三维笛卡儿坐标系中Lagrange流体力学的显式相容有限元方法(英文)

计算物理 ›› 2009, Vol. 26 ›› Issue (5): 671-678.

三维笛卡儿坐标系中Lagrange流体力学的显式相容有限元方法(英文)

贾祖朋, 蔚喜军, 赵桂萍

北京应用物理与计算数学研究所, 计算物理实验室, 北京 100088

收稿日期:2007-06-25 修回日期:2009-02-07 出版日期:2009-09-25 发布日期:2009-09-25
作者简介:贾祖朋(1967-),male,Hunan,Ph.D.,research in computational mathematics and CFD.
基金资助:
Supported by the National 973 Project of China(2005CB321700);the National Nature Science Foundation of China(10771019,10671025);the Science and Technology Foundation of the Chinese Academy of Engineering Physics(2007A09006)

Explicit Compatible Finite Element Method for Lagrangian Hydrodynamics in Three-dimensional Cartesian Geometry

JIA Zupeng, YU Xijun, ZHAO Guiping

Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

Received:2007-06-25 Revised:2009-02-07 Online:2009-09-25 Published:2009-09-25
Supported by:
Supported by the National 973 Project of China(2005CB321700);the National Nature Science Foundation of China(10771019,10671025);the Science and Technology Foundation of the Chinese Academy of Engineering Physics(2007A09006)

摘要/Abstract

摘要： 将Caramana等人提出的相容算法思想和有限元方法相结合,提出三维笛卡儿坐标系中Lagrange流体力学的显式相容有限元方法.采用三线性六面体单元和交错网格进行空间离散,利用质量集中进行显式求解,无需求解线性代数方程组.时间离散可采用两步显式Runge-Kutta格式.用边人工粘性消除激波振荡,用子网格扰动压力抑制网格的非物理变形.给出若干标准算例.数值算例表明,该方法具有较高的计算精度和计算效率,同时具有很好的对称性和总能量守恒性,总能量计算误差为计算机浮点计算截断误差.

关键词: 三维笛卡尔坐标系, Lagrange流体力学, 显式相容有限元方法

Abstract: We present an explicit compatible finite element method for fluid dynamics problems in three-dimensional Cartesian geometry.Trilinear brick elements with a staggered-grid placement of the spatial variables are used to discretize fluid equations.An edge-centered artificial viscosity whose magnitude is regulated by local velocity gradients is used to capture shocks.Subzonal perturbed pressure is adopted to resist spurious grid motions.Artificial viscosity forces and subzonal pressure forces agree well with general compatibility.Numerical examples show accuracy and robustness of the method.

Key words: three-dimensional Cartesion coordinates, Lagrangian hydrodynamics, explicit compatible finite element method

中图分类号:

O241.82

贾祖朋, 蔚喜军, 赵桂萍. 三维笛卡儿坐标系中Lagrange流体力学的显式相容有限元方法(英文)[J]. 计算物理, 2009, 26(5): 671-678.

JIA Zupeng, YU Xijun, ZHAO Guiping. Explicit Compatible Finite Element Method for Lagrangian Hydrodynamics in Three-dimensional Cartesian Geometry[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 26(5): 671-678.

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