The POD Dirichlet Boundary Control of the Navier-Stokes Equations: A Low-dimensional Approach to Optimal Control with High Smoothness

dc.contributor.authorWang, Ying
dc.contributor.authorTröltzsch, Fredi
dc.contributor.authorBärwolff, Günter
dc.date.accessioned2022-05-11T12:11:49Z
dc.date.available2022-05-11T12:11:49Z
dc.date.issued2009-12-01
dc.description.abstractThe proper orthogonal decomposition(POD) is an approach to capture a reduced order basis functions for a dynamical system. Utilizing the order reduction property of POD basis for minimizing computational cost to unsteady fluid flow control problem, we present a POD-based framework of the unsteady Dirichlet boundary control problem for Navier-Stokes equations. An extra basis function can be therefor constructed and appended into the general POD subspace, which as a key step enables the POD approach to the Dirichlet boundary control and results in the control problem merely in time scale. In the paper the excellent quality and flexibility of the POD approach to Dirichlet boundary flow control are confirmed numerically in several flow matching control examples.en
dc.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/16912
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-15690
dc.language.isoen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subject.ddc510 Mathematiken
dc.subject.otherDirichlet boundary controlen
dc.subject.otherGalerkin POD methoden
dc.subject.otherreduced order modelsen
dc.subject.otherNavier-Stokes equationsen
dc.titleThe POD Dirichlet Boundary Control of the Navier-Stokes Equations: A Low-dimensional Approach to Optimal Control with High Smoothnessen
dc.typeResearch Paperen
dc.type.versionsubmittedVersionen
tub.accessrights.dnbfree
tub.affiliationFak. 2 Mathematik und Naturwissenschaften>Inst. Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2009, 23en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200049K20 Problems involving partial differential equationsen
tub.subject.msc200076D55 Flow control and optimizationen
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