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## Efficient Monte Carlo algorithm of time-dependent particle transport problem in multi-physics coupling calculation

Shangguan Dan-Hua, Yan Wei-Hua, Wei Jun-Xia, Gao Zhi-Ming, Chen Yi-Bing, Ji Zhi-Cheng
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• #### 摘要

多物理耦合计算在众多领域都有重要应用. 如果其包含粒子输运过程, 用蒙特卡罗方法模拟粒子输运常占据大部分的计算时间, 因此多物理耦合计算中动态输运问题的高效蒙特卡罗模拟方法意义重大, 其不可避免地依赖于大规模并行. 基于动态输运问题的特点, 本文提出了两种新方法: 一是针对输运燃耗耦合计算的新型计数规约算法; 二是动态输运计算样本数自适应算法. 两种算法都能在保持计算结果基本不变的前提下使计算时间大幅减少, 从而提高了效率.

#### Abstract

Multi-physics coupling calculation has applications in many important research fields. If particle transport process is included in this calculation, Monte Carlo method is often used to simulate this process and usually a large amount of calculation time is needed. So, efficient Monte Carlo algorithm for time-dependent particle transport problem is important for an efficiently coupling calculation, which inevitably relies on large-scale parallel calculation. Based on the characteristic of time-dependent particle transport problem, two methods are proposed in this paper to achieve high- efficiency calculation. One is a tally-reducing algorithm which is used in the coupling of transport simulation and burnup calculation. By reducing the quantity of data which should be reduced necessarily, this method can reduce the calculation time largely. It can be seen that a new coupling mode for these two processes in MPI environment has a larger value when model scale is larger than the sample size. The other method is an adaptive method of setting the sample size of Monte Carlo simulation. The law of large number assures that the Monte Carlo method will obtain an exact solution when the sample scale tends to infinity. But generally, no one knows which sample scale is big enough for obtaining a solution with target precision in advance. So, the common strategy is to set a huge-enough sample scale by experience and conduct the posterior check for all results. Apparently, this way cannot be efficient because the calculation will go on after the precision of solution has reached an object value. Another popular method is to set the sample size to rely on the relative error of some single calculation. The sample size is enlarged without a break until the relative error is less than some presetting value. This method is not suitable either, because Monte Carlo particle transport simulation will gives feedbacks to other process which is composed of many tallies. It is inappropriate to adjust the sample size according to the relative error of any calculation. Relying on the generalization of the Shannon entropy concept and an on-the-fly diagnosis rule for a entropy value sequence, the adaptive method proposed in this paper can reduce the original huge sample scale to a reasonable level. By numerically testing some non-trivial examples, both algorithms can reduce the calculation time largely, with the results kept almost unchanged, so the efficiency is high in these cases.

#### 作者及机构信息

###### 通信作者: 姬志成, ji_zc@139.com
• 基金项目: 中国工程物理研究院科学基金(批准号: CX20200028)和国家自然科学基金青年科学基金(批准号: 11705011)资助的课题

#### Authors and contacts

###### Corresponding author: Ji Zhi-Cheng, ji_zc@139.com
• Funds: Project supported by the Science Foundation of China Academy of Engineering Physics, China (Grant No. CX20200028) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11705011)

#### 施引文献

• 图 1  新旧方法计数与燃耗计算时间之和的对比

Fig. 1.  Comparison of the total time of tally reduce and burnup calculation by using old and new methods.