An efficient simplified phase-field lattice Boltzmann method for super-large-density-ratio multiphase flow

Abstract

With the aim of efficiently simulating multiphase flows with complex interfaces and extremely large density ratios, we propose a simplified phase-field lattice Boltzmann method (SPFLBM). In this method, the recently developed simplified multiphase lattice Boltzmann method (SMLBM) that reflects the direct and explicit evolution of the macroscopic variables within the lattice Boltzmann framework is utilized as the basic flow solver. The conservative Allen-Chan equation is chosen as the target equation for interface tracking and is resolved by the simplified lattice Boltzmann method. Compared with the conventional lattice Boltzmann model, the SPFLBM consumes less virtual memory and allows direct implementation of physical boundary conditions. Meanwhile, the SPFLBM not only inherits the capability of describing microscopic interactions from the standard lattice Boltzmann method, but also enjoys good numerical stability from the reconstruction strategy in SMLBM. Several two-dimensional numerical examples are given to demonstrate the robustness of the proposed method for multiphase flow simulations. Results show that the SPFLBM can easily handle complex interface deformation, even in extreme cases where the density ratios are in the order of O (105). In the meantime, the proposed method has nice conservation capability, which allows the recovery of subtle multiphase flow phenomena such as the entrapped small bubbles, separation to the splashing fingers, and formation of satellite droplets.