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 \(D2Q9\) 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., \(\frac{dH \left( t \right) }{dt}\) 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.