Premium
The cause and cure (?) of the spurious pressures generated by certain FEM solutions of the incompressible Navier‐Stokes equations: Part 1
Author(s) -
Sani R. L.,
Gresho P. M.,
Lee R. L.,
Griffiths D. F.
Publication year - 1981
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650010104
Subject(s) - spurious relationship , discretization , finite element method , compressibility , interpolation (computer graphics) , convergence (economics) , context (archaeology) , mathematics , pressure correction method , navier–stokes equations , mathematical analysis , mechanics , classical mechanics , physics , geology , motion (physics) , paleontology , statistics , economics , economic growth , thermodynamics
The spurious pressures and ostensibly acceptable velocities which sometimes result from certain FEM approximate solutions of the incompressible Navier–Stokes equations are explained in detail. The concept of pressure modes, physical and spurious, pure and impure, is introduced and their effects on discretized solutions is analysed, in the context of both mixed interpolation and penalty approaches. Pressure filtering schemes, which are capable of recovering useful pressures from otherwise polluted numerical results, are developed for two particular elements in two‐dimensions and one element in three‐dimensions. Implications regarding the effect of spurious pressure modes on accuracy and ultimate convergence with mesh refinement are discussed and a list of unanswered questions presented. Sufficient numerical examples are discussed to corroborate the theory presented herein.