Finite element solution of the Orr-Sommerfeld equation using high precision Hermite elements: plane Poiseuille flow

摘要

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.