求解不可压缩Navier-Stokes方程的GLS平面八节点单元
The Planar Element with Eight Nodes for Solving Incompressible Navier-Stokes Equations

作者: 魏晓娟 :四川电力职业技术学院动力工程系,成都; 刘力菱 :西南交通大学材料科学与工程学院,成都; 谢凌志 , 易丽清 , 魏泳涛 :四川大学建筑与环境学院应用力学系,成都;

关键词: Galerkin/最小二乘有限元稳定因子单元长度逆估计常数Galerkin/Least Squares FEM Stabilization Factor Element Length Inverse Estimate Constant

摘要:

给出了求解不可压缩Navier-Stokes方程的GLS平面八节点单元的“单元长度”的定义和相应的逆估计常数,由此可计算出该单元的GLS稳定因子。给出的“单元长度”只依赖单元形状且易于计算;各种形状的直边四边形单元的逆估计常数的最大值由遗传算法得出。对Reynolds数为20,000的方腔上盖板流的数值模拟表明,本文所提出的单元长度和逆估计常数的正确性。

Abstract: The definition of the element length and the inverse estimate constant of straight-edged quadrilateral element with eight nodes for solving incompressible Navier-Stokes equations was proposed, based on this, the stabilization factor was readily calculated. The element length was only dependent on the quadrilateral geometry and easy to compute, and the largest inverse estimate constant among various quadrilateral was obtained by means of the optimization method of genetic algorithm (GA). The numerical solutions of the classical lid-driven cavity flow problem were ob- tained for Reynolds number of 20,000 which demonstrated the validity of the element length and the inverse estimate constant proposed.

文章引用: 魏晓娟 , 刘力菱 , 谢凌志 , 易丽清 , 魏泳涛 (2013) 求解不可压缩Navier-Stokes方程的GLS平面八节点单元。 流体动力学, 1, 15-20. doi: 10.12677/IJFD.2013.12003

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