基于特征理论的二维无粘Lagrange流体力学有限体积法

计算物理 ›› 2011, Vol. 28 ›› Issue (1): 19-26.

基于特征理论的二维无粘Lagrange流体力学有限体积法

孙宇涛¹, 任玉新², 于明¹, 张树道¹

1. 北京应用物理与计算数学研究所, 北京 100094;
2. 清华大学工程力学系, 北京 l00084

收稿日期:2009-12-11 修回日期:2010-06-03 出版日期:2011-01-25 发布日期:2011-01-25
通讯作者: 于明,E-mail:yuming9999l@sina.com
作者简介:孙宇涛(1979-),男,辽宁新民,助理研究员,博士,主要从事计算流体力学研究.
基金资助:
国家自然科学基金(10932005和11072040);中国工程物理研究院科学发展基金(2010B0201030)资助项目

A Finite Volume Method for 2D Inviscous Lagrangian Hydrodynamics Based on Characteristics Theory

SUN Yutao¹, REN Yuxin², YU Ming¹, ZHANG Shudao¹

1. Institute of Applied Physics and Computational Mathematics, Beijing 100094, China;
2. Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China

Received:2009-12-11 Revised:2010-06-03 Online:2011-01-25 Published:2011-01-25

摘要/Abstract

摘要： 提出一个求解二维无粘Lagrange流体力学方程的中心型有限体积方法.采用特征理论求解网格节点处的速度及压力,并利用这些物理量更新节点位置及计算网格界面通量.方法适用于结构网格与非结构网格.典型数值实验的结果表明,格式具有较好的收敛性、对称性、能量守恒性及鲁棒性,且能自然地求解多物质流动问题.

关键词: 二维Lagrange流体力学, 特征理论, 中心型格式

Abstract: We present a cell-centered finite volume method for 2D invicsous Lagrangian hydrodynamics.Velocity and pressure on vertex of a cell are computed with characteristics theory,which is derived from governing equations of Lagrangian form linearized by freezing Jacobian matrices about a known reference state.The velocity is used to update coordinate of vertex of a cell.Product of two variables is used to compute numerical flux through cell interface by a trapezoidal integration rule.Convergency,symmetry and conservation of total energy of the method are demonstrated.The method can be applied to structured or unstructured grids,and does well spontaneously for multi-material flows in a robust way.The scheme is one order precision,and can be easily draw on two order precision.

Key words: 2D Lagrangian hydrodynamics, characteristics theory, cell-centered scheme

中图分类号:

O351

孙宇涛, 任玉新, 于明, 张树道. 基于特征理论的二维无粘Lagrange流体力学有限体积法[J]. 计算物理, 2011, 28(1): 19-26.

SUN Yutao, REN Yuxin, YU Ming, ZHANG Shudao. A Finite Volume Method for 2D Inviscous Lagrangian Hydrodynamics Based on Characteristics Theory[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2011, 28(1): 19-26.

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