A semi-implicit three-step method based on SUPG finite element formulation for flow in lid driven cavities with different geometries

• Published in: Journal of Zhejiang University. A. Science Vol. 12; no. 1; pp. 33 - 45
• Main Authors: Huang, Cheng, Zhou, Dai, Bao, Yan
• Format: Journal Article
• Language: English
• Published: Hangzhou Zhejiang University Press 2011
• Subjects: Civil Engineering; Classical and Continuum Physics; Engineering; Industrial Chemistry/Chemical Engineering; Mechanical Engineering; Stokes方程; 不可压缩粘性流体; 几何形状; 半隐式; 有限元方程; 非线性有限元; 驱动流; Semi-implicit three-step method; TU3; Unsteady incompressible flows; Lid driven cavity problem; Streamline upwind/Petrov-Galerkin (SUPG) finite element method (FEM)
• ISSN: 1673-565X; 1862-1775
• DOI: 10.1631/jzus.A1000098

A numerical algorithm using a bilinear or linear finite element and semi-implicit three-step method is presented for the analysis of incompressible viscous fluid problems. The streamline upwind/Petrov-Galerkin （SUPG） stabilization scheme is used for the formulation of the Navier-Stokes equations. For the spatial discretization, the convection term is treated explicitly, while the viscous term is treated implicitly, and for the temporal discretization, a three-step method is employed. The present method is applied to simulate the lid driven cavity problems with different geometries at low and high Reynolds numbers. The results compared with other numerical experiments are found to be feasible and satisfactory.