DNS and LES of decaying isotropic turbulence with and without frame rotation using lattice Boltzmann method

The objective of the paper is to assess the effectiveness of the lattice Boltzmann equation (LBE) as a computational tool for performing direct numerical simulations (DNS) and large-eddy simulations (LES) of turbulent flows. Decaying homogeneous isotropic turbulence (HIT) in inertial and rotating frames is considered for this investigation. We perform three categories of simulations. The first category involves LBE-DNS of HIT. In the inertial frame of reference, the decay exponents of the kinetic energy k, the dissipation rate ε and the low wave-number scaling of the energy spectrum are studied. The LBE results agree well with established classical results. In the case of turbulence subject to frame rotation, the LBE simulations confirm that the energy decay rate decreases with Rossby number as the energy cascade is inhibited by rotation. Second, we carry out LBE-LES for decaying HIT in inertial frame. We compute kinetic energy decay, energy spectrum and flow structures. By comparing LBE-LES and LBE-DNS results, we observe that LBE-LES accurately captures prominent large scale flow behavior. We find that the Smagorinsky constant CS in LBE-LES should be smaller than the typical value used in traditional Navier-Stokes (NS) LES approaches. Finally, we compare the LBE-LES and NS-LES (of comparable order of numerical accuracy) results for HIT and observe that the LBE-LES simulations appear to preserve instantaneous flow fields somewhat more accurately. Our results clearly indicate that the LBE method can accurately capture important features of decaying HIT and is potentially a reliable computational tool for turbulence simulations.