n this paper a numerical approach for binary fluid mixtures is proposed. A lattice Boltzmann algorithm for the continuity and the Navier-Stokes equations is coupled to a finite-difference scheme for the convection-diffusion equation. A free-energy is used to derive the thermodynamic quantities related to the equilibrium properties of the system. Spurious velocities are reduced by using a general stencil scheme for discretizing spatial derivatives.

Thermal phase separation process, which follows a sudden quench in the coexistence region, is con- sidered for binary fluid mixtures. It is studied applying a new version of an hybrid lattice Boltzmann model, where non-ideal terms of the pressure tensor, which takes into account thermal and concen- tration gradient contribution, are included as a body force in the LBM equations, used to solve the Navier-Stokes equations. The equations for concentration and temperature are solved using a finite dif- ference scheme. Domains are observed to order preferably with interfaces parallel to the cold walls and this behavior is more pronounced at higher viscosities. An intermediate regime with two characteristics scales for the domain size, one close to the walls and the other in the middle of the system, has been also observed.

A hybrid lattice Boltzmann method (LBM) for binary mixtures based on the free-energy approach is proposed. Nonideal terms of the pressure tensor are included as a body force in the LBM kinetic equations, used to simulate the continuity and Navier-Stokes equations. The convection-diffusion equation is studied by finite-difference methods. Differential operators are discretized in order to reduce the magnitude of spurious velocities. The algorithm has been shown to be stable and reproducing the correct equilibrium behavior in simple test configurations and to be Galilean invariant. Spurious velocities can be reduced by approximately an order of magnitude with respect to standard discretization procedure.