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一种基于幅值和波数的耗散控制方法

魏皇生1,黄柱1,席光2   

  1. 1. 西安交通大学
    2. 西安交通大学能源与动力工程学院流体机械与工程系
  • 收稿日期:2021-10-29 修回日期:2022-01-09 出版日期:2022-01-11 发布日期:2022-01-11
  • 通讯作者: 席光
  • 基金资助:
    国家自然科学基金

A Dissipation Control Method Based on Amplitude and Wavenumber

  • Received:2021-10-29 Revised:2022-01-09 Online:2022-01-11 Published:2022-01-11
  • Supported by:
    National Natural Science Foundation of China

摘要: 激波捕捉格式可以根据局部流场的光滑程度自适应地控制耗散,以抑制小尺度的非物理波动并解析更多的大尺度流动结构。为了更好地识别激波捕捉过程中产生的小尺度非物理波动,进而更精确地控制耗散,本文提出一种基于局部流场的幅值和波数控制耗散的方法。对于激波主导的或各向同性湍流的具有强烈非定常性的问题,根据一维非定常欧拉方程,推导小尺度下不同物理量之间的关系,并通过数值实验或Kolmogorov尺度理论确定小尺度波动幅值的阈值。最后,基于傅里叶分析及小尺度波动幅值的阈值,建立耗散大小与局部流场的幅值和波数的关系。为了获得激波捕捉能力,将该格式与TENO格式进行混合构造了混合格式。一系列激波主导的基准算例显示,该格式在计算过程中产生的小尺度非物理波动的波数更低,幅值更小,并对大尺度的流动结构具有更好的分辨率。

关键词: Kolmogorov尺度, 可压缩流动, 各向同性湍流, 耗散控制, 激波捕捉格式

Abstract: The shock capture scheme can adaptively control the dissipation according to the smoothness of the local flow field to suppress the small-scale non-physical fluctuations generated when calculating the compressible flow. In order to better identify the small-scale non-physical fluctuations produced in the shock capture process, and then control dissipation more accurately, this paper proposes a dissipation control method based on amplitude and wavenumber of the local flow field. For problems with strong unsteady, such as shock-dominated or isotropic turbulence problems, according to the one-dimensional unsteady Euler equation, the relationship between different physical quantities at small scales is derived, and the threshold of the small-scale fluctuation amplitude are determined by numerical experiments or Kolmogorov scale theory. Finally, based on Fourier analysis and the threshold of the small-scale fluctuation amplitude, the relationship between the magnitude of the dissipation and the amplitude and wavenumber of the local flow field is established. In order to obtain the shock-capturing capability, the scheme is hybridized with the TENO scheme to form a hybrid scheme. A series of benchmark examples involving shocks or turbulence show that this scheme has good resolution and can effectively suppress non-physical fluctuations.

Key words: Kolmogorov scale, compressible flow, isotropic turbulence, dissipation control, shock capture scheme

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