NDLI: Nonlinear model reduction for fluid flows

Content Provider	IEEE Xplore Digital Library
Author	Sahyoun, S. Djouadi, S.M.
Copyright Year	2011
Description	Author affiliation: Dept. of Electr. Eng. & Comput. Sci., Univ. of Tennessee, Knoxville, TN, USA (Sahyoun, S.; Djouadi, S.M.)
Abstract	Model Reduction is an essential tool that has been applied in many control applications such as control of fluid flows. Most model reduction algorithms assume linear models and fail when applied to nonlinear high dimensional systems, in particular, fluid flow problems with high Reynolds numbers. For example, proper orthogonal decomposition (POD) fails to capture the nonlinear degrees of freedom in these systems, since it assumes that data belong to a linear space and therefore relies on the Euclidean distance as the metric to minimize. However, snapshots generated by nonlinear partial differential equations (PDEs) belong to manifolds for which the geodesies do not correspond in general to the Euclidean distance. A geodesic is a curve that is locally the shortest path between points. In this paper, we propose a model reduction method which generalizes POD to nonlinear manifolds which have a differentiable structure at each of their points. Moreover, an optimal method in constructing reduced order models for the two-dimensional Burgers' equation subject to boundary control is presented and compared to the POD reduced models.
Sponsorship	Control Syst. Soc.
Starting Page	1765
Ending Page	1769
File Size	748315
Page Count	5
File Format	PDF
ISBN	9781457700804
ISSN	07431619
e-ISBN	9781457700811
DOI	10.1109/ACC.2011.5991592
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-06-29
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	American Automatic Control Council(AACC)
Subject Keyword	Manifolds Mathematical model Reduced order systems Boundary conditions Aerodynamics Geometry Computational modeling
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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