Conservative phase-field lattice Boltzmann model for interface tracking equation

Abstract

Based on the phase-field theory, we propose a conservative lattice Boltzmann method to track the interface between two different fluids. The presented model recovers the conservative phase-field equation and conserves mass locally and globally. Two entirely different approaches are used to calculate the gradient of the phase field, which is needed in computation of the normal to the interface. One approach uses finite-difference stencils similar to many existing lattice Boltzmann models for tracking the two-phase interface, while the other one invokes central moments to calculate the gradient of the phase field without any finite differences involved. The former approach suffers from the nonlocality of the collision operator while the latter is entirely local making it highly suitable for massive parallel implementation. Several benchmark problems are carried out to assess the accuracy and stability of the proposed model.

Improved lattice Boltzmann modeling of binary flow based on the conservative Allen-Cahn equation

“…Through the Chapman-Enskog analysis, we note that in the SRT algorithm by Geier et al [27], another deviated term, i.e., ( ) and they are linked to the mobility through…”

“…Our improved model (denoted as Model I) is compared with two models: the high-order FDM for the conservative ACE (denoted as Model II) and the original SRT model by Geier et al [27] (denoted as Model III).…”

“…In terms of the conservative ACE, Geier et al [27,28] first proposed the single-relaxation-time (SRT) algorithm, and showed better accuracy and better convergence rate over the CHE. Moreover, they offered an alternative algorithm to calculate the interface curvature locally, which greatly reduced computational expense but meanwhile brought an accuracy loss.…”

Phase-field lattice Boltzmann simulation of minute droplet onto isotropic porous media

“…本研究で用いる保存形 Allen-Cahn 方程式(1)は，元々の非保存形 Allen-Cahn 方程式に，次の平衡界面プロファ イルを課すための項を付加したものである (Geier et al, 2015…”

Alternative formulation to incorporate forcing terms in a lattice Boltzmann scheme with central moments

“…This particular one-way coupling implies that the collision is configured as a structured hierarchical pyramidal sequence of relaxation in an ascending order of moments, hence the name "cascaded" LBM. These models are characterized by very high properties in terms of accuracy, stability, and convergence [18][19][20][21][22][23][24][25].…”