A finite element approximation of the unsteady two-dimensional Navier–Stokes equations

✍ Scribed by F. N. Van De Vosse; A. Śegal; A. A. Van Steenhoven; J. D. Janssen

• Publisher: John Wiley and Sons
• Year: 1986
• Tongue: English
• Weight: 726 KB
• Volume: 6
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/fld.1650060703

✦ Synopsis

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 (El) 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.