## Abstract

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.

Original language | English (US) |
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Pages (from-to) | 115-129 |

Number of pages | 15 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 189 |

Issue number | 1-2 |

DOIs | |

State | Published - Feb 15 2004 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics

## Keywords

- Compressible flows
- Galerkin projection
- Model reduction
- Proper orthogonal decomposition