  The standard lattice Boltzmann equation (LBE) method usually fails to capture
the physical equilibrium state of a two-phase fluid system, i.e., zero velocity
and constant chemical potential. Consequently, spurious velocities and
inconsistent thermodynamic density properties are frequently encountered in LBE
simulations. In this work, based on a rigorous analysis of the discrete balance
equation of LBE, we identify the structure of the force imbalance due to
discretization errors from different parts. Then a well-balanced LBE is
proposed which can achieve the discrete equilibrium state. The well-balanced
properties of the LBE are confirmed by some numerical tests of a flat interface
problem and a droplet system.
