Pressure stabilized finite elements simulation for steady and unsteady Newtonian fluids

A numerical simulation of an incompressible viscous flow using the finite element method is presented. In this study, the pressure stabilization technique is suggested for the treatment of the incompressibility constraint for both steady and unsteady flow cases. To the best of the authors’ knowledge, the pressure stabilization technique is used for steady flows only. The proposed technique allows for equal low-order interpolation polynomials to be used for all variables which circumvent the so-called LBB compatibility condition without pressure checker boarding and solution instabilities. Results are obtained for two benchmark problems, namely, lid-driven cavity flow and the vortex-shedding behind a circular cylinder. The results are compared with published numerical and experimental works with an apparent degree of success.