Discrete velocity and lattice Boltzmann models for binary mixtures of nonideal fluids

In this paper, a discrete velocity model and a lattice Boltzmann model are proposed for binary mixtures of nonideal fluids based on the Enskog theory. The velocity space of the Enskog equation for each component is first discretized by applying a Gaussian quadrature, resulting in a discrete velocity model that can be solved by suitable numerical schemes. A lattice Boltzmann model is then derived from the discrete velocity model with a slightly modified equilibrium. The hydrodynamics of each model are also derived through the Chapmann-Enskog procedure.