A difference-free conservative phase-field lattice Boltzmann method

TL;DR

This paper introduces a difference-free lattice Boltzmann scheme combining CPF and one-fluid methods, improving efficiency and accuracy in simulating large-scale two-phase flows without finite difference formulations.

Contribution

It develops a novel difference-free scheme that enhances computational efficiency and accuracy for two-phase flow simulations using lattice Boltzmann methods.

Findings

47% increase in computational efficiency

Accurate simulation of droplet dynamics and Rayleigh-Taylor instability

Effective modeling of bubble breakup in vortex flows

Abstract

We propose an innovative difference-free scheme that combines the one-fluid lattice Boltzmann method (lBM) with the conservative phase-field (CPF) lBM to effectively solve large-scale two-phase fluid flow problems. The difference-free scheme enables the derivation of the derivative of the order parameter and the normal vector through the moments of the particle distribution function (PDF). We further incorporate the surface tension force in a continuous surface stress form into the momentum equations by modifying the equilibrium PDF to eliminate the divergence operator. Consequently, the entire computation process, executed without any inter-grid finite difference formulation, demonstrates improved efficiency, making it an ideal choice for high-performance computing applications. We conduct simulations of a single static droplet to evaluate the intensity of spurious currents and assess the accuracy of the scheme. We then introduce the density or viscosity ratio and apply an external body force to model the Rayleigh-Taylor instability and the behavior of a single rising bubble, respectively. Finally, we employ our method to study the phenomenon of a single bubble breaking up in a Taylor-Green vortex. The comparison between the difference-free scheme and the finite difference method demonstrates the scheme's capability to yield accurate results. Furthermore, based on the performance evaluation, the current scheme exhibits an impressive $47\% $ increase in efficiency compared to the previous method.