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Drag Minimization of the Cylinder Wake by Trust-Region Proper Orthogonal Decomposition

hal.structure.identifierModélisation, contrôle et calcul [MC2]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBERGMANN, Michel
hal.structure.identifierLaboratoire d'études aérodynamiques [UMR 6609] [LEA [Poitiers]]
dc.contributor.authorCORDIER, Laurent
hal.structure.identifierLaboratoire d'Energétique et Mécanique Théorique et Appliquée [LEMTA ]
dc.contributor.authorBRANCHER, Jean-Pierre
dc.contributor.editorRudibert King
dc.date.issued2007
dc.date.conference2006-09-27
dc.description.abstractEnIn this paper we investigate the optimal control approach for the active control of the circular cylinder wake flow considered in the laminar regime (Re = 200). The objective is the minimization of the mean total drag where the control function is the time harmonic angular velocity of the rotating cylinder. When the Navier-Stokes equations are used as state equations, the discretization of the optimality system leads to large scale discretized optimization problems that represent a tremendous computational task. In order to reduce the number of state variables during the optimization process, a Proper Orthogonal Decomposition (POD) Reduced-Order Model (ROM) is then derived to be used as state equation. Since the range of validity of the POD ROM is generally limited to the vicinity of the design parameters in the control parameter space, we propose to use the Trust-Region Proper Orthogonal Decomposition (TRPOD) approach, originally introduced by Fahl (2000), to update the reduced-order models during the optimization process. Benefiting from the trust-region philosophy, rigorous convergence results guarantee that the iterates produced by the TRPOD algorithm will converge to the solution of the original optimization problem defined with the Navier-Stokes equations. A lot of computational work is indeed saved because the optimization process is now based only on low-fidelity models. The key enablers to an accurate and robust POD ROM for the pressure and velocity fields are the extension of the POD basis functions to the pressure data, the introduction of a time-dependent eddy-viscosity estimated for each POD mode as the solution of an auxiliary optimization problem, and the inclusion in the POD ROM of different non-equilibrium modes. When the TRPOD algorithm is applied to the wake flow configuration, this approach converges to the minimum predicted by an open-loop control approach and leads to a relative mean drag reduction of 30% for reduced numerical costs (a cost reduction factor of 1600 is obtained for the memory and the optimization problem is solved approximately 4 times more quickly).
dc.language.isoen
dc.source.titleActive Flow Control:Papers contributed to the Conference “Active Flow Control 2006”, Berlin, Germany, September 27 to 29, 2006
dc.title.enDrag Minimization of the Cylinder Wake by Trust-Region Proper Orthogonal Decomposition
dc.typeCommunication dans un congrès
dc.identifier.doi10.1007/978-3-540-71439-2_19
dc.subject.halInformatique [cs]/Modélisation et simulation
dc.subject.halPhysique [physics]/Mécanique [physics]/Mécanique des fluides [physics.class-ph]
dc.subject.halMathématiques [math]/Optimisation et contrôle [math.OC]
bordeaux.page309-324
bordeaux.volume95
bordeaux.conference.titleActive Flow Control 2006
bordeaux.countryFR
bordeaux.title.proceedingActive Flow Control:Papers contributed to the Conference “Active Flow Control 2006”, Berlin, Germany, September 27 to 29, 2006
bordeaux.conference.cityBerlin
bordeaux.peerReviewedoui
hal.identifierinria-00338822
hal.version1
hal.invitednon
hal.proceedingsnon
hal.conference.end2006-09-29
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//inria-00338822v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.btitle=Active%20Flow%20Control:Papers%20contributed%20to%20the%20Conference%20%E2%80%9CActive%20Flow%20Control%202006%E2%80%9D,%20Berlin,%20Germany,%20September%2027%20to%2029,&rft.date=2007&rft.volume=95&rft.spage=309-324&rft.epage=309-324&rft.au=BERGMANN,%20Michel&CORDIER,%20Laurent&BRANCHER,%20Jean-Pierre&rft.genre=unknown


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