Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (5): 723-736.doi: https://doi.org/10.1007/s10483-017-2195-9

• 论文 • 上一篇    下一篇

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

Chao ZHANG, Zhenhua WAN, Dejun SUN   

  1. Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, China
  • 收稿日期:2016-05-05 修回日期:2016-09-18 出版日期:2017-05-01 发布日期:2017-05-01
  • 通讯作者: Zhenhua WAN E-mail:wanzh@ustc.edu.cn
  • 基金资助:

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

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

Chao ZHANG, Zhenhua WAN, Dejun SUN   

  1. Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, China
  • Received:2016-05-05 Revised:2016-09-18 Online:2017-05-01 Published:2017-05-01
  • Contact: Zhenhua WAN E-mail:wanzh@ustc.edu.cn
  • Supported by:

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

摘要:

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.

关键词: Liénard type system, oscillating solution, necessary and sufficient condition, Galerkin projection, proper orthogonal decomposition (POD), reduced-order model (ROM), supersonic cavity flow

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.

Key words: Liénard type system, oscillating solution, necessary and sufficient condition, proper orthogonal decomposition (POD), reduced-order model (ROM), supersonic cavity flow, Galerkin projection

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