(untitled) (Advances in Applied Mathematics and Mechanics, 2024)
In this study, an efficient regularized lattice Boltzmann model aimed at solving the consistent and conservative phase-field model is developed. This model is composed of the conservative Allen-Cahn equation, the momentum equation featuring a modified mass flux, and the associated consistency conditions. Consequently, two distribution functions are introduced within the framework of the regularized lattice Boltzmann model: one dedicated to the conservative Allen-Cahn equation, and the other designed for addressing the fluid dynamics equations. In order to accurately recover the momentum equation and ensure the consistency of mass and momentum transport, a simple force distribution function with a auxiliary term is incorporated into the regularized lattice Boltzmann model. To assess the capabilities of the current regularized lattice Boltzmann model, simulations of various two-phase flow problems with substantial density ratios have been conducted, including layered Poiseuille flow and spinodal decomposition. These simulations demonstrate excellent agreement with previously published numerical results. Additionally, numerical investigations into Rayleigh-Taylor instability indicate that the present regularized lattice Boltzmann model can accurately and stably track interfaces with high precision.