Premium
Consistent Petrov–Galerkin finite element simulation of channel flows
Author(s) -
Sheu Tony W.H.,
Tsai S.F.
Publication year - 1999
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/(sici)1097-0363(19991230)31:8<1297::aid-fld925>3.0.co;2-4
Subject(s) - finite element method , petrov–galerkin method , laminar flow , curvature , galerkin method , quadratic equation , mathematics , flow (mathematics) , computational fluid dynamics , mechanics , mathematical analysis , geometry , physics , engineering , structural engineering
In this paper, Navier–Stokes fluid flows in curved channels are considered. Upstream of the backward‐facing step, there exists a channel with a 90° bend and a fixed curvature of 2.5. The purpose of conducting this study was to apply a finite element code to study the effect of the distorted upstream velocity profile developing over the bend on laminar expansion flows behind the step. The size of the eddies formed downstream of the step is addressed. The present work employs primitive velocities, which stagger the pressure working variable, to assure satisfaction of the inf–sup stability condition. In quadratic elements, spatial derivatives are approximated within the consistent Petrov–Galerkin finite element framework. Use of this method aids stability in the sense that artificial damping is solely added to the direction parallel to the flow direction. Through analytical testing, in conjunction with two other benchmark tests, the integrity of applying the computer code in quadratic elements is verified. Copyright © 1999 John Wiley & Sons, Ltd.