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Spectral/ hp penalty least‐squares finite element formulation for unsteady incompressible flows
Author(s) -
Prabhakar V.,
Reddy J. N.
Publication year - 2008
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1708
Subject(s) - penalty method , finite element method , mathematics , pressure correction method , navier–stokes equations , reynolds number , incompressible flow , spectral element method , compressibility , mathematical analysis , vorticity , mixed finite element method , flow (mathematics) , mathematical optimization , turbulence , physics , mechanics , vortex , geometry , thermodynamics
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 © 2008 John Wiley & Sons, Ltd.