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Smoothing techniques for certain primitive variable solutions of the Navier–Stokes equations
Author(s) -
Lee Robert L.,
Gresho Philip M.,
Sani Robert L.
Publication year - 1979
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620141204
Subject(s) - smoothing , mathematics , extrapolation , quadrilateral , vorticity , navier–stokes equations , mathematical analysis , finite element method , function (biology) , physics , vortex , mechanics , statistics , compressibility , thermodynamics , evolutionary biology , biology
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.