A Well-Balanced Lattice Boltzmann Model for Binary Fluids Based on the Incompressible Phase-Field Theory
Year: 2025
Author: Long Ju, Peiyao Liu, Bicheng Yan, Jin Bao, Shuyu Sun, Zhaoli Guo
Communications in Computational Physics, Vol. 37 (2025), Iss. 5 : pp. 1305–1326
Abstract
Spurious velocities arising from the imperfect offset of the undesired term at the discrete level are frequently observed in numerical simulations of equilibrium multiphase flow systems using the lattice Boltzmann equation (LBE) method. To capture the physical equilibrium state of two-phase fluid systems and eliminate spurious velocities, a well-balanced LBE model based on the incompressible phase-field theory is developed. In this model, the equilibrium distribution function for the Cahn-Hilliard (CH) equation is designed by treating the convection term as a source to avoid the introduction of undesired terms, enabling achievement of possible discrete force balance. Furthermore, this approach allows for the attainment of a divergence-free velocity field, effectively mitigating the impact of artificial compression effects and enhancing numerical stability. Numerical tests, including a flat interface problem, a stationary droplet, and the coalescence of two droplets, demonstrate the well-balanced properties and improvements in the stability of the present model.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2023-0307
Communications in Computational Physics, Vol. 37 (2025), Iss. 5 : pp. 1305–1326
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Well-balanced scheme lattice Boltzmann method phase-field method Cahn-Hilliard equation.