Inertial range statistics of the entropic lattice Boltzmann method in three-dimensional turbulence

We present a quantitative analysis of the inertial range statistics produced by entropic lattice Boltzmann method (ELBM) in the context of three-dimensional homogeneous and isotropic turbulence. ELBM is a promising mesoscopic model particularly interesting for the study of fully developed turbulent flows because of its intrinsic scalability and its unconditional stability. In the hydrodynamic limit, the ELBM is equivalent to the Navier-Stokes equations with an extra eddy viscosity term. From this macroscopic formulation, we have derived a new hydrodynamical model that can be implemented as a large-eddy simulation closure. This model is not positive definite, hence, able to reproduce backscatter events of energy transferred from the subgrid to the resolved scales. A statistical comparison of both mesoscopic and macroscopic entropic models based on the ELBM approach is presented and validated against fully resolved direct numerical simulations. Besides, we provide a second comparison of the ELBM with respect to the well-known Smagorinsky closure. We found that ELBM is able to extend the energy spectrum scaling range preserving at the same time the simulation stability. Concerning the statistics of higher order, inertial range observables, ELBM accuracy is shown to be comparable with other approaches such as Smagorinsky model.