logo

SCIENTIA SINICA Informationis, Volume 46 , Issue 10 : 1489-1509(2016) https://doi.org/10.1360/N112016-00068

Review of convergence acceleration methods in Monte Carlo criticality calculations for reactor analysis

More info
  • ReceivedMar 29, 2016
  • AcceptedAug 25, 2016
  • PublishedOct 25, 2016

Abstract


Funded by

国家重点基础研究发展计划(973计划)

(2011CB309705)


References

[1] X-5 Monte Carlo Team. MCNP--a General N-Particle Transport Code, Version 5-Volume 1: Overview and Theory. LA-UR-03-1987, Los Alamos National Laboratory, 2003. Google Scholar

[2] Griesheimer D P, Gill D F, Nease B R, et al. MC21 V.6.0 -- a continuous-energy Monte Carlo particle transport code with integrated reactor feedback capabilities. Ann Nucl Energy, 2015, 82: 29-40. Google Scholar

[3] Romano P K, Horelik N E, Herman B R, et al. OpenMC: a state-of-the-art Monte Carlo code for research and development. Ann Nucl Energy, 2015, 82: 90-97 CrossRef Google Scholar

[4] Leppanen J, Pusa M, Viitanen T, et al. The serpent Monte Carlo code: status, developments. Ann Nucl Energy, 2015, 82: 142-145. Google Scholar

[5] Wang K, Li Z, She D, et al. RMC -- a Monte Carlo code for reactor core analysis. Ann Nucl Energy, 2015, 82: 121-129 CrossRef Google Scholar

[6] Deng L, Li G, Zhang B Y, et al. Simulation of full-core pin-by-pin model by JMCT Monte Carlo neutron-photon transport code. Atom Energy Sci Tech, 2014, 6: 1061-1066 [邓力, 李刚, 张宝印, 等. JMCT 蒙特卡罗中子-光子输运全堆芯Pin-by-Pin 模型的模拟. 原子能科学技术, 2014, 6: 1061-1066]. Google Scholar

[7] Wu Y, Song J, Zheng H, et al. CAD-based Monte Carlo program for integrated simulation of nuclear system superMC. Ann Nucl Energy, 2015, 82: 161-168 CrossRef Google Scholar

[8] Brown F B. Recent advances and future prospects for Monte Carlo. In: Proceedings of Supercomputing in nuclear applications & Monte Carlo, Tokyo, 2010. 17-21. Google Scholar

[9] Martin W R. Challenges and prospects for whole-core Monte Carlo analysis. Nucl Eng Tech, 2012, 44: 151-160 CrossRef Google Scholar

[10] Yamamoto T, Miyoshi Y. Reliable method for fission source convergence of Monte Carlo criticality calculation with Wielandt's method. J Nucl Sci Tech, 2004, 41: 99-107 CrossRef Google Scholar

[11] Kiedrowski B C, Brown F. Using Wielandt's method to estimate confidence interval under prediction bias in MCNP5 criticality calculations. Trans Am Nucl Soc, 2008, 99: 338-340. Google Scholar

[12] She D, Wang K, Yu G. Asymptotic Wielandt method and superhistory method for convergence in Monte Carlo criticality calculation. Nucl Sci Eng, 2012, 172: 127-137 CrossRef Google Scholar

[13] Carter L L, McCormick N J. Source convergence in Monte Carlo calculations. Nucl Sci Eng, 1969, 36: 438-441 CrossRef Google Scholar

[14] Kadotani H, Hariyama Y, Shiota M, et al. Acceleration of fission distribution convergence using eigenvectors from matrix K calculations in the KENO code. In: Proceedings of International Conference on Nuclear Criticality Safety, Oxford, 1991. Google Scholar

[15] Kitada T, Takeda T. Effective convergence of fission source distribution in Monte Carlo simulation. J Nucl Sci Tech, 2001, 38: 324-329 CrossRef Google Scholar

[16] Urbatsch T J. Iterative acceleration methods for Monte Carlo and deterministic criticality calculations. Dissertation for Ph.D. Degree. Los Alamos: Los Alamos National Laboratory, 1995. Google Scholar

[17] Pan L, Wang R, Jiang S. Monte Carlo Fission matrix acceleration method with limited inner iteration. Nucl Sci Eng, 2015, 180: 199-208. Google Scholar

[18] Dufek J, Gudowski W. Fission matrix based Monte Carlo criticality calculations. Ann Nucl Energy, 2009, 36: 1270-1275 CrossRef Google Scholar

[19] Carney S E, Brown F B, Kiedrowski B C, et al. Fission Matrix Capability for MCNP Monte Carlo. LA-UR-12-24533, Los Alamos National Laboratory, 2012. Google Scholar

[20] Dufek J, Gudowski W. An efficient parallel computing scheme for Monte Carlo criticality calculations. Ann Nucl Energy, 2009, 36: 1276-1279 CrossRef Google Scholar

[21] Wenner M, Haghighat A. A fission matrix based methodology for achieving an unbiased solution for eigenvalue Monte Carlo simulations. Prog Nucl Sci Tech, 2011, 2: 886-892 CrossRef Google Scholar

[22] Smith K S. Nodal method storage reduction by nonlinear iteration. Trans Am Nucl Soc, 1983, 44: 265-266. Google Scholar

[23] Cho Y J, Joo H G, Lee C C, et al. Cell based CMFD formulation for acceleration of whole-core method of characteristics calculation. J Korean Nucl Soc, 2002, 34: 250-258. Google Scholar

[24] Zhong Z P, Downar T J, Xu Y L, et al. Implementation of two-level coarse-mesh finite difference acceleration in an arbitrary geometry, two-dimensional discrete ordinates transport method. Nucl Sci Eng, 2008, 158: 289-301 CrossRef Google Scholar

[25] Cho N Z, Lee G S, Park C J. Partial Current-based CMFD acceleration of the 2D/1D fusion method for 3D whole-core transport calculations. Tran Am Nucl Soc, 2003, 594: 88-89. Google Scholar

[26] Cho N Z, Yun S, Lee K T, et al. Speedup of Monte Carlo k-eigenvalue calculations via p-CMFD rebalance. Trans Am Nucl Soc, 2004, 90: 550. Google Scholar

[27] Lee M J, Joo H G, Lee D, et al. Investigation of CMFD acceleration Monte Carlo eigenvalue calculation with simplified low dimensional multigroup formulation. In: Proceedings of the International Conference on the Physics of Reactors, Pittsburgh, 2010. 9-14. Google Scholar

[28] Yun S, Cho N Z. Acceleration of source convergence in Monte Carlo k-eigenvalue problem via anchoring with a p-CMFD deterministic method. Ann Nucl Energy, 2010, 37: 1649-1658 CrossRef Google Scholar

[29] Wolters E R, Larsen E W, Martin W R. Hybrid Monte Carlo-CMFD methods for accelerating fission source convergence. Nucl Sci Eng, 2013, 174: 286-299 CrossRef Google Scholar

[30] Lee M J, Joo H G, Lee D, et al. Coarse mesh finite difference formulation for accelerated Monte Carlo eigenvalue calculation. Ann Nucl Energy, 2014, 65: 101-113 CrossRef Google Scholar

[31] Larsen E W, Yang J. A functional Monte Carlo methods for k-eigenvalue problems. Nucl Sci Eng, 2008, 159: 107-126 CrossRef Google Scholar

[32] Zhang D, Rahnema F. An efficient hybrid stochastic/deterministic coarse mesh neutron transport method. Ann Nucl Energy, 2012, 41: 1-11 CrossRef Google Scholar

[33] Gelbard E M, Roussel B. Proposed solution to the ``keff of the world" problem. Trans Amer Nucl Soc, 1995, 73: 201. Google Scholar

[34] Yun S, Cho N Z. Monte Carlo anchoring method for loosely-coupled k-eigenvalue problems. In: Proceedings of International Conference on Advances in Mathematics, Computational Methods, and Reactor Physics. New York: Springs, 2009. 3-7. Google Scholar

[35] Yang J, Natio Y. The sandwich method for detering source convergence in Monte Carlo calculation. In: Proceeding of the 7th International Conference on Nuclear Criticality Safety, Ibaraki, 2003. 19. Google Scholar

[36] Ibrahim A M, Peplow D E, Wagner J C, et al. Acceration of Monte Carlo criticality calculations using deterministic-based starting sources. In: Proceedings of the International Conference on the Physics of Reactors, Knoxville, 2012. Google Scholar

[37] Booth T E. A weight window/importance generator for Monte Carlo streaming problems. In: Proceedings of the 6th International Conference on Radiation Shielding, Tokyo, 1983. Google Scholar

[38] Lewis E E, Miller W F. Computational Methods of Neutron Transport. New York: John Wiley & Sons, 1984. Google Scholar

[39] Kong R, Spanier J. Geometric convergence of adaptive Monte Carlo algorithms for radiative transport problems based on importance sampling methods. Nucl Sci Eng, 2011, 168: 197-225 CrossRef Google Scholar

[40] Vanwijk A J, Vandeneynde G, Hoogenboom J E. An easy to implement global variance reduction procedure for MCNP. Ann Nucl Energy, 2011, 38: 2496-2503 CrossRef Google Scholar

[41] Wagner J C, Peplow D E, Mosher S W, et al. Review of hybrid (determinitistic/Monte Carlo) rdiation transport methods, codes, and applications at Oak Ridge National Laboratory. In: Proceedings of Joint International Conference on Supercomputing in Nuclear Applications and Monte Carlo 2010 (SNA + MC2010), Tokyo, 2010. Google Scholar

[42] Cooper M A. Automated weight windows for global Monte Carlo particle transport calculations. Nucl Sci Eng, 2001, 137, 1-13. Google Scholar

[43] Becker T L, Wollaber A B, Larsen E W. A hybrid Monte Carlo-deterministic method for global particle transport calculations. Nucl Sci Eng, 2007, 155: 155-167. Google Scholar

[44] Wagner J C, Blakeman E D, Peplow D E. Forward-weighted CADIS method for global variance reduction. Trans Amer Nucl Soc, 2007, 97: 630-633. Google Scholar

[45] Christoforou S, Hoogenboom J E. A zero-variance-based scheme for Monte Carlo criticality calculations. Nucl Sci Eng, 2011, 167: 91-104 CrossRef Google Scholar

[46] Densmore J D, Larsen E W. Variational variance reduction for Monte Carlo eigenvalue and eigenfunction problems. Nucl Sci Eng, 2004, 146: 121-140. Google Scholar

[47] Densmore J D, Larsen E W. Variational variance reduction for particle transport eigenvalue calculations using Monte Carlo adjoint simulation. J Comput Phys, 2003, 192: 387-405 CrossRef Google Scholar

[48] Griesheimer D P, Martin W R, Holloway J P. Convergence properties of Monte Carlo functional expansion tallies. J Comput Phys, 2006, 211: 129-153 CrossRef Google Scholar

[49] Kaushik B, Martin W R. Kernel density estimation method for Monte Carlo global flux tallies. Nucl Sci Eng, 2012, 170: 234-250 CrossRef Google Scholar

[50] Griesheimer D P, Martin W R, Holloway J P. A functional expansion method for Monte Carlo eigenvalue calculations. In: Proceeding of American Nuclear Society Conference, Chattanooga, 2005. Google Scholar

[51] Martin W R, Holloway J P, Banerjee K, et al. Global Monte Carlo Simulation with Higher Order Polynomial Expansions. DE-FG07-04ID14607, University of Michigan, 2007. Google Scholar

[52] Ueki T, Brown F B. Stationarity modeling and informatics-based diagnostics in Monte Carlo criticality calculations. Nucl Sci Eng, 2005, 149: 38-50 CrossRef Google Scholar

[53] Naito Y, Yang J A. The sandwich method for determing source convergence in Monte Carlo calculation. J Nucl Sci Tech, 2004, 41: 559-568 CrossRef Google Scholar

[54] Shim H J, Kim C H. Stopping criteria of inactive cycle Monte Carlo calculations. Nucl Sci Eng, 2007, 157: 132-141 CrossRef Google Scholar

[55] Shim H J, Kim C H. A new approach to check and diagnose the fission source convergence in Monte Carlo criticality calculations. Nucl Sci Eng, 2014, 178: 28-41. Google Scholar

[56] Mervin B T, Mosher S W, Wagner J C, et al. Uncertainty underprediction in Monte Carlo eigenvalue calculations. Nucl Sci Eng, 2013, 173: 276-292 CrossRef Google Scholar

[57] Gelbard E M, Prael R E. Computation of standard deviations in eigenvalue calculations. Prog Nucl Energy, 1990, 24: 237-241 CrossRef Google Scholar

[58] Shim H J, Choi S H, Kim C H. Real variance estimation by grouping histories in Monte Carlo eigenvalue calculations. Nucl Sci Eng, 2014, 176: 58-68. Google Scholar

[59] Ueki T, Mori T, Nakagawa M. Error estimations and their biases in Monte Carlo eigenvalue calculations. Nucl Sci Eng, 1997, 125: 1-11 CrossRef Google Scholar

[60] Shim H J, Kim C H. Real variance estimation using an intercycle fission source correlation for Monte Carlo eigenvalue calculations. Nucl Sci Eng, 2009, 162: 98-108 CrossRef Google Scholar

[61] Romano P K, Forget B. Parallel fission bank algorithms in Monte Carlo criticality calculations. Nucl Sci Eng, 2012, 170: 125-135 CrossRef Google Scholar

[62] Brunner T A, Urbatsch T J, Evans T M, et al. Comparison of Four Parallel Algorithms for Domain Decomposed Implicit Monte Carlo. UCRL-JRNL-208745, LawRence Livermore National Laboratory, 2004. Google Scholar

[63] Siegel A. Analysis of communication costs for domian decomposed Monte Carlo methods in nuclear reactor analysis. J Comput Phys, 2012, 231: 3119-3125 CrossRef Google Scholar