SUMMARYIn this paper we present a stress-based least-squares finite-element formulation for the solution of the Navier-Stokes equations governing flows of viscous incompressible fluids. Stress components are introduced as independent variables to make the system first order. Continuity equation becomes an algebraic equation and is eliminated from the system with suitable modifications. The h and p convergence are verified using the exact solution of Kovasznay flow. Steady flow past a large circular cylinder in a channel is solved to test mass conservation. Transient flow over a backward-facing step problem is solved on several meshes. Results are compared with that obtained using vorticity-based first-order formulation for both benchmark problems.
SUMMARYIn 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. Secondorder 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).
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