| 谢金森,赵守智,于涛,陈珍平,谢芹,刘紫静,曾文杰,何丽华.基于隐式重启Arnoldi算法一维平板堆λ和瞬发α本征值问题谐波计算分析[J].南华大学学报(自然科学版),2016,30(3):9~13.[XIE Jin-sen,ZHAO Shou-zhi,YU Tao,CHEN Zhen-ping,XIE Qin,LIU Zi-jing,ZENG Wen-jie,HE Li-hua.Harmonics Calculation and Analysis of λ and Prompt α Eigenvalue Problems for Slab Reactor Based on the Implicitly Restarted Arnoldi Methods[J].Journal of University of South China(Science and Technology),2016,30(3):9~13.] |
| 基于隐式重启Arnoldi算法一维平板堆λ和瞬发α本征值问题谐波计算分析 |
| Harmonics Calculation and Analysis of λ and Prompt α Eigenvalue Problems for Slab Reactor Based on the Implicitly Restarted Arnoldi Methods |
| 投稿时间：2015-12-14 |
| DOI： |
| 中文关键词: 中子扩散方程 本征值问题 隐式重启Arnoldi算法 一维平板反应堆 |
| 英文关键词:Neutron diffusion equations eigenvalue problems the Implicitly Restarted Arnoldi Methods one dimensional slab reactor |
| 基金项目:国家自然科学基金资助项目(11305088);湖南省自然科学基金资助项目(14JJ2088) |
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| 中文摘要: |
| 中子平衡方程的谐波中子注量率及其本征值在中子时空动力学谐波展开法和外源驱动次临界反应堆中子学空间效应研究中有重要应用价值.本文推导了λ和瞬发α本征值问题的关系,并基于一维平板反应堆扩散问题,采用隐式重启Arnoldi算法(IRAM)进行了λ和α本征值问题计算.结果表明,给出的前10阶本征值数值与解析解符合较好,最大相对偏差小于3%；在λ本征值问题吸收截面中增加时间吸收项αp,n/v后,得到的n阶本征值λn均等于1,结果吻合λ和α本征值问题关系.本文工作证明了IRAM算法求解中子扩散方程本征值问题高阶谐波的有效性和λ和瞬发α本征值问题关系的正确性,为将IRAM方法拓展到多维、多群中子扩散方程奠定基础. |
| 英文摘要: |
| Harmonics and associated eigenvalues of neutron balance queation play an important role in harmonics expansion method of neutron space-time kinetics and studying of neutron spatial effect in external source driven subcritical reactors.In the present paper,relationship between λ and prompt α eigenvalue problems is derived and eigenvalues of one dimensional slab are calucated with the Implitly Restarted Arnoldi Methods.Results show good agreemments of eigenvalues between numerical calculation and analytical solution.For the fisrt ten eigenvalus,the maximum relative erro to analytial solution is less than 3%.When time absorption term αp,n/v added to absorption cross section in λ eigenvalue problem,the nth order eigenvalues λn are all euqal to unity,which conforms the relationship between λ and prompt α eigenvalue problems.Works performed in the present paper prove the effectiveness of IRAM in calcualtion of high order harmonics of diffusion equations and the validaty of relationship between λ and prompt α eigenvalue problems,which makes a successfuel foundation of IRAM to multi-dimentioanl and multi-group diffusion equations. |
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