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

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.