SUPG finite element method based on penalty function for lid-driven cavity flow up to \(Re = 27500\). (English) Zbl 1342.76080
Summary: 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.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
Keywords:
streamline upwind/Petrov-Galerkin (SUPG) finite element method; lid-driven cavity flow; penalty function method; high Reynolds numberReferences:
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