A stabilized finite element method based on characteristic-based polynomial pressure projection scheme for incompressible flows

In this paper, a characteristic-based polynomial pressure projection (CBP3) scheme is proposed to stabilize finite element method for solving incompressible laminar flow. The characteristic-Galerkin (CG) method is adopted as the stabilization for convection caused oscillation in CBP3 scheme. The pressure oscillation caused by incompressible constraint is stabilized by the polynomial pressure projection (P3) technique. Proposed scheme is suitable for any element using the equal-order approximation for velocity and pressure. In this paper, the linear triangular and bilinear quadrilateral elements are adopted. The constant pressure projection is used for triangular elements. The CBP3 formulations for quadrilateral element are derived using both constant and linear pressure projections. Besides, the quasi-implicit second-order time stepping is adopted. The verification of CBP3 scheme implementation and validation of CBP3 scheme are accomplished by calculating several benchmarks. The results of CBP3 scheme reveal that the linear pressure projection for quadrilateral element is not appropriate due to its severe pressure oscillation. The well-agreed results of CBP3 scheme using constant pressure projection demonstrate its good stabilization for FEM to solve both low and relatively high Reynolds number flows.