On the implicit large eddy simulations of homogeneous decaying turbulence

Simulations of homogeneous decaying turbulence (HDT) in a periodic cube have been used to examine in a detailed and quantitative manner the behaviour of high-resolution and high-order methods in implicit large eddy simulation. Computations have been conducted at grid resolutions from 323 to 2563 for seven different high-resolution methods ranging from second-order to ninth-order spatial accuracy. The growth of the large scales, and dissipation of kinetic energy is captured well at resolutions greater than 323, or when using numerical methods of higher than third-order accuracy. Velocity increment probability distribution functions (PDFs) match experimental results very well for MUSCL methods, whereas WENO methods have lower intermittency. All pressure PDFs are essentially Gaussian, indicating a partial decoupling of pressure and vorticity fields. The kinetic energy spectra and effective numerical filter show that all schemes are too dissipative at high wave numbers. Evaluating the numerical viscosity as a spectral eddy viscosity shows good qualitative agreement with theory, however if the effective cut-off wave number is chosen above kmax/2 then dissipation is higher than the theoretical solution. The fifth and higher-order methods give results approximately equivalent to the lower order methods at double the grid resolution, making them computationally more efficient.