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A finite element approximation of the unsteady two‐dimensional Navier–Stokes equations
Author(s) -
Van De Vosse F. N.,
Śegal A.,
Van Steenhoven A. A.,
Janssen J. D.
Publication year - 1986
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.1650060703
Subject(s) - finite element method , mathematics , navier–stokes equations , penalty method , pressure correction method , convergence (economics) , flow (mathematics) , backward euler method , cylinder , compressibility , mathematical analysis , computation , euler equations , mechanics , physics , geometry , mathematical optimization , economics , thermodynamics , economic growth , algorithm
In this paper a penalty finite element solution method for the unsteady Navier–Stokes equations for two‐dimensional incompressible flow is described. The performances of the Euler implicit (EI) and the Crank–Nicolson (CN) time integration methods are analysed. Special attention is payed to the undamped pressure oscillations which can occur when the Crank–Nicolson integration rule is used in combination with the penalty function method. Stability and convergence properties are illustrated by means of the computation of fully developed oscillating flow between two flat plates. Furthermore, the von Karman vortex street past a circular cylinder is computed to demonstrate the behaviour of the time integration schemes for a more complicated flow. It is concluded that the EI method has its advantages over the CN method with respect to the damping of numerical oscillations. However, for flows with an important convective contribution, where physically originated oscillations may be present, the CN method is preferable.