Finite difference lattice Boltzmann model with flux limiters for   liquid-vapor systems
  In this paper we apply a finite difference lattice Boltzmann model to study the phase separation in a two-dimensional liquid-vapor system. Spurious numerical effects in macroscopic equations are discussed and an appropriate numerical scheme involving flux limiter techniques is proposed to minimize them and guarantee a better numerical stability at very low viscosity. The phase separation kinetics is investigated and we find evidence of two different growth regimes depending on the value of the fluid viscosity as well as on the liquid-vapor ratio. 
V. Sofonea, A. Lamura, G. Gonnella, and A. Cristea