An accurate lattice Boltzmann model for immiscible high-density-ratio two-phase flows

In this paper, we propose an accurate lattice Boltzmann (LB) model for solving immiscible high-density-ratio two-phase flows from the perspective of the improved conservative Allen–Cahn equation. This model can be deemed as an extension of our accurate interface-capturing LB model [H. Liang et al., Phys. Rev. E 107, 025302 (2023)] to the hydrodynamic version, in which an LB model for the incompressible Navier–Stokes equations is incorporated. The striking feature of the LB model lies in that it introduces the signed-distance function originating from the level-set method instead of the phase field variable to mimic the fluid-fluid interactions. The signed-distance function change more smoothly across the interface in comparison to the phase field variable that does not contain any jumps. As a result, the present LB model enables to obtain the better numerical accuracy and stability than the previous LB model in solving immiscible two-phase flows, especially at a decreasing interface-thickness scale. Extensive numerical experiments, including static droplet, layered Poiseuille flow, bubble rising dynamics and planar Taylor bubble, have been carried out to validate the present LB model. It is shown that the present LB model indeed can be stable and accurate than the previous LB model, and the obtained numerical results also agree well with the analytical solutions or some available results.