A difference-free conservative phase-field method for two-phase flows

We propose an innovative difference-free scheme that combines the one-fluid lattice Boltzmann method (LBM) with the conservative phase-field (CPF) LBM to effectively solve large-scale two-phase fluid flow problems. The difference-free scheme enables the derivation of the derivative of the order parameter and the normal vector through the moments of the particle distribution function (PDF). We further incorporate the surface tension force in a Korteweg stress form into the momentum equations by modifying the equilibrium PDF to eliminate the divergence operator. Consequently, the entire computation process, executed without any inter-grid finite difference formulation, demonstrates an improved efficiency, making it an ideal choice for high-performance computing applications. We conduct simulations of a single static droplet to evaluate the intensity of spurious currents and assess the accuracy of the scheme. We then introduce the density or viscosity ratio and apply an external body force to model the Rayleigh-Taylor instability and the behavior of a single rising bubble, respectively. Finally, we employ our method to study the phenomenon of a single bubble breaking up in a Taylor-Green vortex. The comparison between the difference-free scheme and the finite difference method demonstrates the scheme's capability to yield accurate results. Furthermore, based on the performance evaluation, the current scheme exhibits an impressive 47% increase in efficiency compared to the previous method.