Acta Mechanica Sinica

, Volume 32, Issue 1, pp 54–63 | Cite as

SUPG finite element method based on penalty function for lid-driven cavity flow up to \(Re = 27500\)

  • Da-Guo WangEmail author
  • Qing-Xiang Shui
Research Paper


A streamline upwind/Petrov–Galerkin (SUPG) finite element method based on a penalty function is proposed for steady incompressible Navier–Stokes equations. The SUPG stabilization technique is employed for the formulation of momentum equations. Using the penalty function method, the continuity equation is simplified and the pressure of the momentum equations is eliminated. The lid-driven cavity flow problem is solved using the present model. It is shown that steady flow simulations are computable up to \(Re = 27500\), and the present results agree well with previous solutions. Tabulated results for the properties of the primary vortex are also provided for benchmarking purposes.


Streamline upwind/Petrov–Galerkin (SUPG) finite element method Lid-driven cavity flow Penalty function method High Reynolds number 



This project was supported by the National Natural Science Foundation of China (Grants 41372301 and 51349011) and the Preeminent Youth Talent Project of Southwest University of Science and Technology (Grant 13zx9109).


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of Environment and ResourcesSouthwest University of Science and TechnologyMianyangChina

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