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。 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.

The Planar Element with Eight Nodes for Solving Incompressible Navier-Stokes Equations

A comparative study of the bi-linear and bi-quadratic quadrilateral elements and the quadratic triangular element for solving incompressible viscous flows is presented. These elements make use of the stabilized finite element formulation of the Galerkin/least-squares method to simulate the flows, with the pressure and velocity fields interpolated with equal orders. The tangent matrices are explicitly derived and the Newton–Raphson algorithm is employed to solve the resulting nonlinear equations. The numerical solutions of the classical lid-driven cavity flow problem are obtained for Reynolds numbers between 1000 and 20 000 and the accuracy and converging rate of the different elements are compared. The influence on the numerical solution of the least square of incompressible condition is also studied. The numerical example shows that the quadratic triangular element exhibits a better compromise between accuracy and converging rate than the other two elements. Copyright © 2008 John Wiley & Sons, Ltd.

Yongtao Wei

Papers

A comparative study of GLS finite elements with velocity and pressure equally interpolated for solving incompressible viscous flows