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.

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