Lattice BBGKY scheme for two-phase flows: One-dimensional case

A novel lattice Boltzmann model for two-phase fluids is presented. We begin with the two-body BBGKY equation, and perform a coordinate transformation to split it into a Boltzmann equation for the one-body distribution, coupled to a kinetic equation for the correlation function. The coupling is accomplished by a self-consistent force. The resulting lattice Boltzmann model for nonideal fluids is grounded in the physics of the two-body distribution function. The discrete velocity model is described in detail, and numerical results are given for phase separation in one dimension.