A BBGKY-based density gradient approximation of interparticle forces: Application for discrete Boltzmann methods

The force term accounting for interparticle interactions, with application to discrete Boltzmann simulation methods, is derived using a density gradient expansion of the BBGKY collision operator. It is shown that previous calculations, based on essentially the same mean-field-theory philosophy, do not apply the density gradient approximation in a self consistent fashion. Thus these previous models have errors in the second virial coefficient as well as coefficients associated with gradient terms in the pressure tensor. This new treatment corrects these shortcomings.