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Finite element solution of the Orr–Sommerfeld equation using high precision Hermite elements: plane Poiseuille flow
Author(s) -
Mamou M.,
Khalid M.
Publication year - 2004
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.661
Subject(s) - hagen–poiseuille equation , laminar flow , reynolds number , finite element method , perturbation (astronomy) , mathematics , mechanics , hydrodynamic stability , plane (geometry) , numerical analysis , mathematical analysis , flow (mathematics) , physics , geometry , turbulence , quantum mechanics , thermodynamics
This paper presents a comprehensive review of the numerical techniques used during the past half century and their accuracy in hydrodynamic stability analysis of plane parallel flows. The paper also describes a finite element solution of the Orr–Sommerfeld equation using high precision Hermite elements. A stability analysis technique is performed by imposing an infinitesimal perturbation to the laminar base flow to determine the thresholds of neutral instabilities or the growth rate of the perturbation for any Reynolds and wave numbers. Validation of the present numerical technique is performed for plane Poiseuille flow. The numerical results, obtained with uniform and nonuniform meshes, show excellent agreement with the most accurate results available in the literature. Copyright © 2004 John Wiley & Sons, Ltd.