一种基于幅值和波数的耗散控制方法  

A dissipation control method based on amplitude and wavenumber

作　　者：魏皇生 黄柱 席光[1] WEI Huangsheng;HUANG Zhu;XI Guang(School of Energy and Power Engineering,Xi’an Jiaotong University,Xi’an 710049,China)

机构地区：[1]西安交通大学能源与动力工程学院,西安710049

出　　处：《航空学报》2023年第4期41-58,共18页Acta Aeronautica et Astronautica Sinica

基　　金：国家自然科学基金(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。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 bet⁃ter 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,accord⁃ing 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 ampli⁃tude,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(Tar⁃geted 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.

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 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]