A generalized Bhatnagar–Gross–Krook model for nonequilibrium flows

Abstract

The Bhatnagar–Gross–Krook (BGK) model approximates the collision term of the Boltzmann equation by a single relaxation process from a nonequilibrium state to an equilibrium state. From the BGK model, the Navier–Stokes, Burnett, and Super-Burnett equations can be derived. However, the success of these derived macroscopic equations in the description of highly nonequilibrium flow is limited. In order to extend the validity of the BGK model to cope with complicated physical relaxation processes, we propose a generalized BGK (GBGK) model, where the gas distribution function settles to an equilibrium state through multiple particle collisional processes. The GBGK model can be used to capture the transitional, rotational, and vibrational nonequilibrium flow phenomena. More importantly, it may provide a theoretical framework to derive new macroscopic governing equations which are valid in the near continuum flow regime.