Analysis and computation of extremum points with application to boundary-layer stability
type: Item
instance of: scholarly article
title: Analysis and computation of extremum points with application to boundary-layer stability
zbMATH Open document ID: 0863.65045
published in: Journal of Computational Physics
publication date: 1997-06-08T00:00:00Z
review text: A method for analysis and computation of derivatives and extremum points of variable-coefficients differential eigenvalue problems is presented. The method utilizes the orthogonality of the adjoint eigenfunctions to the homogeneous part of the once or more differentiated problem to derive an analytical expression for the rate of change of the eigenvalue with respect to a free parameter. The extremum point can be analyzed and computed by setting and driving, respectively, the first rate of change of the eigenvalue with respect to the free parameters to zero. Higher-order derivatives can be computed by solving, sequentially, sets of inhomogeneous two-point boundary value problems. The method is applied to analyze and compute the most amplified inviscid instability wave in two-dimensional compressible boundary layers and the most amplified viscous instability wave in three-dimensional incompressible boundary layers. It is shown analytically that while the most-amplified spatial instability wave in two-dimensional incompressible boundary layer is two-dimensional, the corresponding most amplified wave in three-dimensional boundary layer is generally oblique. It is also shown analytically that the most-amplified disturbance in three-dimensional boundary layer is generally a traveling disturbance. Furthermore, it is shown analytically that the inviscid growth rate is an extremum point.
reviewed by: Fuhua Ling
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 76N20
Mathematics Subject Classification ID: 76D10
Mathematics Subject Classification ID: 34L15
zbMATH DE Number: 947713
zbMATH Keywords: dissipative system
zbMATH Keywords: stability
zbMATH Keywords: extremum points
zbMATH Keywords: differential eigenvalue problems
zbMATH Keywords: eigenfunctions
zbMATH Keywords: inviscid instability wave
zbMATH Keywords: compressible boundary layers
zbMATH Keywords: viscous instability wave
zbMATH Keywords: incompressible boundary layers
author: Jamal A. Masad
MaRDI profile type: Publication
full work available at URL: jcph.1996.0187
OpenAlex ID: W2092819671
DOI: 10.1006/JCPH.1996.0187
description: scientific article; zbMATH DE number 947713