A non-local quasi-equilibrium state in the Bhatnagar-Gross-Krook Boltzmann equation for thermo-hydrodynamics: Conservation laws, the Boltzmann H-theorem, and the fluctuation-dissipation theorem
arXiv:2210.02221 · doi:10.1007/s10955-023-03119-1
Abstract
The Bhatnagar-Gross-Krook (BGK) Boltzmann equation with the Maxwellian-Boltzmann-type equilibrium state leads to the set of thermo-hydrodynamic equations such as the continuity, the Navier-Stokes, and the heat-transfer equations in the scaling limit. With its efficient and promising framework handling multi-scale physics, the collision model has been studied with both of theoretical and numerical approaches to apply it for extensive flow conditions such as the flexible choices of the Prandtl number. In this study, using an analytic technique of the kinetic generator, we employ a non-local formulation for the equilibrium state leading to the thermo-hydrodynamic equations with flexible choices of transport coefficients and the equation of state (EOS). The equilibrium state includes the quasi-equilibrium state intrinsically, being formulated with the non-local macroscopic quantities so that the longer-range interaction is explicitly involved. According to the new formulation, the consistency with conservation laws, the Boltzmann H-theorem, and the fluctuation-dissipation theorem are examined.
References in corpus (12)
- Simulation of non-ideal gases and liquid-gas phase transitions by lattice Boltzmann equation
- Simulation of Rayleigh-Bénard convection using lattice Boltzmann method
- Lattice Boltzmann Thermohydrodynamics
- Entropic lattice Boltzmann methods
- Lattice Boltzmann method with self-consistent thermo-hydrodynamic equilibria
- Quasi-Equilibrium Lattice Boltzmann Method
- Recovery of Galilean Invariance in Thermal Lattice Boltzmann Models for Arbitrary Prandtl Number
- A Comparison and Unification of Ellipsoidal Statistical and Shakhov BGK Models
- Microscopic Derivation of Non-Markovian Thermalization of a Brownian Particle
- Enskog kinetic theory of rheology for a moderately dense inertial suspension
- Time dependence of advection-diffusion coupling for nanoparticle ensembles
- Inverse Chapman-Enskog Derivation of the Thermohydrodynamic Lattice-BGK Model for the Ideal Gas