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Feedback Stabilization of an Oscillating Vertical Cylinder by POD Reduced‐Order Model
Author(s) -
Tissot Gilles,
Cordier Laurent,
Noack Bernd R.
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410347
Subject(s) - point of delivery , cylinder , mathematics , reynolds number , control theory (sociology) , flow (mathematics) , constraint (computer aided design) , quadratic equation , fictitious domain method , domain (mathematical analysis) , lagrange multiplier , mathematical analysis , mechanics , physics , geometry , mathematical optimization , turbulence , computer science , control (management) , artificial intelligence , agronomy , biology
The objective of this paper is to demonstrate the use of Reduced‐Order Models (ROM) based on Proper Orthogonal Decomposition (POD) to stabilize by vertical oscillations the flow over a circular cylinder at a Reynolds number equal to 60. Since in Fluid‐Structure Interaction, the POD algorithm cannot be applied directly, we then implement the fictitious domain method of [1] where the solid domain is treated as a fluid undergoing an additional constraint. The POD‐ROM is classically obtained by projecting the Navier‐Stokes equations on a small number of POD modes. The cylinder movement is then enforced in the POD‐ROM through the introduction of Lagrange multipliers. A Linear Quadratic Regulator framework is used to determine the optimal control law, in our case the vertical velocity of the cylinder, such that the flow is stabilized. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)