Phase-field lattice Boltzmann model with adjustable bulk viscosity for quasi-incompressible two-phase flows

In this paper, a lattice Boltzmann model with a single-relaxation-time collision operator is proposed for two-phase flows at high Reynolds numbers based on the quasi-incompressible phase-field theory. The proposed model consists of two lattice Boltzmann equations (LBEs), one for the Cahn-Hilliard equation with singular mobility, and the other for the quasi-incompressible Navier-Stokes equations (qINSE). Particularly, the LBE for the qINSE adopts an equilibrium distribution function containing a free parameter related to the flow compressibility. As a result, the bulk viscosity of fluid can be independently adjusted to improve the numerical stability of the model. Several numerical tests including double periodic shear layers, static droplet, Rayleigh-Taylor instability, and rising bubble are conducted to verify the accuracy and stability of the proposed model. The results demonstrate that the enhanced bulk viscosity successfully suppresses high-frequency oscillations in the velocity and pressure fields, improving the numerical stability of the proposed model in simulating two-phase flows at high Reynolds numbers.