  Spurious velocities arising from the imperfect offset of the undesired term
at the discrete level are frequently observed in numerical simulations of
equilibrium multiphase flow systems using the lattice Boltzmann equation (LBE)
method. To capture the physical equilibrium state of two-phase fluid systems
and eliminate spurious velocities, a well-balanced LBE model based on the
incompressible phase-field theory is developed. In this model, the equilibrium
distribution function for the Cahn-Hilliard (CH) equation is designed by
treating the convection term as a source to avoid the introduction of undesired
terms, enabling achievement of possible discrete force balance. Furthermore,
this approach allows for the attainment of a divergence-free velocity field,
effectively mitigating the impact of artificial compression effects and
enhancing numerical stability. Numerical tests, including a flat interface
problem, a stationary droplet, and the coalescence of two droplets, demonstrate
the well-balanced properties and improvements in the stability of the present
model.
