Model Reduction for Flow Analysis and Control

Clarence Worth Rowley, Scott T.M. Dawson

Research output: Contribution to journalReview article

155 Scopus citations

Abstract

Advances in experimental techniques and the ever-increasing fidelity of numerical simulations have led to an abundance of data describing fluid flows. This review discusses a range of techniques for analyzing such data, with the aim of extracting simplified models that capture the essential features of these flows, in order to gain insight into the flow physics, and potentially identify mechanisms for controlling these flows. We review well-developed techniques, such as proper orthogonal decomposition and Galerkin projection, and discuss more recent techniques developed for linear systems, such as balanced truncation and dynamic mode decomposition (DMD). We then discuss some of the methods available for nonlinear systems, with particular attention to the Koopman operator, an infinite-dimensional linear operator that completely characterizes the dynamics of a nonlinear system and provides an extension of DMD to nonlinear systems.

Original languageEnglish (US)
Pages (from-to)387-417
Number of pages31
JournalAnnual Review of Fluid Mechanics
Volume49
DOIs
StatePublished - Jan 3 2017

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics

Keywords

  • Balanced truncation
  • Dynamic mode decomposition
  • Galerkin projection
  • Kernel method
  • Koopman operator
  • Proper orthogonal decomposition

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