积分梯度法的两种格式

计算物理 ›› 2008, Vol. 25 ›› Issue (5): 525-534.

积分梯度法的两种格式

勇珩^1,2, 袁国兴¹, 王政¹

1. 北京应用物理与计算数学研究所, 北京 100088;
2. 中国工程物理研究院研究生部, 北京 100088

收稿日期:2007-05-17 修回日期:2007-11-23 出版日期:2008-09-25 发布日期:2008-09-25
作者简介:勇珩(1974-),女,山东威海,副研究员,博士生,从事辐射流体力学计算方法与数值模拟工作,北京8009信箱12分箱100088.
基金资助:
国家863高技术惯性约束聚变主题、中物院科学技术发展基金(2007B09009,2007A09002);中物院科学技术基金(20060106);计算物理国家重点实验室项目(9140C6902010603);国家自然科学基金(10572028)资助项目

Two Schemes of Integrated Gradient Method

YONG Heng^1,2, YUAN Guoxing¹, WANG Zheng¹

1. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;
2. Graduate School of China Academy of Engineering Physics, Beijing 100088, China

Received:2007-05-17 Revised:2007-11-23 Online:2008-09-25 Published:2008-09-25

摘要/Abstract

摘要： 在二维柱坐标系下Lagrange流体力学的计算中,积分梯度法是动量方程的一种有效离散方法.积分梯度法中,IGT(Integral Gradient Total)格式不能保持柱几何下一维球对称性;IGA(Integral Gradient Average)格式可以保持一维球对称性,但当相邻网格质量相差比较大时,会得到远远脱离真实物理现象的加速度.深入研究IGA和IGT格式发现,当相邻网格边界压力取为质量加权时,即使相邻网格质量相差较大,对于一维平面和一维柱问题,IGT与IGA等价;在二维情形下,可以缩小IGT和IGA之间的差异.理论证明,IGA格式不能保持系统的动量守恒,IGT格式能保持系统的动量守恒性.数值模拟结果进一步显示了这两个格式的优缺点.

关键词: 积分梯度法, IGT格式, IGA格式, 球对称性, 守恒性

Abstract: In a cylinderical coordinate system, integrated gradient method is an effective discrctization for equations of Lagrangian hydrodynamics. In the method IGT (Integral Gradient Total) scheme does not preserve spherical symmetry while IGA (Integral Gradient Average) scheme overcomes nonsymmetry in cylinderical coordinate system. However, IGA results in abnormally large acceleration in case of large mass ratios, where the mass of one subcell around a node is smaller than that of the other three subcells. If boundary force between neighbouring cells is taken as weighted mass average, IGA scheme is equivalent to IGT scheme in both a planar problem and a cylinderical problem even if there exists a large mass ratio. It is shown that IGT scheme preserves total momentum conservation but IGA scheme does not. Numerical results demonstrate advantages and disadvantages of the two schemes.

Key words: integrated gradient method, integral gradient total scheme, integral gradient average scheme, spherical symmetry, conservation

中图分类号:

勇珩, 袁国兴, 王政. 积分梯度法的两种格式[J]. 计算物理, 2008, 25(5): 525-534.

YONG Heng, YUAN Guoxing, WANG Zheng. Two Schemes of Integrated Gradient Method[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2008, 25(5): 525-534.

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