Numerical smoothing techniques applied to some finite element solutions of the Navier--Stokes equations

Two categories of smoothing techniques which generate continuous approximations of vorticity and pressure from finite-element solutions of the Navier--Stokes equation are considered and qualitative comparisons are made from numerical solution of the steady-state driven cavity problems.

Abstract

Two categories of smoothing techniques which generate continuous approximations (i.e., nodal values) of vorticity and pressure from finite-element solutions of the Navier--Stokes equation are considered. The simplest schemes, developed for quadrilateral elements, are those based on combinations of linear extrapolation and/or averaging algorithms which bring element-wise Gauss point evaluations out to node points. 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 several schemes is obtained by comparing with an analytical function. Next, qualitative comparisons are made from numerical solutions of the steady-state driven cavity problems. Finally, applications of smoothing techniques to discontinuous pressure fields are demonstrated.