An Efficient Regularized Lattice Boltzmann Method to Solve Consistent and Conservative Phase Field Model for Simulating Incompressible Two-Phase Flows (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 iscomposed 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, andthe other designed for addressing the fluid dynamics equations. In order to accuratelyrecover the momentum equation and ensure the consistency of mass and momentumtransport, a simple force distribution function with a auxiliary term is incorporatedinto 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 Poiseuilleflow and spinodal decomposition. These simulations demonstrate excellent agreementwith previously published numerical results. Additionally, numerical investigationsinto Rayleigh-Taylor instability indicate that the present regularized lattice Boltzmannmodel can accurately and stably track interfaces with high precision.