Minimal entropic kinetic models for simulating hydrodynamics

We derive minimal discrete models of the Boltzmann equation consistent with equilibrium thermodynamics, and which recover correct hydrodynamics in arbitrary dimensions. A simple analytical procedure of constructing the equilibrium for the nonisothermal hydrodynamics is established. A new discrete velocity model is proposed for the simulation of the Navier-Stokes-Fourier equation and is tested in the set up of Taylor vortex flow. For the lattice Boltzmann method of isothermal hydrodynamics, the explicit analytical form of the equilibrium distribution is presented.