Investigation of Galilean Invariance of multi-phase lattice Boltzmann methods

TL;DR

This paper investigates the Galilean invariance of two-phase lattice Boltzmann methods, identifying key sources of violation and proposing correction techniques that enhance invariance and stability.

Contribution

It demonstrates that including a specific cubic velocity term correction significantly improves Galilean invariance and stability in multi-phase lattice Boltzmann simulations.

Findings

Inclusion of the correction term improves Galilean invariance by up to an order of magnitude.

The correction extends the stability range of multi-phase algorithms.

Both forcing-based and pressure tensor-based methods benefit from the correction.

Abstract

We examine the Galilean invariance of standard lattice Boltzmann methods for two-phase fluids. We show that the known Galilean invariant term that is cubic in the velocities, and is usually neglected, is the main source of Galilean invariance violations. We show that incorporating a correction term can improve the Galilean invariance of the method by up to an order of magnitude. Surprisingly incorporating this correction term can also noticeably increase the range of stability for multi-phase algorithms. We found that this is true for methods in which the non-ideality is incorporated by a forcing term as well as methods in which non-ideality is directly incorporated in a non-ideal pressure tensor.