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Model reduction for compressible flows using POD and Galerkin projection

Rowley, Clarence W. and Colonius, Tim and Murray, Richard M. (2004) Model reduction for compressible flows using POD and Galerkin projection. Physica D, 189 (1-2). pp. 115-129. ISSN 0167-2789. doi:10.1016/j.physd.2003.03.001.

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We present a framework for applying the method of proper orthogonal decomposition (POD) and Galerkin projection to compressible fluids. For incompressible flows, only the kinematic variables are important, and the techniques are well known. In a compressible flow, both the kinematic and thermodynamic variables are dynamically important, and must be included in the configuration space. We introduce an energy-based inner product which may be used to obtain POD modes for this configuration space. We then obtain an approximate version of the Navier–Stokes equations, valid for cold flows at moderate Mach number, and project these equations onto a POD basis. The resulting equations of motion are quadratic, and are much simpler than projections of the full compressible Navier–Stokes equations.

Item Type:Article
Related URLs:
URLURL TypeDescription
Rowley, Clarence W.0000-0002-9099-5739
Colonius, Tim0000-0003-0326-3909
Murray, Richard M.0000-0002-5785-7481
Additional Information:© 2003 Published by Elsevier B.V. Received 25 March 2002, Revised 27 January 2003, Accepted 25 March 2003, Available online 6 December 2003. This work was supported by AFOSR under grants F49620-98-1-0095 and F49620-03-1-0081, with technical monitors Dr. Thomas Beutner and Dr. John Schmisseur.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)F49620-98-1-0095
Air Force Office of Scientific Research (AFOSR)F49620-03-1-0081
Subject Keywords:Proper orthogonal decomposition; Compressible flows; Galerkin projection; Model reduction
Issue or Number:1-2
Record Number:CaltechAUTHORS:20190214-075224908
Persistent URL:
Official Citation:Clarence W. Rowley, Tim Colonius, Richard M. Murray, Model reduction for compressible flows using POD and Galerkin projection, Physica D: Nonlinear Phenomena, Volume 189, Issues 1–2, 2004, Pages 115-129, ISSN 0167-2789, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92916
Deposited By: Tony Diaz
Deposited On:14 Feb 2019 17:49
Last Modified:16 Nov 2021 16:54

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