Eliminating spurious velocities in the free energy lattice Boltzmann method

TL;DR

This paper analyzes the causes of unphysical spurious velocities in the free energy lattice Boltzmann method and proposes improvements to significantly reduce these velocities through optimized equilibrium distributions and a momentum conserving forcing method.

Contribution

The paper introduces a new approach to minimize spurious velocities in the free energy lattice Boltzmann method by optimizing equilibrium distributions and derivative calculations, including a momentum conserving forcing technique.

Findings

Spurious velocities can be reduced by an order of magnitude with optimized equilibrium distributions.

A momentum conserving forcing method further decreases spurious velocities by a factor of ~5.

19 velocity vectors are necessary for accurate three-dimensional simulations.

Abstract

Spurious velocities are unphysical currents that appear close to curved interfaces in diffuse interface methods. We analyse the causes of these spurious velocities in the free energy lattice Boltzmann algorithm. By making a suitable choice of the equilibrium distribution, and by finding the best way to numerically calculate derivatives, we show that these velocities may be decreased by an order of magnitude compared to previous models. Furthermore, we propose a momentum conserving forcing method that reduces spurious velocities by another factor of ~5. In three dimensions we find that 19 velocity vectors is the minimum number necessary.