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Traditionally, the Monte Carlo criticality calculation must set a maximum inactive step by experience to ensure that a fission source distribution has converged. The tallying process can only be invoked after this maximum inactive step to avoid the system error caused by the non-converged fission source distribution. In the same way, the uniform fission site algorithm for increasing the whole efficiency of global tallying should also be invoked after the fission source distribution has converged fully. The calculation must reach a maximum iteration step, then, this process can be stopped and the tallies can be printed. This old strategy has two defects. Firstly, the appointed maximum inactive step can only be set by experience, which will be insufficient in some cases; secondly, some iteration steps can be wasted because the precision of tallies has been enough and no one knows it. So, a new strategy is proposed in this article to overcome these defects. Based on an on-the-fly diagnostic method for the convergence of Shannon entropy sequence corresponding to the fission source distribution of each iteration step, the uniform fission site algorithm will be invoked after the iteration step whose serial number is the maximum of the first active step and the first converged step diagnosed by the above-mentioned rule. This rule will be helpful in ensuring that the uniform fission site algorithm can use enough accurate data to bias the secondary fission neutron number, thus avoiding the system error to some degree. Then, a global precision index will be calculated at each fixed step to judge whether the precision standard is reached. If so, the whole calculation is stopped. This process will be repeated until the pre-set maximum step number is reached. In this way, superfluous calculations can be skipped but the calculation precision can be guaranteed. In a word, this new strategy is beneficial to increasing the efficiency of global tallying in the Monte Carlo criticality calculation when appropriate parameters are adopted. This conclusion can be proved by the numerical result from the C5G7 benchmark model.
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Keywords:
- criticality calculation /
- global tallying /
- Monte Carlo method /
- Shannon entropy
[1] Martin W 2012 Nucl. Eng. Tech. 44 2
[2] 李刚, 邓力, 张宝印, 李瑞, 史敦福, 上官丹骅, 胡泽华, 付元光, 马彦 2016 65 052801
Google Scholar
Li G, Deng L, Zhang B Y, Li R, Shi D F, Shangguan D H, Hu Z H, Fu Y G, Ma Y 2016 Acta Phys. Sin. 65 052801
Google Scholar
[3] Veluri V K, Sengupta S, Mammen S, Bhattacharya S 2018 Nucl. Technol. 204 1
Google Scholar
[4] Maul L 2018 Ann. Nucl. Energy 115 523
Google Scholar
[5] Daniel J K, Tomas M S, Stephen C W 2012 Proceedings of PHYSOR 2012-Advances in Reactor Physics-Linking Research, Industry, and Education Knoxville, Tennessee, USA, April 15−20, 2012
[6] Daniel J K, Brian N A, Bryan R H 2013 Proceedings of M&C 2013 Sun Valley, Idaho, USA, May 5−9, 2013 p2962
[7] Jessica L H, Thomas M S 2013 Proceedings of M&C 2013 Sun Valley, Idaho, USA, May 5−9, 2013 p2780
[8] 上官丹骅, 邓力, 李刚, 张宝印, 马彦, 付元光, 李瑞, 胡小利, 2016 65 062801
Google Scholar
Shangguan D H, Deng L, Li G, Zhang B Y, Ma Y, Fu Y G, Li R, Hu X L 2016 Acta Phys. Sin. 65 062801
Google Scholar
[9] Shangguan D H, Li G, Zhang B Y, Deng L, Ma Y, Fu Y G, Li R, Hu X L 2016 Nucl. Sci. Eng. 182 555
Google Scholar
[10] Ueki T, Brown F B 2005 Nucl. Sci. Eng. 149 38
Google Scholar
[11] Natio Y, Yang J 2004 J. Nucl. Sci. Tech. 41 559
Google Scholar
[12] Ueki T 2008 Nucl. Sci. Eng. 160 242
Google Scholar
[13] Shangguan D H, Deng L, Li G, Zhang B Y 2018 High Power Laser and Particle Beams 30 016004
[14] Cavarec C, Perron J, Verwaerde D, West J 1994 The DECD/NEA Benchmark Calculations of Power Distributions within Assemblies (Electricité de France)
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图 1 C5G7模型图
Figure 1. C5G7 model.
图 2 基准解裂变源分布对应香农熵的变化
Figure 2. Shannon entropy of fission source distribution for benchmark result.
图 3 不启动策略时有无UFS算法的裂变源分布对应香农熵的变化
Figure 3. Shannon entropy of fission source distribution for two cases (without strategy and with or without UFS algorithm).
表 1 结果比较
Table 1. Comparison of results.
方法 keff 计算时间/s E_global Pre_95 no_stra_no_UFS 1.17660 8816.0 0.7689 0.00284 no_stra_with_UFS 1.17650 10189.2 1.2567 0.00259 with_stra_no_UFS (在第224启动计数, 在第944步结束) 1.17657 5580.4 1.9800 0.00396 with_stra_with_UFS (在第224启动计数, 在第824步结束) 1.17629 4831.1 0.5616 0.00396 
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[1] Martin W 2012 Nucl. Eng. Tech. 44 2
[2] 李刚, 邓力, 张宝印, 李瑞, 史敦福, 上官丹骅, 胡泽华, 付元光, 马彦 2016 65 052801
Google Scholar
Li G, Deng L, Zhang B Y, Li R, Shi D F, Shangguan D H, Hu Z H, Fu Y G, Ma Y 2016 Acta Phys. Sin. 65 052801
Google Scholar
[3] Veluri V K, Sengupta S, Mammen S, Bhattacharya S 2018 Nucl. Technol. 204 1
Google Scholar
[4] Maul L 2018 Ann. Nucl. Energy 115 523
Google Scholar
[5] Daniel J K, Tomas M S, Stephen C W 2012 Proceedings of PHYSOR 2012-Advances in Reactor Physics-Linking Research, Industry, and Education Knoxville, Tennessee, USA, April 15−20, 2012
[6] Daniel J K, Brian N A, Bryan R H 2013 Proceedings of M&C 2013 Sun Valley, Idaho, USA, May 5−9, 2013 p2962
[7] Jessica L H, Thomas M S 2013 Proceedings of M&C 2013 Sun Valley, Idaho, USA, May 5−9, 2013 p2780
[8] 上官丹骅, 邓力, 李刚, 张宝印, 马彦, 付元光, 李瑞, 胡小利, 2016 65 062801
Google Scholar
Shangguan D H, Deng L, Li G, Zhang B Y, Ma Y, Fu Y G, Li R, Hu X L 2016 Acta Phys. Sin. 65 062801
Google Scholar
[9] Shangguan D H, Li G, Zhang B Y, Deng L, Ma Y, Fu Y G, Li R, Hu X L 2016 Nucl. Sci. Eng. 182 555
Google Scholar
[10] Ueki T, Brown F B 2005 Nucl. Sci. Eng. 149 38
Google Scholar
[11] Natio Y, Yang J 2004 J. Nucl. Sci. Tech. 41 559
Google Scholar
[12] Ueki T 2008 Nucl. Sci. Eng. 160 242
Google Scholar
[13] Shangguan D H, Deng L, Li G, Zhang B Y 2018 High Power Laser and Particle Beams 30 016004
[14] Cavarec C, Perron J, Verwaerde D, West J 1994 The DECD/NEA Benchmark Calculations of Power Distributions within Assemblies (Electricité de France)
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