Constructing thermodynamically consistent models with a non-ideal   equation of state
  A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model fluids with excluded volume effects. This is achieved through the use of biased stochastic multi-particle collisions which depend on local velocities and densities and conserve momentum and kinetic energy. The equation of state is derived and criteria for the correct choice of collision probabilities are discussed. In particular, it is shown how a naive implementation can lead to inconsistent density fluctuations. 
Erkan Tuzel, Thomas Ihle, Daniel M. Kroll