Consistent Lattice Boltzmann Method

TL;DR

This paper introduces a thermodynamically consistent lattice Boltzmann model that conserves energy, enabling accurate simulation of nearly-incompressible flows and extending the method's applicability.

Contribution

A new energy-conserving lattice Boltzmann model derived from kinetic theory is proposed, improving thermodynamic consistency in flow simulations.

Findings

Simulation results agree with exact solutions for micro-flow at various Knudsen numbers.

The model accurately recovers full thermo-hydrodynamics in small temperature variation regimes.

The approach extends standard lattice Boltzmann methods to thermodynamically consistent simulations.

Abstract

The problem of energy conservation in the lattice Boltzmann method is solved. A novel model with energy conservation is derived from Boltzmann's kinetic theory. It is demonstrated that the full thermo-hydrodynamics pertinent to the Boltzmann equation is recovered in the domain where variations around the reference temperature are small. Simulation of a Poiseuille micro-flow is performed in a quantitative agreement with exact results for low and moderate Knudsen numbers. The new model extends in a natural way the standard lattice Boltzmann method to a thermodynamically consistent simulation tool for nearly-incompressible flows.