A Comparative Study of Hydrodynamic Lattice Boltzmann Equation in Phase-Field-Based Multiphase Flow Models (Communications in Computational Physics, 2024)
In recent years, phase-field-based models for multiphase flows have gainedsignificant popularity, particularly within the lattice Boltzmann (LB) community. Thesemodels typically use two lattice Boltzmann equations (LBEs), one for interface trackingand the other for solving hydrodynamic properties. However, for the purposes of thispaper, we focus only on the LB model for hydrodynamics. Our goal is to undertake acomparative investigation into the differences between three classical hydrodynamicLB models proposed by Lee et al. [1], Liang et al. [2] and Fakhari et al. [3]. The interface-tracking equation used in this study is based on the conservative phase-field model.We provide a detailed derivation of the governing equations in each model using theChapman-Enskog analysis. Additionally, three discretization methods for the interaction forces are introduced, and a modified method for the gradient term is proposedbased on the nonequilibrium distribution method. The accuracy of three LB modelsin combination with four discretization methods is examined in this study. Based onthe results, it appears that different combinations of models and methods are appropriate for different types of problems. However, some suggestions for the selection ofhydrodynamic models and discrete methods for the gradient term are provided in thispaper.
Keywords: Lattice Boltzmann method; multiphase; phase-field method; hydrodynamic lattice Boltzmann equation.