Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
DISCRETE AND CONTINUOUS SPECTRAL METHODS APPLIED TO BOUNDARY LAYER STABILITY
Submission Author:
Juan Carlos Assis da Silva , RJ
Co-Authors:
Juan Carlos Assis da Silva, Rômulo Bessi Freitas, Leonardo Santos de Brito Alves
Presenter: Juan Carlos Assis da Silva
doi://10.26678/ABCM.COBEM2021.COB2021-0174
Abstract
Matrix forming is arguably the most used technique to solve linear stability problems. It generates and solves an algebraic generalized eigenvalue problem constructed from the linear differential eigenvalue problem that models the time asymptotic behavior of small amplitude disturbances. This construction is quite often done using spectral methods, but finite difference methods are used as well. In a previous study of the Orr-Sommerfeld equation modeling the linear, local and modal stability of the plane Poiseuille flow, it was shown that discrete and continuous spectral methods have equivalent performances in terms of absolute error versus CPU time. This flow, however, has an analytical steady-state. This means that the required integral coefficients in a continuous spectral method can be calculated analytically. In the present work, the plane boundary layer forming over a flat plate is investigated instead. It is significantly more difficult for continuous spectral methods because its numerical steady-state requires the integral coefficients to be calculated numerically as well. Comparisons between continuous and discrete Chebyshev transforms was preformed in terms of absolute error versus CPU time and the results show an advantage for the discrete spectral methodology.
Keywords
stability analysis, Spectral Methods, Eigenvalue Problem
