Lattice Boltzmann simulations of liquid-gas and binary fluid systems

We present the details of a lattice Boltzmann approach to phase separation in nonideal one- and two-component fluids. The collision rules are chosen such that the equilibrium state corresponds to an input free energy and the bulk flow is governed by the continuity, Navier-Stokes, and, for the binary fluid, a convection-diffusion equation. Numerical results are compared to simple analytic predictions to confirm that the equilibrium state is indeed thermodynamically consistent and that the kinetics of the approach to equilibrium lie within the expected universality classes. The approach is compared to other lattice Boltzmann simulations of nonideal systems. \textcopyright{} 1996 The American Physical Society.