Smoothing techniques for certain primitive variable solutions of the Navier-Stokes equations

Several types of smoothing technique are considered which generate continuous approximation (i.e. nodal values) for vorticity and pressure from finite element solutions of the Navier-Stokes equations using quadrilateral elements. The simpler schemes are based on combinations of linear extrapolation and/or averaging algorithms which convert elementwise. Gauss point values to nodal point values. More complicated schemes, based on a global smoothing technique which employ the mass matrix (consistent or lumped), are also presented.An initial assessment of the accuracy of the several schemes is obtained by comparing the approximate vorticities with an analytical function. Next, qualitative vorticity comparisons are made from numerical solutions of the steady-state driven cavity problem. Finally, applications of smoothing techniques to discontinuous pressure fields are demonstrated.