A finite difference lattice Boltzmann method (FDLBM) for two-phase flows pe
rtinent to isothermal non-ideal fluids is proposed. This FDLBM introduces p
seudopotential and recovers a full set of hydrodynamic equations for non-id
eal fluid through the Chapman-Enskog expansion procedure. Numerical measure
ment of surface tension agrees well with theoretical predictions. Simulatio
ns of two-phase phenomena, including phase-transition and droplets collisio
n are carried out, showing applicability of the model for two-phase flows.
Finite difference Lattice Boltzmann method ensures numerical stability of t
he scheme. This LB model retains advantages of conventional LB methods such
as a linear advection in the kinetic equation and parallel nature in compu
ting.