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

Abstract

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. © 2001 Elsevier Science B.V. All rights reserved.