流体力学与飞行力学

一种基于幅值和波数的耗散控制方法

  • 魏皇生 ,
  • 黄柱 ,
  • 席光
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  • 西安交通大学 能源与动力工程学院,西安 710049
.E-mail:xiguang@xjtu.edu.cn

收稿日期: 2021-10-29

  修回日期: 2021-11-15

  录用日期: 2022-01-05

  网络出版日期: 2022-01-11

基金资助

国家自然科学基金(51790512)

A dissipation control method based on amplitude and wavenumber

  • Huangsheng WEI ,
  • Zhu HUANG ,
  • Guang XI
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  • School of Energy and Power Engineering,Xi’an Jiaotong University,Xi’an 710049,China

Received date: 2021-10-29

  Revised date: 2021-11-15

  Accepted date: 2022-01-05

  Online published: 2022-01-11

Supported by

National Natural Science Foundation of China(51790512)

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,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(Targeted Essentially Non-Oscillatory)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。

本文引用格式

魏皇生 , 黄柱 , 席光 . 一种基于幅值和波数的耗散控制方法[J]. 航空学报, 2023 , 44(4) : 126589 -126589 . DOI: 10.7527/S1000-6893.2022.26589

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 and resolve large-scale flow structures. In order to better identify the small-scale non-physical fluctuations produced in the shock capture process, and then more accurately control dissipation, this paper proposes a dissipation control method based on amplitude and wavenumber of the local flow field. For problems with strong unsteadiness, 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(Targeted Essentially Non-Oscillatory) scheme to form a hybrid scheme. A series of benchmark examples involving shocks or turbulence show that this scheme produces small-scale nonphysical fluctuations with lower wavenumbers, smaller amplitudes, and better resolution of large-scale flow structures during computations.

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