DOI QR코드

DOI QR Code

SOME OUTSTANDING PROBLEMS IN NEUTRON TRANSPORT COMPUTATION

  • Published : 2009.05.31

Abstract

This article provides selects of outstanding problems in computational neutron transport, with some suggested approaches thereto, as follows: i) ray effect in discrete ordinates method, ii) diffusion synthetic acceleration in strongly heterogeneous problems, iii) method of characteristics extension to three-dimensional geometry, iv) fission source and $k_{eff}$ convergence in Monte Carlo, v) depletion in Monte Carlo, vi) nuclear data evaluation, and vii) uncertainty estimation, including covariance data.

Keywords

References

  1. E.E. Lewis and W.F. Miller, Jr., Computational Methods of Neutron Transport, John Wiley & Sons, 1984
  2. G.I. Bell and S. Glasstone, Nuclear Reactor Theory, Van Nostrand Reinhold, 1970
  3. N.Z. Cho, “Fundamentals and Recent Developments of Reactor Physics Methods,” Nuclear Engineering and Technology, 37, 25 (2005)
  4. L.L. Briggs, W.F. Miller, and E.E. Lewis, “Ray Effect Mitigation in Discrete Ordinate-Like Angular Finite Element Approximations in Neutron Transport,” Nucl. Sci. Eng., 57, 205 (1975) https://doi.org/10.13182/NSE75-A26752
  5. R.N. Blonquist and E.E. Lewis, “Rigorous Treatment of Transverse Buckling Effects in Two-Dimensional Neutron Transport Computations,” Nucl. Sci. Eng., 73, 125 (1980) https://doi.org/10.13182/NSE80-A18693
  6. W.F. Miller, Jr. and W.H. Reed, “Ray Effect Mitigation Methods for Two-Dimensional Neutron Transport Theory,” Nucl. Sci. Eng., 62, 391 (1977) https://doi.org/10.13182/NSE62-391
  7. H.S. Choi and J. K. Kim, “Development of Radiation Shielding Analysis Program Using Discrete Elements Method in X-Y Geometry,” Nuclear Engineering and Technology (formerly J. of Korean Nuclear Society), 25, 51 (1993)
  8. W.E. Filippone, S.Woolf, and R. Lavigne, “Particle Transport Calculations with the Method of Streaming Rays.” Nucl. Sci. Eng., 77, 119 (1981) https://doi.org/10.13182/NSE81-A21346
  9. S.G. Hong and N.Z. Cho, “Extensions of Streaming Rays Method for Streaming Dominant Neutron Transport Problems,” Nuclear Engineering and Technology (formerly J. of Korean Nuclear Society), 28, 320 (1996)
  10. M.L. Adams and E.W. Larsen, “Fast Iterative Methods for Discrete-Ordinates Particle Transport Calculations,” Progress in Nuclear Energy, 40, 3 (2002) https://doi.org/10.1016/S0149-1970(01)00023-3
  11. Y. Azmy, “Impossibility of Unconditional Stability and Robustness of Diffusive Acceleration Schemes,” American Nuclear Society Radiation Protection and Shielding Division Topical Meeting, p. 480, Nashville, TN, U.S.A., April 19- 23, (1998)
  12. Y. Azmy, T. A. Wareing, and J. Morel, “Effect of Material Heterogeneity on the Performance of DSA for Even-Parity SN Methods,” International Conference on Mathematics and Computation, Reactor Physics, and Environmental Analysis in Nuclear Applications, p.55, Madrid, Spain, September 27-30, (1999)
  13. 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
  14. J.S. Warsa, T.A. Wareing, J.E. Morel, J.M. McGhee, and R.B. Lehoucq, “Krylov Subspace Iterations for the Calculation of k-Eigenvalues with SN Transport Codes,” Int. Conf. Nuclear Mathematical and Computational Sciences (M&C 2003), Gatlinburg, USA, April 6-11, 2003, CDROM, American Nuclear Society (2003)
  15. J.R. Askew, “A Characteristics Formulation of the Neutron Transport Equation in Complicated Geometries,” AEEWR- 1108, U.K. Atomic Energy Authority (1972)
  16. M.J. Halsall, “CACTUS, A Characteristics Solutions to the Neutron Transport Equations in Complicated Geometries,” AEEW-R-1291, U.K. Atomic Energy Authority (1980)
  17. S.G. Hong and N.Z. Cho, “CRX: A Code for Rectangular and Hexagonal Lattices Based on the Method of Characteristics,” Ann. of Nucl. Energy, 25, 547 (1998) https://doi.org/10.1016/S0306-4549(97)00113-8
  18. S. Kosaka and E. Saji, “The Characteristics Transport Calculation for a Multi-Assembly System using Neutron Path Linking Technique,” Proc. Int. Conf. Mathematics and Computation, Reactor Physics and Environmental Analysis in Nuclear Applications, p.1890, Madrid, Spain, September 27-30, (1999)
  19. G.S. Lee, N.Z. Cho, and S.G. Hong, “Acceleration and Parallelization of the Method of Characteristics for Lattice and Whole-Core Heterogeneous Calculations,” Proc. PHYSOR 2000, Session II-C, Pittsburgh, USA, May 7-11, (2000); see also N.Z. Cho, et al., “Whole-Core Heterogeneous Transport Calculations and Their Comparison with Diffusion Results,” Trans. Am. Nucl. Soc., 83, 292 (2000)
  20. N.Z. Cho, G.S. Lee, and C.J. Park, “A Fusion Technique of 2-D/1-D Methods for Three-Dimensional Whole-Core Transport Calculations,” Proc. of the Korean Nuclear Society Spring Meeting, May 2002, Kwangju (Full Paper in CD-ROM)
  21. N.Z. Cho, G.S. Lee, 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)
  22. N.Z. Cho, et al., “Refinement of the 2-D/1-D Fusion Method for 3-D Whole-Core Transport Calculation,” Trans. Am. Nucl. Soc., 87, 417 (2002)
  23. J.Y. Cho, et al., “Three-Dimensional Heterogeneous Whole Core Transport Calculation Employing Planar MOC Solutions,” Trans. Am. Nucl. Soc., 87, 234 (2002)
  24. S. Kosaka and T. Takeda, “Diffusion-Like 3-D Heterogeneous Core Calculation with 2-D Characteristics Transport Correction by Non-Linear Iteration Technique,” Int. Conf. Nuclear Mathematical and Computational Sciences (M&C 2003), Gatlinburg, USA, April 6-11, 2003, CD-ROM, American Nuclear Society (2003)
  25. E.M. Gelbard and A.G. Gu, “Biases in Monte Carlo Eigenvalue Calculations,” Nucl. Sci. Eng., 117, 1 (1994) https://doi.org/10.13182/NSE94-A13564
  26. T. Ueki, T. Mori, and M. Nakagawa, “Error Estimates and Their Biases in Monte Carlo Eigenvalue Calculations,” Nucl. Sci. Eng., 125, 1 (1997) https://doi.org/10.13182/NSE97-1
  27. H.J. Shim and C.H. Kim, “Real Variance Estimation Using Inter-Cycle Correlation of Fission Source Distribution in Monte Carlo Eigenvalue Calculations,” Trans. Am. Nucl. Soc., 94, 574 (2006)
  28. E.G. Whitesides, “A Difficulty in Computing the k-Effective of the World,'' Trans. Am. Nucl. Soc., 14, 680 (1971)
  29. B.T. Yamamoto, T. Nakamura, and Y. Miyoshi, “Fission Source Convergence of Monte Carlo Criticality Calculations in Weakly Coupled Fissile Arrays,” J. Nucl. Sci. Technol., 37, 41 (2000) https://doi.org/10.3327/jnst.37.41
  30. F. Brown, “Wielandt Acceleration for MCNP5 Monte Carlo Eigenvalue Calculations,” Joint International Topical Meeting on Mathematics & Computation and Supercomputing in Nuclear Applications (M&C + SNA 2007), Monterey, California, April 15-19, 2007, (CD-ROM) (2007)
  31. H.J. Shim and C.H. Kim, “Real Variance Estimation in Monte Carlo Wielandt Calculations,” PHYSOR'08 Proceedings of the International Conference on the Physics of Reactors, Interlaken, Switzerland, September 14-19 (CD-ROM) (2008)
  32. S. Yun and N.Z. Cho, “Monte Carlo Anchoring Method for Asymmetric Loosely-Coupled k-Eigenvalue Problems,” Annual Meeting of AESJ (AESJ 2009), Tokyo, Japan, March 23-25 (CD-ROM) (2009)
  33. S. Yun and N.Z. Cho, “Monte Carlo Anchoring Method for Loosely-Coupled k-Eigenvalue Problems”, 2009 International Conference on Advances in Mathematics, Computational Methods, and Reactor Physics (M&C 2009), Saratoga Springs, New York, May 3-7 (CD-ROM) (2009)
  34. D.L. Poston and H.R. Trellue, User's Manual, Version 2.0 for MONTEBURNS Version 1.0, LA-UR-99-4999, Los Alamos National Laboratory (1999)
  35. T. Takeda, N. Hirokawa, and T. Noda, “Error Propagation in Monte Carlo Burnup Calculations,” Proc. Int. Conf. Mathematics and Computation, Reactor Physics and Environmental Analysis in Nuclear Applications, pp. 1036- 1044, Madrid, Spain, September 27-30 (1999)
  36. H.J. Shim and C.H. Kim, “Error Propagation Module Implemented in the MC-CARD Monte Carlo Code,” Trans. Am. Nucl. Soc., 86, 325 (2002)
  37. J.C. Davis and J.C. Lee, “Comparison of Monte Carlo and Deterministic Depletion Codes for LWR Fuel Cycle,” Trans. Am. Nucl. Soc., 92, 651 (2005)
  38. S. Yun and N.Z. Cho, “A Monte Carlo Depletion Method with Leakage Corrected Critical Spectrum,” Trans. Korean Nucl. Soc. Spring Meeting, Jeju, Korea, May 21-22 (2009)
  39. J.M. Blatt and V.F. Weisskopf, “Theoretical Nuclear Physics,” Spinger-Verlag (1979)
  40. C.W. Reich and M.S. Moore, “Multilevel Formula for the Fission Process,” Phys. Review, Vol. 111, pp. 929 (1958) https://doi.org/10.1103/PhysRev.111.929
  41. S.F. Mughabghab, “Atlas of Neutron Resonances,” Elsevier (2006)
  42. G.N. Kim et al., “Measurement of neutron total cross section of Dy at Pohang Neutron Facility,” Annals of Nucl. Ener., Vol. 30, pp. 1123 (2003) https://doi.org/10.1016/S0306-4549(03)00052-5
  43. S-Y. Oh, J. Chang, and S. Mughabghab, “Neutron Cross Section Evaluations of Fission Products Below the Fast Energy Region,” BNL-NCS-67469, BNL (April 2000)
  44. S-Y Oh, C-S Gil, and J. Chang, “Evaluation of Neutron Cross Sections of Dy Isotopes in the Resonance Region,” Nuclear Engineering and Technology, Vol. 33, pp. 46 (2001)
  45. Y.D. Lee and J. Chang, “Neutron Cross Section Data Library for Pd-105, Ag-109, Xe-131, and Cs-133,” Nucl. Ener. and Tech. Vol. 37, pp. 101 (2005)
  46. R.D. Lawson, “ABAREX : A Neuntron Spherical Optical Statistical Model Code,” Woskshop on Computation and Analysis of Nuclear Data Relevant to Nuclear Energy and Safety, pp. 447, Trieste, Italy
  47. J. Raynal, “Notes on ECIS,” CEA-N-2772, CEA (1994)
  48. E. Gadioli and P.E. Hodgson, "Pre-Equilibrium Nuclear Reactions," Clarendon Press, (1992)
  49. Y.D. Lee and Y.O. Lee, “Neutron induced cross section data for Ir-191 and Ir-193,” Nucl. Ener. and Tech. Vol. 38, pp. 803 (2006)
  50. M. Herman et al., “EMPIRE - Nuclear Reaction Model Code,” BNL, (2005)
  51. A.J. Koning, S. Hilaire, and M.Duijvestin, “TALYS-1.0 A nuclear reaction program,” NRG, the Netherland (2007)
  52. A. Gandini, “A generalized perturbation method for bilinear functionals of the real and adjoiny neutron fluxed,” J. of Nucl. Ener. Vol. 21, pp.755 (1967) https://doi.org/10.1016/0022-3107(67)90086-X
  53. W. Stacey, “Variational Methods in Nuclear Physics,” Academic Press, 1974
  54. F.R. Andrade Lima, et al., “Recent advances in perturbative methods applied to nuclear engineering problems,” Prog. in Nucl. Ener. Vol. 33, pp. 23 (1997) https://doi.org/10.1016/S0149-1970(97)00098-X
  55. F.H. Kim, et al., “A generalized perturbation theory program for CANDU core analysis,” Ann. of Nucl. Ener. Vol. 28, pp. 169 (2001) https://doi.org/10.1016/S0306-4549(00)00028-1
  56. K. Furuta, et al., “SUSD: A Computer Code for Cross Section Sensitivity and Uncertainty Analysis Including Secondary Neutron Energy and Angular Distributions,” UTNL-R-0185, 1986
  57. B.T. Rearden, "TSUNAMI-3D: Control module for threedimensional cross section sensitivity and uncertainty analysis for criticality," ORNL/TM-2005/39 Vol-I, Sect. C9, 2005
  58. N.G. Carica-Herranz, et al., “Propagation of statical and nuclear data uncertainties in Monte Carlo burn-up calculations,” Ann. of Nuc. Energy Vol. 35, pp.714 (2008) https://doi.org/10.1016/j.anucene.2007.07.022
  59. G. Aliberti et al., “Use of covariance data to select experiments relevant to target systems,” Nucl. Data Sheets, Vol. 109, pp. 2745 (2008) https://doi.org/10.1016/j.nds.2008.11.004
  60. http://en.wikipedia.org/wiki/Kalman_filter - accessed on 2009.3.9
  61. D. Smith, “Summary of the Workshop on Neutron Cross Section Covariances,” Nucl. Data Sheets, Vol. 109, pp. 2915 (2008) https://doi.org/10.1016/j.nds.2008.11.034
  62. D. Smith, “A Unified Monte Carlo Approach to Fast Neutron Cross Section Data Evaluation,” Report ANL/NDM-166, ANL, January (2008)
  63. G. Palmiotti, et al., “A global approach to the physics validation of simulation codes,” Ann. of Nucl. Energy, Vol. 36, pp. 355 (2009) https://doi.org/10.1016/j.anucene.2008.11.012
  64. “Regulatory Guide 1.190 - Calculational and Dosimetry Methods for Determining Pressure Vessel Neutron Fluence,” USNRC (2001)
  65. P. Griffin and R. Paviotti-Corcuera, “Summary Report of the Final Technical Meeting on International Reactor Dosimetry File: IRDF-2002,” INDC(NDS)-448 (2003)
  66. R.C. Little et al., “Low-fidelity Covariance Project,” Nucl. Data Sheets, Vol. 109, pp. 2828 (2008) https://doi.org/10.1016/j.nds.2008.11.018