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Local improvements to reduced-order models using sensitivity analysis of the proper orthogonal decomposition

Published online by Cambridge University Press:  15 June 2009

ALEXANDER HAY ,
JEFFREY T. BORGGAARD  and
DOMINIQUE PELLETIER
ALEXANDER HAY*
Affiliation:
Interdisciplinary Center for Applied Mathematics, Virginia Tech, Blacksburg, VA 24061, USA
JEFFREY T. BORGGAARD
Affiliation:
Interdisciplinary Center for Applied Mathematics, Virginia Tech, Blacksburg, VA 24061, USA
DOMINIQUE PELLETIER
Affiliation:
Département de Génie Mécanique, Ecole Polytechnique de Montréal, Montréal, QC H3C3A7, Canada
*
†Email address for correspondence: hay@vt.edu
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Abstract

The proper orthogonal decomposition (POD) is the prevailing method for basis generation in the model reduction of fluids. A serious limitation of this method, however, is that it is empirical. In other words, this basis accurately represents the flow data used to generate it, but may not be accurate when applied ‘off-design’. Thus, the reduced-order model may lose accuracy for flow parameters (e.g. Reynolds number, initial or boundary conditions and forcing parameters) different from those used to generate the POD basis and generally does. This paper investigates the use of sensitivity analysis in the basis selection step to partially address this limitation. We examine two strategies that use the sensitivity of the POD modes with respect to the problem parameters. Numerical experiments performed on the flow past a square cylinder over a range of Reynolds numbers demonstrate the effectiveness of these strategies. The newly derived bases allow for a more accurate representation of the flows when exploring the parameter space. Expanding the POD basis built at one state with its sensitivity leads to low-dimensional dynamical systems having attractors that approximate fairly well the attractor of the full-order Navier–Stokes equations for large parameter changes.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 629 , 25 June 2009 , pp. 41 - 72
Copyright
Copyright © Cambridge University Press 2009

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