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

Xuming Li, Cheng Peng, Chunhua Zhang, Xinnan Wu, Wenrui Wang

TL;DR

This study conducts a systematic, multi-dimensional comparison of eight representative phase-field lattice Boltzmann models for two-phase flows, spanning conservative AC, nonlocal AC, hybrid AC, and CH formulations. By evaluating 2D laminar benchmarks and 3D turbulent, droplet-laden flows, it quantifies accuracy, numerical stability, mass conservation, and computational efficiency, revealing that conservative AC models offer the best balance of stability, accuracy, and efficiency, while CH models struggle with order-parameter bounding and droplet dissolution under challenging conditions. The work shows that in turbulence, maintaining droplet volume is difficult across all models, with nonlocal AC providing the best volume preservation at the expense of removing small droplets, and singular mobility in CH slowing but not eliminating dissolution. These findings guide practitioners in selecting PF-LB models for 3D turbulent two-phase simulations and highlight areas where PF-LB methods require further development to mitigate volume loss and improve robustness under large deformations.

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.

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

TL;DR

This study conducts a systematic, multi-dimensional comparison of eight representative phase-field lattice Boltzmann models for two-phase flows, spanning conservative AC, nonlocal AC, hybrid AC, and CH formulations. By evaluating 2D laminar benchmarks and 3D turbulent, droplet-laden flows, it quantifies accuracy, numerical stability, mass conservation, and computational efficiency, revealing that conservative AC models offer the best balance of stability, accuracy, and efficiency, while CH models struggle with order-parameter bounding and droplet dissolution under challenging conditions. The work shows that in turbulence, maintaining droplet volume is difficult across all models, with nonlocal AC providing the best volume preservation at the expense of removing small droplets, and singular mobility in CH slowing but not eliminating dissolution. These findings guide practitioners in selecting PF-LB models for 3D turbulent two-phase simulations and highlight areas where PF-LB methods require further development to mitigate volume loss and improve robustness under large deformations.

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.

Paper Structure

This paper contains 26 sections, 55 equations, 24 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Phase-field lattice Boltzmann models
  3. Hydrodynamic equations
  4. Lattice Boltzmann equations
  5. AC based LB models
  6. Fakhari et al.'s conservative AC model
  7. Liang et al's conservative AC model
  8. Chai et al.'s nonlocal AC model
  9. Hu et al.'s hybrid AC model
  10. Liu et al.'s hybrid AC model
  11. CH based LB models
  12. Liang et al.'s CH model with incompressible NS
  13. Yang et al.'s CH model with quasi-incompressible NS
  14. Bao et al.'s singular mobility CH model with quasi-incompressible NS
  15. Two-dimensional laminar flow tests
  16. ...and 11 more sections

Figures (24)

  • Figure 1: Contours of the droplet interface at $t = 0$, $t = T_0$, and $t = 10T_0$.
  • Figure 2: A schematic diagram of bubble rising under gravity.
  • Figure 3: Comparison of bubble centroid positions and roundness with the results of Aland aland2012benchmark.
  • Figure 4: Contours of the nonlocal ACE model.
  • Figure 5: Comparison of bubble interface contours.
  • ...and 19 more figures