期刊导航

论文摘要

求解不可压缩粘性流的GLS单元之比较

A Comparative Study of Different GLS Elements for Solving Incompressible Viscous Flows

作者:魏泳涛(四川大学);于建华(四川大学 建筑与环境学院,四川 成都 610065);Philippe H. Geubelle(Dept. of Aerospace Eng., Univ. of Illinois, Urbana,IL 61801, USA)

Author:Wei Yongtao(Sichuan University);于建华(School of Architecture and Environment, Sichuan Univ., Chengdu 610065,China);Philippe H. Geubelle(Dept. of Aerospace Eng., Univ. of Illinois, Urbana,IL 61801, USA)

收稿日期:2008-06-02          年卷(期)页码:2009,41(1):60-67

期刊名称:工程科学与技术

Journal Name:Advanced Engineering Sciences

关键字:不可压缩粘性流,GLS稳定化有限元,Newton–Raphson迭代

Key words:Incompressible viscous flow; GLS stabilized FEM; Newton–Raphson Iteration

基金项目:国家留学基金委2005年“青年骨干教师出国研修项目”

中文摘要

本文比较了用于求解不可压缩粘性流的四边形双线性、双二次单元及三角形二次单元的性能,这些单元采用GLS稳定化有限元格式,而压力和速度采用等阶数插值。对得出的非线性有限元方程,使用Newton–Raphson迭代来求解,详细推导了计算切线矩阵的所需公式。完成了对雷诺数分别为1000、5000、10000和20000的方腔上板流的数值模拟,并对不同单元的结果的精度和收敛率进行了比较。数值算例显示,较之于另两种单元,三角形的二次单元在精度和收敛性上达到最好的匹配。

英文摘要

A comparative study of the bilinear, biquadratic quadrilateral element and quadratic triangular element for solving incompressible viscous flows was presented. These elements make use of the Galerkin/Least squares(GLS) stabilized finite element formulation, in which the pressures and velocities are interpolated with the equal orders. The Newton–Raphson algorithm was employed in solving the nonlinear FEM equations. All formulae needed for calculating the tangential matrices are derived in details in a form to be easily programmed. Using the method proposed, the numerical solutions of lid–driven cavity flow for Reynolds number of 1000, 5000, 10000 and 20000 are obtained, and the accuracy and converging rate of results from the different elements are compared. The numerical example shows that the quadratic triangular element exhibits the best comprise between the accuracy and convergence rate compared to the other two elements.

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