Penalty function solution of steadystate NavierStokes equations
Abstract
The addition of a penalized term to the Galerkin form of the momentum equations in the finite element solution to the NavierStokes equations for steady, incompressible, two dimensional viscous flow is discussed. The implementation of this penalty function finite element method has been examined using three types of rectangular elements. The eightnoded quadratic (serendipity) element is found to show no advantages over the others except that it can be implemented using reduced integration in both matrices without introducing hourglass modes. Biquadratic elements with nine nodes (Lagrangian) are shown to provide a significantly better accuracy than fournoded bilinear elements in such situations as driven cavity flow. The penalty method has been found to provide excellent mass conservation, with stream functions calculated from the computed velocity field virtually path independent.
 Publication:

AIAA Journal
 Pub Date:
 July 1979
 DOI:
 10.2514/3.61224
 Bibcode:
 1979AIAAJ..17..789H
 Keywords:

 Finite Element Method;
 Fluid Dynamics;
 NavierStokes Equation;
 Penalty Function;
 Steady Flow;
 Viscous Flow;
 Cavity Flow;
 Flow Geometry;
 Incompressible Fluids;
 Two Dimensional Flow;
 Fluid Mechanics and Heat Transfer