  A new method for the computation of flows at the micrometer scale is
presented. It is based on the recently introduced minimal entropic kinetic
models. Both the thermal and isothermal families of minimal models are
presented, and the simplest isothermal entropic lattice Bhatnagar-Gross-Krook
(ELBGK) is studied in detail in order to quantify its relevance for microflow
simulations. ELBGK is equipped with boundary conditions which are derived from
molecular models (diffusive wall). A map of three-dimensional kinetic equations
onto two-dimensional models is established which enables two-dimensional
simulations of quasi-two-dimensional flows. The ELBGK model is studied
extensively in the simulation of the two-dimensional Poiseuille channel flow.
Results are compared to known analytical and numerical studies of this flow in
the setting of the Bhatnagar-Gross-Krook model. The ELBGK is in quantitative
agreement with analytical results in the domain of weak rarefaction
(characterized by Knudsen number Kn, the ratio of mean free path to the
hydrodynamic scale), up to Kn=0.01, which is the domain of many practical
microflows. Moreover, the results qualitatively agree throughout the entire
Knudsen number range, demonstrating Knudsen's minimum for the mass flow rate at
moderate values of Kn, as well as the logarithmic scaling at large Kn. The
present results indicate that ELBM can complement or even replace
computationally expensive microscopic simulation techniques such as kinetic
Monte Carlo and/or molecular dynamics for low Mach and low Knudsen number
hydrodynamics pertinent to microflows.
