Consistent and conservative phase-field based lattice Boltzmann method for incompressible two-phase flows

TL;DR

This paper introduces a new lattice Boltzmann method for simulating incompressible two-phase flows that ensures consistency, conservation, and accuracy, effectively handling complex flow phenomena like Rayleigh-Taylor instability and dam break scenarios.

Contribution

A novel lattice Boltzmann method is developed that accurately recovers a consistent phase-field model with enhanced force terms and improved mass conservation for complex two-phase flows.

Findings

The method accurately simulates droplet deformation and spreading.

Numerical results agree well with analytical solutions.

The approach is robust for high Reynolds number flows with large density ratios.

Abstract

In this work, we consider a general consistent and conservative phase-field model for the incompressible two-phase flows. In this model, not only the Cahn-Hilliard or Allen-Cahn equation can be adopted, but also the mass and the momentum fluxes in the Navier-Stokes equations are reformulated such that the consistency of reduction, consistency of mass and momentum transport, and the consistency of mass conservation are satisfied. We further develop a lattice Boltzmann (LB) method and show that through the direct Taylor expansion, the present LB method can correctly recover the consistent and conservative phase-field model. Additionally, if the divergence of the extra momentum flux is seen as a force term, the extra force in the present LB method would include another term which has not been considered in the previous LB models. To quantitatively evaluate the incompressibility and the consistency of the mass conservation, two statistical variables are introduced in the study of the deformation of a square droplet, and the results show that the present LB method is more accurate. The layered Poiseuille flow and a droplet spreading on an ideal wall are further investigated, and the numerical results are in good agreement with the analytical solutions. Finally, the problems of the Rayleigh-Taylor instability and dam break with the high Reynolds numbers and/or large density ratios are studied, and it is found that the present consistent and conservative LB method is robust for such complex two-phase flows.