Comparative study and critical assessment of phase-field lattice Boltzmann models for laminar and turbulent two-phase flow simulations

TL;DR

This paper systematically compares various phase-field lattice Boltzmann models for simulating laminar and turbulent two-phase flows, highlighting their strengths and limitations, especially in three-dimensional turbulent cases with high Weber numbers.

Contribution

It provides the first comprehensive comparison of multiple LB models across 2D and 3D flows, including turbulent regimes, revealing their relative performance and limitations.

Findings

All models perform well in 2D laminar flows.

Significant droplet volume loss occurs in turbulent flows at high Weber numbers.

Conservative Allen-Cahn models offer the best stability and accuracy balance.

Abstract

Phase field lattice Boltzmann (LB) models have undergone continuous development, resulting in multiple variants widely used for simulating multiphase flows. However, direct performance comparisons remain limited, especially for three-dimensional cases. In this study, we present a systematic comparative analysis of several recent and representative phase-field LB models, covering four major categories: conservative Allen-Cahn, nonlocal Allen-Cahn, hybrid Allen-Cahn, and Cahn-Hilliard models. Their accuracy, numerical stability and mass/volume conservation are assessed through a series of canonical two-phase flow problems. Beyond the commonly tested two-dimensional laminar cases, we extend the evaluation to three-dimensional droplet-laden turbulent flows, which expose more critical limitations of the existing models. The results show that while all models perform satisfactorily in two dimensions, they still suffer from substantial droplet volume loss in turbulence, particularly at high Weber numbers. Overall, conservative Allen-Cahn-based LB models exhibit the most favorable balance of numerical stability, accuracy and computational efficiency.