Shielding Calculations,” Technical Report RT/11-5242, CEA (2011).
   Google Scholar
• M. L. WILLIAMS, “Correction of Multigroup Cross Sections for Resolved Resonance Interference in Mixed Absorbers,” Nucl. Sci. Eng., 83, 37 (1983); http://dx.doi.org/10.13182/NSE83-2.
   Google Scholar
• P. MOSCA, “Conception et développement d’un mailleur énergétique adaptatif pour la génération des bibliothèques multi-groupes des codes de transport,” PhD Thesis, Paris-Sud (2009).
   Google Scholar
• P. RIBON and J.-M. MAILLARD, “Les tables de probabilité: application au traitement des sections efficaces pour la neutronique,” Technical Report CEA-N-2485, CEA (1986). See also as public reference: P. RIBON and J.-M. MAILLARD, “Probability Tables and Gauss Quadrature; Application to Neutron Cross-Sections in the Unresolved Energy Range,” Proc. Topl. Mtg. Advances in Reactor Physics and Safety, Saratoga Springs, New York, September 17–19, 1986.
   Google Scholar
• M. COSTE-DELCLAUX, “GALILEE: A Nuclear Data Processing System for Transport Depletion and Shielding Codes,” Proc. PHYSOR 2008, Interlaken, Switzerland, September 14–19, 2008.
   Google Scholar
• T. TONE, “A Numerical Study of Heterogeneity Effects in Fast Reactor Critical Assemblies,” J. Nucl. Sci. Technol., 12, 8, 467 (1975); http://dx.doi.org/10.1080/18811248.1975.9733139.
   Google Scholar
• L. MAO, I. ZMIJAREVIC, and R. SANCHEZ, “Resonance Self-Shielding Treatments in Fast Reactor Calculation—Comparison of a New Tone’s Method to the Subgroup Method in APOLLO3,” Nucl. Sci. Eng. ( accpeted for publication).
   Google Scholar
• M. ISHIKAWA, “Consistency Evaluation of JUPITER Experiment and Analysis for Large FBR Cores,” Proc. PHYSOR 96, Mito, Japan, September 16–20, 1996, Vol. 2, p. E-36 ( 1996).
   Google Scholar
• A. M. WEINBERG and E. P. WIGNER, The Physical Theory of Neutron Chain Reactors, University of Chicago Press, Chicago, Illinois (1958).
   Google Scholar
• H. YU, T. ENDO, and A. YAMAMOTO, “Resonance Calculation for Large and Complicated Geometry Using Tone’s Method by Incorporating the Method of Characteristics,” J. Nucl. Sci. Technol., 48, 3, 330 (2011); http://dx.doi.org/10.1080/18811248.2011.9711707.
   Google Scholar
• R. SANCHEZ and N. J. McCORMICK, “A Review of Neutron Transport Approximations,” Nucl. Sci. Eng., 80, 481 (1982); http://dx.doi.org/10.13182/NSE80-04-481.
   Google Scholar
• R. J. J. STAMM’LER and M. J. ABBATE, Methods of Steady State Reactor Physics in Nuclear Design, Academic Press, London, United Kingdom (1983).
   Google Scholar
• G. CHIBA, “A Combined Method to Evaluate the Resonance Self-Shielding Effect in Power Fast Reactor Fuel Calculation,” J. Nucl. Sci. Technol., 40, 7, 537 (2003); http://dx.doi.org/10.1080/18811248.2003.9715389.
   Google Scholar
• C. R. CALABRESE and C. GRANT, “HUEMUL: A Two-Dimensional Multigroup Collision Probability Code for General Geometries,” Ann. Nucl. Energy, 18, 2, 63 (1991); http://dx.doi.org/10.1016/0306-4549(91)90064-5.
   Google Scholar
• R. SANCHEZ, “Approximate Solutions of the Two-Dimensional Integral Transport Equation by Collision Probability Methods,” Nucl. Sci. Eng., 64, 2, 384 (1977); http://dx.doi.org/10.13182/NSE64-384.
   Google Scholar
• R. SANCHEZ, “Les Options TDT Du Code APOLLOII,” Internal Technical Report CEA/SERMA (2000).
   Google Scholar
• D. ALTIPARMAKOV and R. WIERSMA, “The Collision Probability Method in Today’s Computer Environment,” Nucl. Sci. Eng., 182, 395 (2016); http://dx.doi.org/10.13182/NSE15-28.
   Google Scholar
• P. ARCHIER et al., “Validation of the Newly Implemented 3D TDT-MOC Solver of APOLLO3® Code on a Whole 3D SFR Heterogeneous Assembly,” Proc. PHYSOR 2016, Sun Valley, Idaho, May 1–5, 2016, American Nuclear Society (2016).
   Google Scholar
• L. C. PIERRE, J.-F. SAUVAGE, and J.-P. SERPANTIE, “Sodium-Cooled Fast Reactors: The Astrid Plant Project,” Proc. ICAPP 2011, Nice, France, May 2–6, 2011.
   Google Scholar
• G. RIMPAULT et al.,“The ERANOS Code and Data System for Fast Reactor Neutronic Analyses,” Proc. PHYSOR 2002, Seoul, South Korea, October 7–10, 2002.
   Google Scholar
• D. SCIANNANDRONE, “Acceleration and Higher Order Schemes of a Characteristic Solver for the Solution of the Neutron Transport Equation in 3D Axial Geometries,” PhD Thesis, Orsay (Oct. 2015).
   Google Scholar
• D. SCIANNANDRONE et al., “Coupled Fine-Group Three-Dimensional Flux Calculation and Subgroups Method for a FBR Hexagonal Assembly with the APOLLO3® Core Physics Analysis Code,” Proc. M&C+SNA+MC 2015, Nashville, Tennessee, April 19–23, 2015.
   Google Scholar
• P. MOSCA et al., “Improvements in Transport Calculations by the Energy-Dependent Fission Spectra and Subgroup Method for Mutual Self-Shielding,” Nucl. Sci. Eng., 175, 266 (2013); http://dx.doi.org/10.13182/NSE12-63.
   Google Scholar
• M. SALVATORES and G. PALMIOTTI, “Methods and Issues for the Combined Use of Integral Experiments and Covariance Data,” NEA/NSC/WPEC/DOC(2013)445, Organisation for Economic Co-operation and Development/Nuclear Energy Agency (2013).
   Google Scholar
• S. SANTANDREA, R. SANCHEZ, and P. MOSCA, “A Linear Surface Characteristics Approximation for Neutron Transport in Unstructured Meshes,” Nucl. Sci. Eng., 160, 23 (2008); http://dx.doi.org/10.13182/NSE07-69.
   Google Scholar
• R. SANCHEZ and S. SANTANDREA, “Convergence Analysis for the Method of Characteristics in Unstructured Meshes,” Nucl. Sci. Eng., 183, 2, 196 (2016); http://dx.doi.org/10.13182/NSE15-78.
   Google Scholar