Minimal entropic kinetic models for athermal and thermal hydrodynamics

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Abstract
We derive minimal discrete models of the Boltzmann equation, which are consistent with the H theorem, and which recover correct hydrodynamics in arbitrary dimensions. For the entropic lattice Boltzmann method of athermal hydrodynamics, the explicit analytical form of the equilibrium distribution is presented. A simple analytical procedure of constructing the equilibrium for the thermal hydrodynamics is established. Examples of numerical implementation in the athermal case are presented.

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