Collocation methods for exploring perturbations in linear stability analysis

Elman, Howard C. and Silvester, David J. (2017) Collocation methods for exploring perturbations in linear stability analysis. [MIMS Preprint]

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Abstract

Eigenvalue analysis is a well-established tool for stability analysis of dynamical systems. However, there are situations where eigenvalues miss some important features of physical models. For example, in models of incompressible fluid dynamics, there are examples where linear stability analysis predicts stability but transient simulations exhibit significant growth of infinitesimal perturbations. This behavior can be predicted by pseudo-spectral analysis. In this study, we show that an approach similar to pseudo-spectral analysis can be performed inexpensively using stochastic collocation methods and the results can be used to provide quantitative information about instability. In addition, we demonstrate that the results of the perturbation analysis provide insight into the behavior of unsteady flow simulations.

Item Type: MIMS Preprint
Uncontrolled Keywords: stability analysis, collocation, pseudospectra, flow simulation
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: professor david silvester
Date Deposited: 27 Feb 2017
Last Modified: 20 Oct 2017 14:13
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2533

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