  In this paper, a generalized lattice Boltzmann (LB) model with a mass source
is proposed to solve both incompressible and nearly incompressible
Navier-Stokes (N-S) equations. This model can be used to deal with single-phase
and two-phase flows problems with a mass source term. From this generalized
model, we can not only get some existing models, but also derive new models.
Moreover, for the incompressible model derived, a modified pressure scheme is
introduced to calculate the pressure, and then to ensure the accuracy of the
model. In this work, we will focus on a two-phase flow system, and in the frame
work of our generalized LB model, a new phase-field-based LB model is developed
for incompressible and quasi-incompressible two-phase flows. A series of
numerical simulations of some classic physical problems, including a spinodal
decomposition, a static droplet, a layered Poiseuille flow, and a bubble rising
flow under buoyancy, are performed to validate the developed model. Besides,
some comparisons with previous quasi-incompressible and incompressible LB
models are also carried out, and the results show that the present model is
accurate in the study of two-phase flows. Finally, we also conduct a comparison
between quasi-incompressible and incompressible LB models for two-phase flow
problems, and find that in some cases, the proposed quasi-incompressible LB
model performs better than incompressible LB models.
