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Fourier analysis of an equal‐order incompressible flow solver stabilized by pressure gradient projection
Author(s) -
Buscaglia Gustavo C.,
Basombrío Fernando G.,
Codina Ramon
Publication year - 2000
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 - 10.1002/1097-0363(20000915)34:1<65::aid-fld56>3.0.co;2-j
Subject(s) - spurious relationship , projection (relational algebra) , fourier transform , incompressible flow , mathematics , solver , finite element method , pressure correction method , mathematical analysis , compressibility , navier–stokes equations , reynolds number , projection method , extrapolation , pressure gradient , fourier analysis , flow (mathematics) , computational fluid dynamics , galerkin method , physics , geometry , mathematical optimization , mechanics , algorithm , dykstra's projection algorithm , statistics , turbulence , thermodynamics
Fourier analysis techniques are applied to the stabilized finite element method (FEM) recently proposed by Codina and Blasco for the approximation of the incompressible Navier–Stokes equations, here denoted by pressure gradient projection (SPGP) method. The analysis is motivated by spurious waves that pollute the computed pressure in start‐up flow simulation. An example of this spurious phenomenon is reported. It is shown that Fourier techniques can predict the numerical behaviour of stabilized methods with remarkable accuracy, even though the original Navier–Stokes setting must be significantly simplified to apply them. In the steady state case, good estimates for the stabilization parameters are obtained. In the transient case, spurious long waves are shown to be persistent when the element Reynolds number is large and the Courant number is small. This can be avoided by treating the pressure gradient projection implicitly, though this implies additional computing effort. Standard extrapolation variants are unfortunately unstable. Comparisons with Galerkin–least‐squares (GLS) method and Chorin's projection method are also addressed. Copyright © 2000 John Wiley & Sons, Ltd.