Spectral/hp penalty least-squares finite element formulation for unsteady incompressible flows

In this paper, we present spectral/hp penalty least-squares finite element formulation for the numerical solution of unsteady incompressible Navier-Stokes equations. Pressure is eliminated from Navier-Stokes equations using penalty method, and finite element model is developed in terms of velocity, vorticity and dilatation. High-order element expansions are used to construct discrete form. Unlike other penalty finite element formulations, equal-order Gauss integration is used for both viscous and penalty terms of the coefficient matrix. For time integration, space-time decoupled schemes are implemented. Second-order accuracy of the time integration scheme is established using the method of manufactured solution. Numerical results are presented for impulsively started lid-driven cavity flow at Reynolds number of 5000 and transient flow over a backward-facing step. The effect of penalty parameter on the accuracy is investigated thoroughly in this paper and results are presented for a range of penalty parameter. Present formulation produces very accurate results for even very low penalty parameters (10-50). Copyright (C) 2008 John Wiley & Sons, Ltd.