Galilean invariance of lattice Boltzmann models

TL;DR

This paper investigates the Galilean invariance of lattice Boltzmann models, identifying criteria for correct transport coefficients and demonstrating invariance through numerical experiments, addressing unphysical velocity-dependent viscosity issues.

Contribution

It provides specific criteria for recovering transport coefficients and demonstrates Galilean invariance in LB models through numerical validation.

Findings

Galilean invariance can be restored in LB models under certain criteria.

Numerical experiments confirm the invariance of transport coefficients.

Unphysical velocity dependence in viscosity can be mitigated.

Abstract

It is well-known that the original lattice Boltzmann (LB) equation deviates from the Navier-Stokes equations due to an unphysical velocity dependent viscosity. This unphysical dependency violates the Galilean invariance and limits the validation domain of the LB method to near incompressible flows. As previously shown, recovery of correct transport phenomena in kinetic equations depends on the higher hydrodynamic moments. In this Letter, we give specific criteria for recovery of various transport coefficients. The Galilean invariance of a general class of LB models is demonstrated via numerical experiments.