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Model reduction for supersonic cavity flow using proper orthogonal decomposition (POD) and Galerkin projection

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Abstract

The reduced-order model (ROM) for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition (POD) and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are based on an isentropic assumption, valid only for flows at low or moderate Mach numbers. A new ROM is constructed involving primitive variables of the fully compressible Navier-Stokes (N-S) equations, which is suitable for flows at high Mach numbers. Compared with the direct numerical simulation (DNS) results, the proposed model predicts flow dynamics (e.g., dominant frequency and amplitude) accurately for supersonic cavity flows, and is robust. The comparison between the present transient flow fields and those of the DNS shows that the proposed ROM can capture self-sustained oscillations of a shear layer. In addition, the present model reduction method can be easily extended to other supersonic flows.

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Acknowledgements

In the DNS, the authors especially thank the OpenFOAM Foundation for the free, open source computational fluid dynamics software package OpenFOAM. The author Zhenhua WAN especially thanks the Fundamental Research Funds for the Central Universities.

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Authors and Affiliations

  1. Department of Modern Mechanics, University of Science and Technology of China, Hefei, 230027, China

    Chao Zhang, Zhenhua Wan & Dejun Sun

Authors
  1. Chao Zhang
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  2. Zhenhua Wan
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  3. Dejun Sun
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Corresponding author

Correspondence to Zhenhua Wan.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11232011, 11402262, 11572314, and 11621202)

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Zhang, C., Wan, Z. & Sun, D. Model reduction for supersonic cavity flow using proper orthogonal decomposition (POD) and Galerkin projection. Appl. Math. Mech.-Engl. Ed. 38, 723–736 (2017). https://doi.org/10.1007/s10483-017-2195-9

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  • DOI: https://doi.org/10.1007/s10483-017-2195-9

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

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