Dergiler / Turkish Journal of Engineering and Environmental Sciences / 1999 / Cilt: 23 - Sayı: 6
Single Value Decomposition For Stability Analysis of Nonlinear Poiseuille Flows
- Sayfa
- 403–410
- DOI
- —
Özet
In nonlinear analysis of fluid mechanics problems, small amplitude oscillations near the Hopf bifurcation point are well-described by the Ginzburg-Landau equation. The coefficients of the Ginzburg-Landau equation can be computed efficiently and conveniently by Singular Value Decomposition (SVD). In this study, the Ginzburg-Landau equation is derived for plane Poiseuille flow problem of a Newtonian fluid and the SVD method is applied in order to show how to find the coefficients of the Ginzburg-Landau equation. The analysis indicates that SVD is easy to implement and straightforward; making it the method of choice for the numerical computations of the coefficients of amplitude equations.
Abstract
In nonlinear analysis of fluid mechanics problems, small amplitude oscillations near the Hopf bifurcation point are well-described by the Ginzburg-Landau equation. The coefficients of the Ginzburg-Landau equation can be computed efficiently and conveniently by Singular Value Decomposition (SVD). In this study, the Ginzburg-Landau equation is derived for plane Poiseuille flow problem of a Newtonian fluid and the SVD method is applied in order to show how to find the coefficients of the Ginzburg-Landau equation. The analysis indicates that SVD is easy to implement and straightforward; making it the method of choice for the numerical computations of the coefficients of amplitude equations.