Proper Orthogonal Decomposition in Optimal Control of Fluids

Ravindran, S. S.

In this article, we present a reduced order modeling approach suitable for active control of fluid dynamical systems based on proper orthogonal decomposition (POD). The rationale behind the reduced order modeling is that numerical simulation of Navier-Stokes equations is still too costly for the purpose of optimization and control of unsteady flows. We examine the possibility of obtaining reduced order models that reduce computational complexity associated with the Navier-Stokes equations while capturing the essential dynamics by using the POD. The POD allows extraction of certain optimal set of basis functions, perhaps few, from a computational or experimental data-base through an eigenvalue analysis. The solution is then obtained as a linear combination of these optimal set of basis functions by means of Galerkin projection. This makes it attractive for optimal control and estimation of systems governed by partial differential equations. We here use it in active control of fluid flows governed by the Navier-Stokes equations. We show that the resulting reduced order model can be very efficient for the computations of optimization and control problems in unsteady flows. Finally, implementational issues and numerical experiments are presented for simulations and optimal control of fluid flow through channels.

Document ID

19990035926

Acquisition Source

Langley Research Center

Document Type

Technical Memorandum (TM)

Authors

Date Acquired

September 6, 2013

Publication Date

March 1, 1999

Subject Category

Report/Patent Number

Funding Number(s)

Distribution Limits

Public

Work of the US Gov. Public Use Permitted.

Available Downloads

Name

Type

19990035926.pdf

STI

No Preview Available

NTRS

NTRS - NASA Technical Reports Server

Available Downloads

Related Records