  We present a quantitative analysis of the inertial range statistics produced
by Entropic Lattice Boltzmann Method (ELBM) in the context of 3d 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 [1]. From this macroscopic formulation, we have derived a new
hydrodynamical model that can be implemented as a Large-Eddy Simulation (LES)
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 (DNS). 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.
