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A lattice Boltzmann equation method for simulating multiphase immiscible fluid flows with variation of density and viscosity, based on the model proposed by Gunstensen et al. for two-component immiscible fluids [Phys. Rev. A 43, 4320 (1991)] is developed. 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.
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