Study of Kinetic Equation for Non-Ideal Gases Using Lattice Boltzmann Method: Interparticle Forces from BBGKY Hierarchy

The first equation of the BBGKY hierarchy is closed with a truncation scheme which conserves mass, momentum and total energy. Resulting kinetic equation is solved numerically using the lattice Boltzmann method over an isothermal D 2 Q 9 lattice. The inter particle forces are derived using a density gradient approximation to the collision term of the BBGKY hierarchy and the resulting non-ideal equation of state is calculated. In this paper, we show analytically that the time rate of change of Boltzmann’s H-function i.e., d H t d t is zero for this truncation scheme, implying reversibility in time. Therefore, a BGK term is added to the collision integral to describe the macroscopic irreversibility. Both the local and global H -functions are calculated numerically for significant variations in the density. We also have simulated a switching experiment over this system and obtained the non-equilibrium work distributions.