Improved well-balanced free-energy lattice Boltzmann model for two-phase flow with high Reynolds number and large viscosity ratio

Spurious velocities and inaccurate density properties arising from the imbalance of discretized forces at discrete level are frequently observed in numerical simulation of multiphase flows based on lattice Boltzmann equation (LBE) models. In this paper, an improved well-balanced free-energy LBE model is proposed for two phase flows with high Reynolds numbers and large viscosity differences based on the well-balanced LBE [Guo et al., Phys. Fluids 33, 031709 (2021)]. To this end, a free parameter associated with the shear rate is introduced into the equilibrium distribution function. This results in a fluid viscosity that is dependent not only on the relaxation time but also on the introduced parameter. The relaxation time can be chosen to improve the numerical stability and accuracy, while the viscosity is mainly determined by the new parameter. To test the capability of the present model in capturing discrete equilibrium states, both one-dimensional flat interface and two-dimensional stationary droplet are simulated. Numerical results show that the present model is capable of eliminating spurious velocities and maintaining a constant chemical potential when the system reaches an equilibrium state. To further validate the performance of the present LBE for dynamic problems, both binary droplet collision and single bubble rising are performed, which demonstrates that the present model has the capability to deal with two phase flows with high Reynolds number and large viscosity ratio.