Penalty Function Solution of Steady-State Navier-Stokes Equations

Abstract

I the numerical solution of the Navier-Stokes equations for steady, incompressible viscous flow using the finiteelement method, the use of primitive fluid variables in two dimensions offers advantages which have led to an increasing interest in their use, especially when extensions to threedimensional flows are in mind. ! The main problem faced when primitive variables are considered arise from imposing the incompressibility constraint. This usually has been achieved by weighting the continuity equation using the interpolation functions for the pressure in a Galerkin formulation, and, in some cases, through the use of interpolation functions for the velocity field that satisfy the continuity equation a priori, elementwise. 3 A third possibility is the addition of a penalized term to the Galerkin form of the momentum equations with the advantage that the pressure is eliminated as a dependent variable. The latter approach has been called the penalty function finite-element method. In this Note, conclusions obtained from extensive quantitative evaluation using three types of rectangular elements are discussed, and the advantages of using biquadratic interpolation functions are pointed out. We consider the solution of the two-dimensional, NavierStokes equations for an incompressible fluid with constant physical properties