Constructions of Simple Kinetic Equations for a Dense Gas

Constructions of simple kinetic equations for a dense gas are presented, with a special emphasis on a couple of modelling based on the Ellipsoidal-Statistical (ES)-type collision model. First, two previous models are reviewed: one based on a simple relaxation model with the isothermal assumption and the other based on the Bhatnagar–Gross–Krook (BGK)-type collision model. These models have a monotone functional that enables one to make thermodynamic interpretations on simulation results for phase change phenomena. They are, however, not designed so as to reproduce appropriate transport properties for a dense gas. Two types of the Ellipsoidal-Statistical (ES)-based model are proposed and described in detail. Both ES-based models reproduce appropriate transport properties, which is an advantage over the previous models. The difference of their monotone property in time is also discussed in detail.