Nuclear Engineering and Technology

  • 제44권2호
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  • Pages.113-150
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  • 2012
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  • 1738-5733(pISSN)
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  • 2234-358X(eISSN)
한국원자력학회 (Korean Nuclear Society)
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PROSPECTS IN DETERMINISTIC THREE-DIMENSIONAL WHOLE-CORE TRANSPORT CALCULATIONS

  • Sanchez, Richard (Commissariat a l'Energie Atomique et aux Energies Alternatives Direction de l'Energie Nucleaire Service d.Etudes de Reacteurs et de Mathematiques Appliquees)
  • 투고 : 2011.03.23
  • 심사 : 2012.02.12
  • 발행 : 2012.03.25
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초록

The point we made in this paper is that, although detailed and precise three-dimensional (3D) whole-core transport calculations may be obtained in the future with massively parallel computers, they would have an application to only some of the problems of the nuclear industry, more precisely those regarding multiphysics or for methodology validation or nuclear safety calculations. On the other hand, typical design reactor cycle calculations comprising many one-point core calculations can have very strict constraints in computing time and will not directly benefit from the advances in computations in large scale computers. Consequently, in this paper we review some of the deterministic 3D transport methods which in the very near future may have potential for industrial applications and, even with low-order approximations such as a low resolution in energy, might represent an advantage as compared with present industrial methodology, for which one of the main approximations is due to power reconstruction. These methods comprise the response-matrix method and methods based on the two-dimensional (2D) method of characteristics, such as the fusion method.

키워드

참고문헌

  1. Worshop on High end computing for nuclear fission science and engineering (http://www.inl.gov/cams/ workshops/ highendcomputing), Salt Lake City, Salt Lake, USA, Feb. 23-24, 2005.
  2. R. Sanchez, I. Zmijarevic, M. Coste-Delclaux, E. Masiello, S. Santandrea, E. Martinolli, L. Villate, N. Schwartz and N. Guler, "APOLLO2 year 2010," Nucl. Eng. and Technology, 42,474-499, 2010. https://doi.org/10.5516/NET.2010.42.5.474
  3. R. Sanchez and G.C. Pomraning, "A statistical analysis of the double heterogeneity problem," Ann. Nucl. Energy, 18, 371-, 1991. https://doi.org/10.1016/0306-4549(91)90073-7
  4. R. Sanchez, "Renormalized treatment of the double heterogeneity with the method of characteristics," Proc. Int. Conf. The Physics of Fuel Cycles and Advanced Nuclear Systems (PHYSOR 2004), Chicago, IL, USA, April 25-29, 2004.
  5. K.S. Smith and J.D. Rhodes, "CASMO-4 characteristic method for two-dimensional PWR and BWR core calculations," Trans. Am. Nucl. Soc., 83, 294, 2000.
  6. K.S. Smith and J.D. Rhodes, III, "Full-Core, 2-D, LWR Core Calculations with CASMO-4E," Proc. Int. Conf. on Reactor Physics Safety and High-Performance Computing (PHYSOR 2002), Seoul, Korea, 7-10 October, 2002.
  7. N.Z. Cho, G.S. Lee, S.G. Hong, C.K. Jo and K.T. Lee, "Whole-Core heterogeneous transport calculations and their comparisons with diffusion results," Trans. Am. Nucl. Soc., 83, 292, 2000.
  8. J-Y. Cho, K-S. Kim, H-J. Shim, J-S. Song, C-C. Lee and H-G. Joo, "Whole Core Transport Calculation Employing Hexagonal Modular Ray Tracing and CMFD Formulation," Journal of Nucl. Sci. and Technology, 45, 740-751, 2008 https://doi.org/10.3327/jnst.45.740
  9. V.N. Kucukboyaci, M. Ouisloumen, and F. Franceschini, "Two-Dimensional Whole Core Transport calculations using PARAGON," Proc. Int. Conf. on Mathematics, Computational Methods & Reactor Physics (M&C 2009), Saratoga Springs, New York, May 3-7, 2009.
  10. N. Huot, A. Aggery, D. Blanchet, C. D'Aletto, J. Di Salvo, C. Döder-lein1, P. Sireta1 and G. Willermoz2, "The JHR Neutronics Calculation Scheme Based on the Method of Characteristics," Proc. Int. Top. Mtg. on Mathematics and Computation, Supercomputing, Reactor Physics and Nuclear and Biological Applications (M&C 2005), Avignon, France, Sept 12-15, 2005.
  11. S. Santandrea, R. Sanchez and P. Mosca, "A linear surface characteristics scheme for neutron transport in unstructured meshes," Nuc. Sci. Eng. 160, 22, 2008.
  12. H.G. Joo, J.Y. Cho, Kim, C.C. Lee and S.Q. Zee, "Methods and Performance of a Three-Dimensional Whole-Core Transport Code De-CART," Proc. Int. Conf. on the Physics of Fuel Cycles and Advanced Nuclear Systems (PHYSOR 2004), Chicago, IL, USA, April 25-29,2004.
  13. D. Zhang and F. Rahnema, "An Efficient Hybrid Stochastic /Deterministic Coarse Mesh Neutron Transport Method," Ann. Nucl. Energy, 41, 1-11, 2012. https://doi.org/10.1016/j.anucene.2011.09.024
  14. N.Z. Cho, 'Fundamentals and recent developments of reactor physics methods,' Nucl. Eng. and Technology, 37 (1), 25-78, 2005.
  15. E.E. Lewis, C.B. Carrico and G. Palmiotti, "Variational Nodal Formulation for the Spherical Harmonics Equations," Nucl. Sci. Eng., 122, 194, 1996. https://doi.org/10.13182/NSE96-1
  16. E.E. Lewis, M.A. Smith and G. Palmiotti, "Three-dimensional neutron transport with novel local.global coupling," Proc. Int. Conf. on the Physics of Reactors "Nuclear Power: A Sustainable Resource," Casino-Kursaal Conference Center, Interlaken, Switzerland, Septem-ber 14-19, 2008.
  17. E.E. Lewis, M.A. Smith and G. Palmiotti, "A New Paradigm for Local-Global Coupling in Whole Core Neutron Transport," Nucl.Sci.Eng. 161, 2791, 2009.
  18. M. Eaton, C.C. Pain, C.R.E. de Oliveira and A. Goddard, 'A High-Order Riemann Method for the Boltzmann Transport Equation,' Proc. Int. Top. Mtg. on Nuclear Mathematical and Computational Sciences: A Century in Review, a Century Anew (M&C 2003), Gatlinburg, Tennessee, April 6-11, 2003.
  19. W.J.Martin, C.R.E. de Oliveira and H. Park, "Nonlinear acceleration methods for even-parity neutron transport," Proc. Int. Conf. on Advances in Reactor Physics to Power the Nuclear Renaissance (PHYSOR 2010), Pittsburgh PA, USA, May. 9-14, 2010.
  20. http://amcg.ese.ic.ac.uk/index.php?title= Radiation_ Transport.
  21. M.A. Jessee and C.E. Yehnert, "Interpolation Methods and Splice Options for Three-Dimensional Transport Calculations Using PARTISN," Proc. Joint Int. Top. Mtg. on Mathematics & Computation and Supercomputing in Nuclear Applications (M&C + SNA 2007), Monterey, CA, USA, April 15-19, 2007.
  22. http://www.ccs.lanl.gov/ccs4/projects.shtml.
  23. G.E. Sjoden and A. Haghighat, "PENTRAN - Parallel Environment Neutral Particle TRANsport in 3-D Cartesian Geometry," Proc. Int. Conf. on Mathematics, Computational Methods & Reactor Physics (M&C 2009), Saratoga Springs, New York, May 3-7, 2009.
  24. http://hswtech.com/Pentran.htm.
  25. I. Zmijarevic, "Multidimensional Discrete Ordinates Nodal and Characteristics Methods for APOLLO2 Code," Proc. Int. Conf. on Mathematics and Computation, Reactor Physics and Environmental Analysis in Nuclear Applications (M&C'99), Madrid, Spain, Sept. 27-30, 1999.
  26. I. Zmijarevic, "IDT solution to the 3D transport benchmark over a range in parameter space," Proc. Int. Conf. on Physics of Reactors, "Nuclear Power: A Sustainable Resource," (PHYSOR 2008), Interlaken, Switzerland, Sept. 14.19, 2008.
  27. I.R.Suslov, O.G.Komlev, N.N.Novikova, E.A.Zemskov, I.V.Tormyshev, K.G.Mel'nikov and E.B.Sidorov, "Method of the Characteristics for Calculation of VVER Without Homogenization," Proc. Int. Top. Mtg. on Mathematics and Computation, Supercomputing, Reactor Physics and Nuclear and Biological Applications (M&C 2005), Avignon, France, Sept 12-15, 2005.
  28. N. Martin, A. Hebert and G. Marleau, 'DRAGON solutions to the 3D transport benchmark over a range in parameter space,' Ann. Nucl. Energy, 37, 1107.1114, 2010. https://doi.org/10.1016/j.anucene.2010.04.003
  29. S.T. Keller, T.S. Palmer and T. A. Wareing, "Modeling a TRIGA Mark II Reactor Using the AttilaTM Three-Dimensional Deterministic Transport Code," Proc. Int. Top. Mtg. on Mathematics and Computation, Supercomputing, Reactor Physics and Nuclear and Biological Applications (M&C 2005), Avignon, France, Sept 12-15, 2005.
  30. http://www.transpireinc.com/Software/Attila.aspx.
  31. J-Y. Moller and J-J. Lautard, "MINARET, a Deterministic Neutron Transport Solver for Nuclear Core Applications," Proc. Int. Conf. on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C 2011), Rio de Janeiro, RJ, Brazil, May 8-12, 2011.
  32. G. Palmiotti, M. Smith, C. Rabiti, M. Leclere, D. Kaushik, A. Siegel, B. Smith and E. E. Lewis, "UNÌC: Ultimate Neutronic Investigation Code." Proc. Joint Int. Top. Mtg. on Mathematics & Computation and Supercomputing in Nuclear Applications (M&C + SNA 2007), Monterey, CA, USA, April 15-19, 2007.
  33. M.A. Smith, D. K'aushik, A. Wollaber, W.S. Yang, B. Smith, C. Rabiti and G. Palmiotti, "Recent Research Progress on UNIC at Argonne National Laboratory," Proc. Int. Conf. on Mathematics, Computational Methods & Reactor Physics (M&C 2009), Saratoga Springs, New York, May 3-7, 2009.
  34. W.S. Yang, M.A. Smith, C.H. Lee, A. Wollaber, D. Kausshik and A.S. Mohamed, "Neutronic Modeling and Simulation of SHARP for Fast Reactor Analysis," Nucl. Eng. and Technology, 42,520-545, 2010. https://doi.org/10.5516/NET.2010.42.5.520
  35. D. Kaushi, M. Smith, A. Wollaber, B. Smith, A. Siegel and W.S. Yang, "Enabling High Fidelity Neutron Transport Simulations on Petascale Architectures," Proc. Int. Conf. on High Performance Computing Networking, Storage and Analysis (SC 09), Portland, Oregon, Nov. 14-20, 2009.
  36. T. Takeda and H. Ikeda, "3-D Neutron transport benchmarks," OECD/NEA Committee on Reactor Physics, NEACRP-L-330, 1991.
  37. M.A. Smith, E.E. Lewis and B. C. Na, "Benchmark on Deterministic Transport Calculation without Spatial Homogenization: MOX Fuel Assembly 3-D extension case," OECD/NEA report, NEA/NSC/DOC (2005)16, 2005.
  38. S. Douglass, F. Rahnema and J. Margulies, "A stylized three dimensional PWR whole-core benchmark problem with Gadolinium," Ann. Nucl. Energy, 37, 1384-403, 2010. https://doi.org/10.1016/j.anucene.2010.01.015
  39. F. Rahnema, S. Douglass and R. Hon, "A stylized 3-Dimensional Pressurized Water Reactor Benchmark Problem with UO2 and MOX Fuel," Nuclear Technology, submitted November 2011.
  40. J.M. Pounders, F. Rahnema, D. Serghiuta and J. Tholammakkil, "A 3D stylized half-core CANDU benchmark problem," Ann. Nucl. Energy, 38, 876-896, 2011. https://doi.org/10.1016/j.anucene.2010.10.018
  41. J.M. Pounders, F. Rahnema and D. Serghiuta, "Analysis of a multigroup stylized CANDU half-core benchmark," Ann. Nucl. Energy, 38, 2024-2078, 2011. https://doi.org/10.1016/j.anucene.2011.03.011
  42. G.I. Bell and S. Glasstone, Nuclear Reactor Theory, Van Nostrand Rein-hold, New York, 1970.
  43. R. Sanchez and J. Ragusa, "On the Construction of Galerkin Angular Quadratures," Nuc. Sci. Eng. 169, 133-154, 2011. https://doi.org/10.13182/NSE10-31
  44. L. Mao, R. Sanchez, I. Zmijarevic and Z. Stankovski, "RZ calculations for selfshielded multigroup cross sections," Proc. Int. Conf. Advances in Nuclear Analysis and Simulation (PHYSOR 2006), Vancouver B.C., Canada, Sept. 10-14, 2006.
  45. M. Ouisloumen and R. Sanchez, "A model for neutron scattering off heavy isotopes that accounts for thermal agitation effects," Nucl. Sci. Eng., 107, 189-, 1991. https://doi.org/10.13182/NSE89-186
  46. R. Dagan, J. Rowlands, A. Courcelle and C.R. Lubitz, "On the treatment of neutron scattering in the resonance range," Proc. Int. Conf. on Nuclear Data for Science and Technology, Nice, France, April 22-27, 2007.
  47. Y. Danon, E. Liu, D.P. Barry, T.I. Rio and R. Dagan, "Benchmark experiment of neutron resonance scattering models in Monte Carlo," Proc. Int. Conf. on Mathematics, Computational Methods & Reactor Physics (M&C 2009), Saratoga Springs, New York, May 3-7, 2009.
  48. C. J. Dean, R. J. Perry, "Weighting spectra for the Xmas group scheme," Winfrith Technology Center, 1990.
  49. J.F. Vidal, O. Litaize, D. Bernard, A. Santamarina and C. Vaglio-Gaudard, "New modelling of LWR assemblies using the APOLLO2 code package," Proc. Joint Int. Top. Mtg. on Mathematics & Computation and Supercomputing in Nuclear Applications (M&C + SNA 2007), Monterey, CA, USA, April 15-19, 2007.
  50. J. M. Del Grande and K. Mathews, "Nonnegative Anisotropic Group Cross Sections: A Hybrid Monte Carlo-Discrete Elements-Discrete Ordinates Approach", Nucl. Sci. Eng., 139, 33-46, 2001. https://doi.org/10.13182/NSE00-69
  51. D. Gerts and K. Mathews, "Non-negative Anisotropic Piecewise-Average Multigroup Cross Sections", Proc. Int. Top. Mtg. on Nuclear Mathematical and Computational Sciences: A Century in Review, a Century Anew (M&C 2003), Gatlinburg, Tennessee, April 6-11, 2003.
  52. R. Sanchez and N.J. McCormick, 'Discrete ordinate solutions for highly forward peaked scattering,' Nucl. Sci. Eng., 147, 249-274, 2004. https://doi.org/10.13182/NSE04-A2432
  53. A. Calloo, J. F. Vidal, R. Le Tellier, G. Rimpault, "Angular finite volume method for solving the multigroup transport equation with piecewise average scattering cross sections," Proc. Int. Conf. on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C 2011), Rio de Janeiro, RJ, Brazil, May 8-12, 2011.
  54. A. Calloo, "Developpement d'une nouvelle modelisation de la loi de choc dans les codes de transport neutronique multigroupes : application au calcul des réacteurs de Generations III et IV," Ph.D. thesis (in French), in preparation, 2012.
  55. R. Sanchez, personal communication, 2009.
  56. N.Z. Cho and L. Cao, "Wavelet-theoretic method for solution of neutron transport," Trans. of the Korean Nuclear Society, Spring Meeting, Chuncheon, Korea, May 25-26,.2006.
  57. L. Cao, H. Wu and Y. Zheng, "Solution of neutron transport equation using Daubechies. wavelet expansion in the angular discretization," Ann. Nucl. Energy, 36, 1013-1020, 2009. https://doi.org/10.1016/j.anucene.2009.06.007
  58. R. Sanchez , L. Mao and S. Santandrea, "Treatment of Boundary conditions in trajectory Based Deterministic Transport Methods", Nucl. Sci. Eng. 140, 23, 2002. https://doi.org/10.13182/NSE140-23
  59. V.I. Lebedev, 'Quadratures on a sphere,' Zh. Vychisl. Mat. Mat. Fiz. 16, 293-306, 1976.
  60. V.I. Lebedev and D.N. Laikov, 'A quadrature formula for the sphere of the 131st algebraic order of accuracy,' Dokl. Math. 59, 477.481 (transl. Dokl. Akad. Nauk 1999 36, 741-745), 1999.
  61. S.L. Sobolev, 'Cubature formulas and modern analysis,' Philadelphia, PA: Gordon and Breach Science Publishers, 1992.
  62. C. Ahrens and G. Beylkin, 'Rotationally invariant quadratures for the sphere,' Proc. R. Soc. A, 465, 3103-3125, 2009. https://doi.org/10.1098/rspa.2009.0104
  63. J.-Y. Moller, "Elements finis courbes et accélération pour l'equation du transport," Ph.D. thesis (in French), Universite Henri Poincare, Nancy, France, Jan. 10, 2012.
  64. A. Yamamoto, 'Reduction in spatial discretization error in the method of characteristics by using the mobile-chord ray tracing method,' Nucl. Engineering and Design 238, 2292-2301, 2008. https://doi.org/10.1016/j.nucengdes.2008.03.003
  65. R. Sanchez, 'Numerical methods for the solution of the onegroup linear transport equation in unstructured meshes I: Interface current methods,' Lectures, Frederique Joliot - Otto Hann Summer School, Karlsruhe, Germany, August, 1999.
  66. R. Sanchez and S. Santandrea, "Convergence analysis for the method of characteristics in unstructured meshes," Proc. Int. Conf. on Mathematics, Computational Methods & Reactor Physics (M&C 2009), Saratoga Springs, New York, May 3-7, 2009.
  67. S. Kosada and E. Saji, "Transport theory calculation of a heterogeneous multi-assembly problem by characteristic methods by direct neutron path linking technique,"Journal of Nucl. Sci. and Technology, 37, 1015-1023, 2000. https://doi.org/10.3327/jnst.37.1015
  68. F. Fevotte, S. Santandrea and R. Sanchez, "Tracking on Periodic Lattices for the Method of Characteristics," Proc. Int. Conf. on the Physics of Reactors "Nuclear Power: A Sustainable Resource," Casino-Kursaal Conference Center, Interlaken, Switzerland, September 14-19, 2008.
  69. C. Tag and S. Zhang, 'Development and verification of an MOC code employing assembly modular ray tracing and efficient acceleration techniques,' Ann. Nucl. Energy, 36, 1013-1020, 2009. https://doi.org/10.1016/j.anucene.2009.06.007
  70. F. Fevotte, S. Santandrea and R. Sanchez, "Advanced Transverse Integration for the Method of Characteristics," Proc. Joint Int. Top. Mtg. on Mathematics & Computation and Supercomputing in Nuclear Applications (M&C + SNA 2007), Monterey, CA, USA, April 15-19, 2007.
  71. J.J. Duderstadt and W.R. Martin, Transport Theory, John Wiley and Sons, New York, 1979.
  72. E.J. Allen, "A finite element approach for treating the energy variable in the numerical solution of the neutron transport equation," Transport Theory and Statistical Physics, 15, 449-478, 1986. https://doi.org/10.1080/00411458608212681
  73. P. Mondot and R. Sanchez, "An iterative homogenization technique that preserves assembly core exchanges," Proc. Int. Conf. on Supercomputing in Nuclear Applications, SNA 2003, Paris, France, Sept. 22-24, 2003.
  74. V. Kulik and R. Sanchez, "Core Homogenization Method for Pebble Bed Reactors," Proc. Int. Top. Mtg. on Mathematics and Computation, Supercomputing, Reactor Physics and Nuclear and Biological Applications (M&C 2005), Avignon, France, Sept 12-15, 2005.
  75. M. Grimod, R. Sanchez and F. Damian, "Neutronic modeling for pebble bed reactors," Proc. Int. Top. Mtg. on Mathematics, Computational Methods and Reactor Physics (M&C 2009), Saratoga Spring, NY, May 3-7, 2009.
  76. M. Grimod, "Neutronic modeling of pebble bed reactors in APOLLO2," Ph.D. thesis, Universite de Paris Sud XI, France, 7 Dec., 2010.
  77. F. Rahnema, S. Douglass and B. Forget, "Generalized energy condensation theory," Nucl. Sci. Eng., 160, 41-58, 2008. https://doi.org/10.13182/NSE160-41
  78. S. Douglass and F. Rahnema, "Consistent generalized energy condensation theory," Ann. Nucl. Energy, in press, September, 2011.
  79. L. Zhu and B. Forget, "A discrete generalized multigroup energy expansion theory," Nucl. Sci. Eng., 166, 239-253, 2010. https://doi.org/10.13182/NSE09-84
  80. L. Zhu and B. Forget, "An energy recondensation method using the discrete generalized multigroup energy expansion theory," Ann. Nucl. En-ergy, 38, 1718-1727, 2011. https://doi.org/10.1016/j.anucene.2011.04.008
  81. J.H. Wong and N.Z. Cho, "Discrete ordinates method-like transport computation with equivalent group condensation and angle-collapsing for local/global iteration," Ann. Nucl. Energy, 38, 846-852, 2011. https://doi.org/10.1016/j.anucene.2010.11.012
  82. S. Douglas and F. Rahnema, "Cross section recondensation method via generalized energy condensation theory," Ann. Nucl. Energy, 38, 2105-2110, 2011. https://doi.org/10.1016/j.anucene.2011.04.019
  83. M.Moriwaki, K. Ishii, H. Maruyama andM. Aoyama, "A new direct calculation of response matrices using a Monte Carlo calculation," Journal of Nucl. Sci. and Technology, 36, 877-887, 1999. https://doi.org/10.1080/18811248.1999.9726278
  84. T. Hino, K. Ishii, T. Mitsuyasu and M. Aoyama, "Development of core analysis method using three-dimensional direct response matrix," Proc. Int. Conf. on the Physics of Reactors "Nuclear Power: A Sustainable Resource," Casino-Kursaal Conference Center, Interlaken, Switzerland, September 14-19, 2008.
  85. T. Mitsuyasu, K. Ishii, T. Hino and M. Aoyama, "Development of spectral history methods for pin-by-pin core analysis method using three-dimensional direct response matrix," Proc. Int. Conf. on Mathematics, Computational Methods & Reactor Physics (M&C 2009), Saratoga Springs, New York, May 3-7, 2009.
  86. D. Has and F. Rahnema, "A heterogeneous coarse mesh transport solution," Transport Theory and Statistical Physics, 32, 445-471, 2003. https://doi.org/10.1081/TT-120025062
  87. S.W. Mosher and F. Rahnema, "The incident flux response expansion method for heterogeneous coarse mesh transport problems," Transport Theory and Statistical Physics, 35, 55-86, 2006. https://doi.org/10.1080/00411450600878615
  88. B. Forget and F. Rahnema, "Comet solutions to the 3-D C5G7 MOX benchmark problem," Progress in Nuclear Energy, 48, 467-475, 2006. https://doi.org/10.1016/j.pnucene.2006.01.005
  89. J.M. Pounders and F. Rahnema, "A response-based timedependent neutron transport method," Ann. Nucl. Energy, 37, 1595-1600, 2010. https://doi.org/10.1016/j.anucene.2010.03.010
  90. J.M. Pounders and F. Rahnema, "A Deterministic-Monte Carlo Hybrid Method for Time-Dependent Neutron Transport Problems," Proc. Joint Int. Conf. on Supercomputing in Nuclear Applications and Monte Carlo, Hitotsubashi Memorial Hall, Tokyo, Japan, October 17-21, 2010.
  91. D. Zhang and F. Rahnema, "A heterogeneous coarse mesh method for coupled photon electron transport problems," Transport Theory and Statistical Physics, accepted for publication, July, 2011.
  92. D. Zhang , F. Rahnema, A. Ougouag and F. Gleicher, "Local Response-Function-Based Transport Method for Diffusion-Transport Hybrid Calculations in Pebble Bed Reactors," Proc. HTR 2010, Prague, Czech Republic, October 18-20, 2010.
  93. D. Zhang, F. Rahnema and A. Ougouag, "Local transport method for hybrid diffusion-transport calculations in 2D (r, theta) geometry," Proc. Int. Conf. on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C 2011), Rio de Janeiro, RJ, Brazil, May 8-12, 2011.
  94. D. Zhang and F. Rahnema, "Coarse mesh transport method for whole-core neutronics analysis in cylindrical geometry," Proc.17th Pacific Basin Nuclear Conference, Cancun, Q.R., Mexico, October 24-30, 2010.
  95. K.J. Connolly, F. Rahnema and D. Zhang, "Extension of the COMET method to 2-D hexagonal geometry," Proc. Int. Conf. on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C 2011), Rio de Janeiro, RJ, Brazil, May 8-12, 2011.
  96. D. Zhang and F. Rahnema, "COMET Whole-Core Solution to a stylized 3-Dimensional Pressurized Water Reactor Benchmark Problem with UO2 and MOX Fuel," Int. Conf. on Advances in Reactor Physics .Linking Research, Industry and Education (PHYSOR 2012), Knoxville, TN, USA, April 15-20, 2012, accepted, February 2012.
  97. D. Zhang and F. Rahnema, "Whole-Core COMET Solutions to a 3-Dimensional PWR Whole Core Benchmark Problem with Gadolinium," Int. Conf. on Advances in Reactor Physics - Linking Research, Industry and Education (PHYSOR 2012), Knoxville, TN, USA, April 15-20, 2012, accepted, February 2012.
  98. D. Zhang and F. Rahnema, "COMET Solutions to a Stylized BWR Benchmark Problem," Int. Conf. on Advances in Reactor Physics - Linking Research, Industry and Education (PHYSOR 2012), Knoxville, TN, USA, April 15-20, 2012, accepted, February 2012.
  99. N.Z. Cho, G.S. Lee, and C.J. Park, "A Fusion Technique of 2D/1D Meth-ods for Three-Dimensional Whole-Core Transport Calculations," Proc. Korean Nuclear Society, Kwangju, Korea, May 2002.
  100. 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., 86, 322, 2002.
  101. N.Z. Cho, G.S. Lee, and C.J. Park, "Three-dimensional Heterogeneous Whole Core Transport Calculation Employing Planar MOC Solutions," Trans. Am. Nucl. Soc., 87, 234, 2002.
  102. N.Z. Cho, G.S. Lee, and C.J. Park, "2-D and 3-D Whole- Core Transport Calculations of the OECD Benchmark Problem C5G7 MOX by CRX," Proc. Int. Conf. on Reactor Physics Safety and High-Performance Computing (PHYSOR 2002), Seoul, Korea, 7-10 October, 2002.
  103. S.G. Hong and N.Z. Cho, "CRX : A Code for Rectangular and Hexagonal Lattices Based on the Method of Characteristics," Ann. Nucl. Energy, 25, 547,1998. https://doi.org/10.1016/S0306-4549(97)00113-8
  104. S. Kosaka and T. Takeda, "Diffusion-like 3-D Heterogeneous Core Transport Calculation with 2-D characteristics transport correction by Non-Linear Iteration Technique," Proc. Int. Top. Mtg. on Nuclear Mathematical and Computational Sciences: A Century in Review, a Century Anew (M&C 2003), Gatlinburg, Tennessee, April 6-11, 2003.
  105. S. Kosaka and T. Takeda, "Verification of 3D Heterogeneous Core Transport Calculation Utilizing Non-Linear Iteration Technique," Journal of Nuclear Science and Technology, 41, 645-654, 2004. https://doi.org/10.3327/jnst.41.645
  106. J.Y. Cho and H.G. Cho, "Solution of the C5G7MOX Benchmark Three-Dimensional Extension Problems by the DeCART Direct Whole Core Calculation Code," Progress in Nuclear Energy, 48, 456, 2006. https://doi.org/10.1016/j.pnucene.2006.01.006
  107. G.S. Lee and N.Z. Cho, "2D/1D Fusion Method Solutions of the Three-Dimensional Transport OECD Benchmark Problem C5G7 MOX," Progress in Nuclear Energy, 48, 410-423, 2006. https://doi.org/10.1016/j.pnucene.2006.01.010
  108. J.Y. Cho, K.S. Kim, C.C. Lee, S.Q. Zee, and H.G. Joo, "Axial SPn and Radial MOC Coupled Whole Core Transport Calculation," Journal of Nucl. Sci. and Technology, 44, 1156-1171, 2007. https://doi.org/10.3327/jnst.44.1156
  109. S. G. Hong, K. S. Kang and J. S. Song, "Fourier Convergence Analysis of the Rebalance Methods for Discrete Ordinates Transport Equations in Eigenvalue Problems," Nucl. Sci. Eng., 164, 33, 2010. https://doi.org/10.13182/NSE09-18
  110. N. Z. Cho and C. J. Park, "A Comparison of Coarse Mesh Rebalance and Coarse Mesh Finite Difference Acceleration for the Neutron Transport calculations," Proc. Int. Top. Mtg. on Nuclear Mathematical and Computational Sciences: A Century in Review, a Century Anew (M&C 2003), Gatlinburg, Tennessee, April 6-11, 2003.
  111. J.Y. Cho, H.G. Yoo, S. Kim and S.Q. Zee, "Cell Based CMFD Formulation for Acceleration of Whole-Core Method of Characteristics Calculations," Journal of the Korean Nuclear Society, 34, 250, 2002.
  112. 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. 116
  113. N. Z. Cho, G. S. Lee and C. J. Park, "On a New Acceleration Method for 3D Whole-Core Transport Calculations," Annual Meeting of the Atomic Energy Society of Japan, Japan, March 2003.
  114. Y.R. Park and N. Z. Cho, "Coarse-mesh angular dependent rebalance acceleration of the discrete ordinates transport calculations," Nucl. Sci. Eng., 148, 355-373, 2004. https://doi.org/10.13182/NSE03-12
  115. Y. R. Park and N. Z. Cho, "Coarse-Mesh Angular Dependent Rebalance Acceleration of the Method of Characteristics in x-y Geometry," Nucl. Sci. Eng., 158, 154, 2008. https://doi.org/10.13182/NSE06-23
  116. S. Santandrea, personal communication, Sept. 2011.
  117. E. Masiello, R. Clemente and S. Santandrea, "High Order Method of Characteristics for 2-D Unstructured Meshes," Proc.Int.Conf.on Mathematics, Computational Methods & Reactor Physics (M&C 2009), Saratoga Springs, NY, USA, May 3-7, 2009.
  118. F. Fevotte, "Techniques de tracage pour la methode des caracteristiques appliquee a la resolution de l.equation du transport des neutrons en domaines multidimensionnels," Ph.D. Thesis (in French) , Universitw Paris Sud 11, 2008.
  119. Z. Liu, H. Wu, L. Cao, Q. Chen and Y. Li, "A new threedimensional method of characteristics for the neutron transport calculation," Annals of Nucl. Energy, 38, 447-454, 2011. https://doi.org/10.1016/j.anucene.2010.09.021
  120. A. Yamamoto, "Convergence Property of Response Matrix Method for Various Finite-Difference Formulations Used in the Nonlinear Acceleration Method," Nucl. Sci. Engineering, 149, 259-269, 2005. https://doi.org/10.13182/NSE05-A2492
  121. A. Yamamoto, "Generalized Coarse-Mesh Rebalance Method for Acceleration of Neutron Transport Calculations," Nucl. Sci. Eng. 151, 274 (2005). https://doi.org/10.13182/NSE151-274
  122. E. Masiello, B. Martin and J-M Do, "Domain decomposition and CMFD acceleration applied to discrete-ordinate methods for the solution of the neutron transport equation in xyz geometries," Proc. Int. Conf. on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C 2011), Rio de Janeiro, Brazil, May 8-12, 2011.
  123. E. Masiello, "Analytical Stability Analysis of the Coarse- Mesh Finite Difference Method," Proc. Int. Conf. on Physics of Reactors, "Nuclear Power: A Sustainable Resource," (PHYSOR 2008), Interlaken, Switzerland, Sept. 14-19, 2008.

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