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Weak imposition of boundary conditions for the Navier–Stokes equations by a penalty method
Author(s) -
Caglar Atife,
Liakos Anastasios
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.1950
Subject(s) - boundary value problem , mathematics , stokes flow , navier–stokes equations , nonlinear system , convergence (economics) , finite element method , mathematical analysis , penalty method , inertial frame of reference , slip (aerodynamics) , hagen–poiseuille flow from the navier–stokes equations , computational fluid dynamics , boundary (topology) , no slip condition , flow (mathematics) , mixed boundary condition , geometry , mathematical optimization , classical mechanics , mechanics , physics , compressibility , quantum mechanics , economics , thermodynamics , economic growth
We prove convergence of the finite element method for the Navier–Stokes equations in which the no‐slip condition and no‐penetration condition on the flow boundary are imposed via a penalty method. This approach has been previously studied for the Stokes problem by Liakos (Weak imposition of boundary conditions in the Stokes problem. Ph.D. Thesis , University of Pittsburgh, 1999). Since, in most realistic applications, inertial effects dominate, it is crucial to extend the validity of the method to the nonlinear Navier–Stokes case. This report includes the analysis of this extension, as well as numerical results validating their analytical counterparts. Specifically, we show that optimal order of convergence can be achieved if the computational boundary follows the real flow boundary exactly. Copyright © 2008 John Wiley & Sons, Ltd.