几种常用燃耗方程组求解方法的性能对比分析

谭杰; 张鹏

doi:10.11889/j.0253-3219.2018.hjs.41.030501

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几种常用燃耗方程组求解方法的性能对比分析

核物理、交叉学科研究 | 更新时间：2021-05-19

- 几种常用燃耗方程组求解方法的性能对比分析
- Comparison and analysis of several typical algorithms in solving depletion equations
- 核技术 2018年41卷第3期文章编号：030501
- 作者机构：
  
  水力机械过渡过程教育部重点实验室（武汉大学）武汉 430072
- 作者简介：
  
  [ "谭杰, 女, 1992年出生, 2015年毕业于武汉大学, 现为硕士研究生, 研究领域为核燃料燃耗计算", "TAN Jie, female, born in 1992, graduated from Wuhan University in 2015, master student, focusing on nuclear fuel depletion calculation" ]
  张鹏, E-mail:peng-zhang@whu.edu.cn ZHANG Peng, E-mail:peng-zhang@whu.edu.cn
- 基金信息：
  
  国家自然科学基金(11305036)
- DOI：10.11889/j.0253-3219.2018.hjs.41.030501
  中图分类号： TL329.2
- 收稿日期：2017-08-21，
  
  修回日期：2017-09-28，
  
  纸质出版日期：2018-03-10
- 稿件说明：
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谭杰, 张鹏. 几种常用燃耗方程组求解方法的性能对比分析[J]. 核技术, 2018,41(3):030501

Jie TAN, Peng ZHANG. Comparison and analysis of several typical algorithms in solving depletion equations[J]. Nuclear techniques, 2018, 41(3): 030501
谭杰, 张鹏. 几种常用燃耗方程组求解方法的性能对比分析[J]. 核技术, 2018,41(3):030501 DOI： 10.11889/j.0253-3219.2018.hjs.41.030501.

Jie TAN, Peng ZHANG. Comparison and analysis of several typical algorithms in solving depletion equations[J]. Nuclear techniques, 2018, 41(3): 030501 DOI： 10.11889/j.0253-3219.2018.hjs.41.030501.

摘要

为求解点堆燃耗方程组，通过自主编程燃耗计算模块，分别采用Chebyshev有理近似方法（Chebyshev Rational Approximation Method，CRAM）、Padé近似方法、Krylov Subspace方法以及线性子链法（Transmutation Trajectory Analysis，TTA）对不同规模的点堆燃耗系统进行燃耗计算，并与高精度下16阶系数的CRAM的结果进行对比分析。结果表明，CRAM能够高效地获得精确的计算结果，而且其系数阶数越高，精度越高，步长稳定性越高，因此目前燃耗计算多采用这种方法；Padé近似方法在双精度下对于中小规模燃耗系统能够快速获得精确结果，受步长影响小，而对于大规模燃耗系统需要采用高精度计算，且受步长影响也小；Krylov Subspace方法在双精度下可准确求解中小规模燃耗矩阵，但不适用于大规模燃耗求解；TTA适用于求解各规模燃耗方程，但由于线性链的简化，相对参考值精度较低，求解速度相对较慢。本文所获结果对于不同燃耗计算系统的开发及应用具有较好的借鉴意义。

Abstract

Background

It is very important to trace fuel concentration changing with high precision and efficiency in the current core simulation calculations

where an essential part is to solve depletion equations precisely.

Purpose

This study aims to solve point-core depletion equations in different sizes with various methods and find out the characteristics of these methods by a self-programming burnup module.

Methods

Four methods including Chebyshev rational approximation method (CRAM)

Padé approximation method

Krylov Subspace method and transmutation trajectory analysis (TTA) were used to realize burnup calculations and comparative analysis with the results by CRAM with 16 orders in high precision for different-scale burnup systems.

Results

The results suggested that CRAM could provide very accurate solutions in a very short computing time

and the higher the coefficient order

the higher the precision and step stability. Padé approximation method could get accurate results affected marginally by step length with double precision in small and medium systems quickly

but high precision computation should be adopted for large systems while little affected by step length. Krylov Subspace method had accurate solutions in small and medium systems with double floats. However

it can't be applied to large cases. TTA was applicable to burnup equations at any scale with a weak accuracy and a slower speed because of linear chain simplification.

Conclusion

The four methods can be adapted to the depletion calculations of the cores in different cases

and the responding results can be treated as reference for the development and application of different burnup calculation systems.

关键词

Keywords

references

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