粒子输运方程的子网格平衡格式的稳定性和收敛性

doi:10.12286/jssx.2015.4.439

计算数学 ›› 2015, Vol. 37 ›› Issue (4): 439-448.DOI: 10.12286/jssx.2015.4.439

• 论文 • 上一篇

粒子输运方程的子网格平衡格式的稳定性和收敛性

杨容¹, 袁光伟², 朱少红³

1. 北京应用物理与计算数学研究所, 北京 100094;
2. 北京应用物理与计算数学研究所计算物理实验室, 北京 100094;
3. 南开大学数学科学学院, 天津 300071

收稿日期:2015-01-03 出版日期:2015-11-15 发布日期:2015-11-19
通讯作者: 袁光伟,E-mail: yuan_guangwei@iapcm.ac.cn.
基金资助:
863课题(2012AA01A303);国家自然科学基金(11571048);中国工程物理研究院科学技术发展基金(2014A0202009,2015B0202033,2015B0202034)资助项目.

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杨容, 袁光伟, 朱少红. 粒子输运方程的子网格平衡格式的稳定性和收敛性[J]. 计算数学, 2015, 37(4): 439-448.

Yang Rong, Yuan Guangwei, Zhu Shaohong. Stability and convergence of subcell balance scheme for particle transport equations[J]. Mathematica Numerica Sinica, 2015, 37(4): 439-448.

Stability and convergence of subcell balance scheme for particle transport equations

Yang Rong¹, Yuan Guangwei², Zhu Shaohong³

1. Institute of Applied Physics and Computational Mathematics, Beijing 100094, China;
2. Laboratory of Science and Technology on Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100094, China;
3. School of Mathematical Science, Nan Kai University, Tianjin 300071, China

Received:2015-01-03 Online:2015-11-15 Published:2015-11-19

本文研究四边形网格上求解粒子输运方程的有限体积格式, 其中角方向变量采用离散纵标(Sn)方法, 空间离散采用子网格平衡(SCB)格式. 利用能量估计方法, 证明了在正交网格上该格式的稳定性和离散解的收敛性.数值实验结果验证了格式的稳定性和离散解的收敛性.

关键词： 粒子输运方程, 子网格平衡格式, 稳定性, 收敛性

In this paper a finite volume method for solving particle transport equations is studied, in which the discrete ordinate technique is applied to angular variable and the subcell balance (SCB) scheme is applied to spatial variable. The stability and convergence of the numerical solution are proved by using energy estimation method. Numerical examples are included to demonstrate the performance of the method.

Key words: particle transport equation, subcell balance scheme, stability, convergence

MR(2010)主题分类:

65N12
65Y05

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粒子输运方程的子网格平衡格式的稳定性和收敛性

Stability and convergence of subcell balance scheme for particle transport equations

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