  We develop a lattice Boltzmann equation method for simulating multi-phase
immiscible fluid flows with variation of density and viscosity, based on the
model proposed by Gunstensen {\em et al} for two-component immiscible fluids.
The numerical measurements of surface tension and viscosity agree well with
theoretical predictions. Several basic numerical tests, including spinodal
decomposition, two-phase fluid flows in two-dimensional channels and two-phase
viscous fingering, are shown in agreement of experiments and analytical
solutions.
