Inhalt des Dokuments
Preprint 23-2009
The POD Dirichlet Boundary Control of the Navier-Stokes Equations: A Low-dimensional Approach to Optimal Control with High Smoothness
Author(s) :
Ying Wang
,
Fredi Tröltzsch
,
Günter Bärwolff
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 23-2009
MSC 2000
- 49K20 Problems involving partial differential equations
-
76D55 Flow control and optimization
ZDM : N40
Abstract :
The 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.
Keywords :
Dirichlet boundary control, Galerkin POD method, reduced order models, Navier-Stokes equations