Well-balanced lattice Boltzmann equation for two-phase flows

TL;DR

This paper introduces a well-balanced lattice Boltzmann equation that accurately captures the equilibrium state of two-phase flows, reducing spurious velocities and thermodynamic inconsistencies in simulations.

Contribution

A novel well-balanced LBE method is developed based on analyzing force imbalances, ensuring accurate equilibrium states in two-phase flow simulations.

Findings

Successfully achieves discrete equilibrium state in numerical tests

Reduces spurious velocities in two-phase flow simulations

Improves thermodynamic consistency of LBE methods

Abstract

The standard lattice Boltzmann equation (LBE) method usually fails to capture the physical equilibrium state of a two-phase fluid system, i.e., zero velocity and constant chemical potential. Consequently, spurious velocities and inconsistent thermodynamic density properties are frequently encountered in LBE simulations. In this work, based on a rigorous analysis of the discrete balance equation of LBE, we identify the structure of the force imbalance due to discretization errors from different parts. Then a well-balanced LBE is proposed which can achieve the discrete equilibrium state. The well-balanced properties of the LBE are confirmed by some numerical tests of a flat interface problem and a droplet system.