Development of a finite element solution for the unsteady Navier–Stokes equations using projection method and fractional-θ-scheme Original Research Article

A numerical model for computing non-stationary incompressible Navier–Stokes equations is developed and evaluated. The spatial domain is discretized by the consistent streamline upwind Petrov–Galerkin (SUPG) finite element method to stabilize the convection terms for high Reynolds number flow. The velocity–pressure formulation of the discretized problem is decoupled by the projection method. Moreover, the semi-discretized problem is integrated by the fractional-θ-scheme in the temporal domain. Finally, the resulting symmetric and non-symmetric linear problems are respectively, solved by the preconditioned conjugate gradient method and the preconditioned quasi minimal residual method. Numerical experiments for flows inside a driven cavity, over a backward-facing step and over a square cylinder were performed and compared with experimental measurements and other numerical results.