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Published February 15, 2004 | public
Journal Article

Model reduction for compressible flows using POD and Galerkin projection


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.

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.

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