Single Value Decomposition For Stability Analysis of Nonlinear Poiseuille Flows


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.

Keywords: Poiseuille flow, Stability, Bifurcation theory, Singular Value Decomposition

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