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 it is shown that the requirement of thermodynamic consistency imposes a severe restriction on the choice of collision probability, pApA. The consequences of various choices for pApA are discussed in detail.