Minimal entropic kinetic models for simulating hydrodynamics

TL;DR

This paper develops minimal entropic kinetic models that accurately simulate hydrodynamics and thermodynamics, introducing new discrete velocity models and explicit equilibria for lattice Boltzmann methods, validated through vortex flow simulations.

Contribution

It presents a novel minimal discrete model consistent with thermodynamics and hydrodynamics, including explicit equilibria for nonisothermal and isothermal cases.

Findings

New discrete velocity model for Navier-Stokes-Fourier equations

Explicit equilibrium distribution for lattice Boltzmann method

Validated with Taylor vortex flow simulations

Abstract

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.