  Minimal Boltzmann kinetic models, such as lattice Boltzmann, are often used
as an alternative to the discretization of the Navier-Stokes equations for
hydrodynamic simulations.
  Recently, it was argued that modeling sub-grid scale phenomena at the kinetic
level might provide an efficient tool for large scale simulations. Indeed, a
particular variant of this approach, known as the entropic lattice Boltzmann
method (ELBM), has shown that an efficient coarse-grained simulation of
decaying turbulence is possible using these approaches.
  The present work investigates the efficiency of the entropic lattice
Boltzmann in describing flows of engineering interest. In order to do so, we
have chosen the flow past a square cylinder, which is a simple model of such
flows. We will show that ELBM can quantitatively capture the variation of
vortex shedding frequency as a function of Reynolds number in the low as well
as the high Reynolds number regime, without any need for explicit sub-grid
scale modeling. This extends the previous studies for this set-up, where
experimental behavior ranging from $Re\sim O(10)$ to $Re\leq 1000$ were
predicted by a single simulation algorithm.
