A generalized lattice Boltzmann model for fluid flow system and its application in two-phase flows

TL;DR

This paper introduces a generalized lattice Boltzmann model capable of simulating both single-phase and two-phase fluid flows with mass sources, validated through various physical problem simulations and comparisons.

Contribution

A new generalized LB model with a mass source term is proposed, capable of deriving existing models and creating new ones, especially for two-phase flows.

Findings

The model accurately simulates classic two-phase flow problems.

The quasi-incompressible LB model can outperform traditional incompressible models.

Numerical results validate the model's effectiveness and accuracy.

Abstract

In this paper, a generalized lattice Boltzmann (LB) model with a mass source is proposed to solve both incompressible and nearly incompressible Navier-Stokes (N-S) equations. This model can be used to deal with single-phase and two-phase flows problems with a mass source term. From this generalized model, we can not only get some existing models, but also derive new models. Moreover, for the incompressible model derived, a modified pressure scheme is introduced to calculate the pressure, and then to ensure the accuracy of the model. In this work, we will focus on a two-phase flow system, and in the frame work of our generalized LB model, a new phase-field-based LB model is developed for incompressible and quasi-incompressible two-phase flows. A series of numerical simulations of some classic physical problems, including a spinodal decomposition, a static droplet, a layered Poiseuille flow, and a bubble rising flow under buoyancy, are performed to validate the developed model. Besides, some comparisons with previous quasi-incompressible and incompressible LB models are also carried out, and the results show that the present model is accurate in the study of two-phase flows. Finally, we also conduct a comparison between quasi-incompressible and incompressible LB models for two-phase flow problems, and find that in some cases, the proposed quasi-incompressible LB model performs better than incompressible LB models.