Lattice Boltzmann method with self-consistent thermo-hydrodynamic equilibria

TL;DR

This paper develops a lattice Boltzmann method incorporating self-consistent thermo-hydrodynamic equilibria, accounting for force effects and temperature shifts, to improve modeling of non-ideal fluids.

Contribution

It introduces a new framework that includes temperature shifts in lattice kinetic equations for more accurate thermo-hydrodynamic modeling of non-ideal fluids.

Findings

Theoretical formulation aligns with non-ideal equations of state.

Temperature must be shifted alongside momentum for consistency.

New terms are needed to define macroscopic temperature on the lattice.

Abstract

Lattice kinetic equations incorporating the effects of external/internal force fields via a shift of the local fields in the local equilibria, are placed within the framework of continuum kinetic theory. The mathematical treatment reveals that, in order to be consistent with the correct thermo-hydrodynamical description, temperature must also be shifted, besides momentum. New perspectives for the formulation of thermo-hydrodynamic lattice kinetic models of non-ideal fluids are then envisaged. It is also shown that on the lattice, the definition of the macroscopic temperature requires the inclusion of new terms directly related to discrete effects. The theoretical treatment is tested against a controlled case with a non ideal equation of state.