Recovery of Transport Coefficients in Navier-Stokes Equations from Modeled Boltzmann Equation

Leung te al show that the full set of compressible Navier-Stokes (NS) equations (which consist of the continuity, the momentum, the thermal energy, and the gas equation of state) can be derived from the modeled Boltzmann equation (BE) [1] by suitably modifying the collision relaxation time ... in the commonly assumed Bhatnagar, Gross, and Krook (BGK) model [2]. The modeled BE thus derived is valid for dense gas only when the mean free path between two successive particle collisions is very small compared with the characteristic spatial scale of the fluid system L. It is not sufficient to show that the NS equations are recovered [3-5]; more important, it has to demonstrate that the transport coefficients (such as bulk viscosity ..., thermal conductivity ..., and the specific heat ratio ...) of the fluid can be correctly replicated, because in the solution of the NS equations, these coefficients are specified, but they are part of the solution of the modeled BE. (ProQuest-CSA LLC: ... denotes formulae/symbols omitted.)