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The global tally problem has a wide range of applications in major research fields such as Monte Carlo simulations of pin-by-pin reactor models and time-dependent particle transport problems in multi-physics coupling calculations. Due to the uneven power distribution of the simulated system, the statistical errors of all tallies are unevenly distributed, resulting in some low global efficiency. For this kind of problem with global characteristics, it is necessary to develop global variance reduction techniques to obtain the accurate distribution of target tallies in the entire space. A large number of global variance reduction algorithms have been studied based on the consideration of flattening global tally error distribution, so as to improve global efficiency. This work focuses on the combination of two efficient global variance reduction algorithms, namely, the uniform tally density algorithm and the weight window algorithm, which belong to source bias and transport process bias, respectively. In tally, a method is proposed to adjust the weight window parameters by using the bias factor of the uniform tally density algorithm. Then, the weight window method will be used to reduce the weight fluctuation caused by the uniform tally density method. In this way, an organic combination of these two algorithms can be realized. A series of comparative tests are carried out based on the Hoogenboom-Martin pressurized water reactor benchmark, and it is verified that the hybrid global variance reduction algorithm proposed in this work is better than the single weight window algorithm or the uniform tally density algorithm. In terms of reducing the maximum error, the global efficiency of the hybrid algorithm is 2.6 times and 3 times that of the weight window algorithm and the uniform tally density algorithm, respectively. In addition, through the comparative analysis of computational asymmetry degree and computational efficiency, it is verified that the uniform tally density algorithm has better performance than the classical uniform fission site algorithm, and the performance advantages of the uniform tally density algorithm are quantitatively evaluated based on some new indicators. The results show that the hybrid global variance reduction algorithm proposed in this work can solve the global tally problem efficiently, thereby further promoting research in related fields.
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Keywords:
- Monte Carlo method /
- global variance reduction /
- uniform tally density algorithm /
- weight window algorithm
[1] 张滕飞, 吴宏春, 曹良志, 李云召, 刘晓晶, 熊进标, 柴翔 2019 原子能科学技术 53 1160
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图 1 权窗原理
Figure 1. Working principle of weight window.
图 2 Hoogenboom-Martin基准题 (a) 几何横截面; (b) 功率分布(MW); (c) 统计误差分布
Figure 2. Hoogenboom Martin benchmark: (a) Geometric cross-section; (b) power distribution (MW); (c) statistical error distribution.
图 3 变异系数分布 (a) Basic; (b) UFS; (c) UTD
Figure 3. Distribution of the coefficient of variation: (a) Basic; (b) UFS; (c) UTD.
图 4 偏倚因子的方差分布
Figure 4. Variance distribution of bias factors.
图 5 统计误差的累积分布
Figure 5. Cumulative distribution of statistical errors.
表 1 UTD算法和UFS算法的计算结果对比
Table 1. Comparison of calculation results of UTD and UFS.
计算条件 Remax Re95 计算时间
T/minFOM_
MAXFOM_95 Basic 0.2591 0.0969 13.05 1.1414 8.1610 UFS 0.1486 0.0558 13.06 3.4675 24.5917 UTD 0.1271 0.0532 13.15 4.7074 26.8690 
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表 2 计算结果对比
Table 2. Comparison of calculation results.
计算条件 Remax Re95 计算时间
T/minFOM_
MAXFOM_95 WW 0.0874 0.0333 24.26 5.3962 37.1724 UTD 0.1271 0.0540 13.61 4.5483 25.1973 混合算法 0.0538 0.0324 24.40 14.1594 39.0409
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[1] 张滕飞, 吴宏春, 曹良志, 李云召, 刘晓晶, 熊进标, 柴翔 2019 原子能科学技术 53 1160
Google Scholar
Zhang T F, Wu H C, Cao L Z, Li Y Z, Liu X J, Xiong J B, Chai X 2019 At. Energy Sci. Technol. 53 1160
Google Scholar
[2] 李刚, 雷伟, 张宝印, 邓力, 马彦, 李瑞, 上官丹骅, 付元光, 胡小利 2014 核动力工程 35 228
Li G, Lei W, Zhang B Y, Deng L, Ma Y, Li R, Shangguan D H, Fu Y G, Hu X L 2014 Nucl. Power Eng. 35 228
[3] 上官丹骅, 闫威华, 魏军侠, 高志明, 陈艺冰, 姬志成 2022 71 090501
Google Scholar
Shangguan D H, Yan W H, Wei J X, Gao Z M, Chen Y B, Ji Z C 2022 Acta Phys. Sin. 71 090501
Google Scholar
[4] Davis A, Turner A 2011 Fusion Eng. Des. 86 2689
Google Scholar
[5] Wijk A J V, Eynde G V D, Hoogenboom J E 2011 Ann. Nucl. Energy 38 2496
Google Scholar
[6] Hunter J L, Sutton T M 2013 M&C 2013 Sun Valley, Idaho, USA, May 5–9, 2013 p2780
[7] Kelly D J, Sutton T M, Wilson S C 2012 Proceedings of PHYSOR 2012-Advances in Reactor Physics-Linking Research, Industry, and Education Knoxville, Tennessee, USA, April 15–20, 2012
[8] 上官丹骅, 姬志成, 邓力, 李瑞, 李刚, 付元光 2019 68 122801
Google Scholar
Shangguan D H, Ji Z C, Deng L, Li R, Li G, Fu Y G 2019 Acta Phys. Sin. 68 122801
Google Scholar
[9] Shangguan D H, Li G, Zhang B Y, Deng L, Ma Y, Fu Y G, Li R, Hu X L 2017 Nucl. Sci. Eng. 182 555
Google Scholar
[10] 李新梅, 郑华庆, 郝丽娟, 宋婧, 胡丽琴, 江平 2017 核科学与工程 37 577
Google Scholar
Li X M, Zheng H Q, Hao L J, Song Q, Hu L Q, Jiang P 2017 Nucl. Sci. Eng. 37 577
Google Scholar
[11] Cooper M A, Larsen E W 2001 Nucl. Sci. Eng. 137 1
Google Scholar
[12] Wang K, Li Z G, She D, Liang J G, Xu Q, Qiu Y S, Yu J K, Sun J L, Fan X, Yu G L 2015 Ann. Nucl. Energy 82 121
Google Scholar
[13] 余慧, 全国萍, 秦瑶, 严伊蔓, 陈义学 2021 核动力工程 42 218
Google Scholar
Yu H, Quan G P, Qin Y, Yan Y M, Chen Y X 2021 Nucl. Power Eng. 42 218
Google Scholar
[14] Zhang X, Liu S C, Yan Y M, Qin Y, Chen Y X 2020 Fusion Eng. Des. 159 111875
Google Scholar
[15] Kelly D J, Aviles B N, Herman B R 2013 M&C 2013 Sun Valley Idaho, USA, May 5–9, 2013 p2962
[16] Hoogenboom J E, Martin W R 2009 M&C 2009 Saratoga Springs, NY, USA, May 3–7, 2009
[17] 刘鸿飞, 张彬航, 张澍, 孙光耀, 郝丽娟, 宋婧, 龙鹏程 2016 核技术 39 040604
Google Scholar
Liu H F, Zhang B H, Zhang S, Sun G Y, Hao L J, Song Q, Long P C 2016 Nucl. Tech. 39 040604
Google Scholar
[18] 张显, 刘仕倡, 强胜龙, 张文鑫, 尹强, 崔显涛, 陈义学 2021 原子能科学技术 55 66
Google Scholar
Zhang X, Liu S C, Qiang S L, Zhang W X, Yin Q, Cui X T, Chen Y X 2021 Atomic Energy Sci. Technol. 55 66
Google Scholar
[19] Kiedrowski B C, Ibrahim A 2011 Trans. Am. Nucl. Soc. 104 325
[20] 上官丹骅, 李刚, 邓力, 张宝印, 李瑞, 付元光 2015 64 052801
Google Scholar
Shangguan D H, Li G, Deng L, Zhang B Y, Li R, Fu Y G 2015 Acta Phys. Sin. 64 052801
Google Scholar
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