# Improved three-dimensional color-gradient lattice Boltzmann model for immiscible multiphase flows

## TL;DR

This paper introduces an enhanced three-dimensional color-gradient lattice Boltzmann model that corrects previous inaccuracies, improves numerical accuracy, and better simulates complex immiscible multiphase flows, including large density ratios.

## Contribution

The paper develops an improved 3D color-gradient LB model that eliminates error terms, enhances Galilean invariance, and demonstrates superior accuracy in simulating multiphase flows.

## Key findings

- Improved model shows higher numerical accuracy than previous models.
- Galilean invariance is verified through moving droplet simulations.
- Effective in simulating large density ratio multiphase flows.

## Abstract

In this paper, an improved three-dimensional color-gradient lattice Boltzmann (LB) model is proposed for simulating immiscible multiphase flows. Compared with the previous three-dimensional color-gradient LB models, which suffer from the lack of Galilean invariance and considerable numerical errors in many cases owing to the error terms in the recovered macroscopic equations, the present model eliminates the error terms and therefore improves the numerical accuracy and enhances the Galilean invariance. To validate the proposed model, numerical simulation are performed. First, the test of a moving droplet in a uniform flow field is employed to verify the Galilean invariance of the improved model. Subsequently, numerical simulations are carried out for the layered two-phase flow and three-dimensional Rayleigh-Taylor instability. It is shown that, using the improved model, the numerical accuracy can be significantly improved in comparison with the color-gradient LB model without the improvements. Finally, the capability of the improved color-gradient LB model for simulating dynamic multiphase flows at a relatively large density ratio is demonstrated via the simulation of droplet impact on a solid surface.

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Source: https://tomesphere.com/paper/1904.03618