Variable Sphere Molecular Model in the Monte Carlo Simulation of Rarefied Gas Flow

Abstract

The variable sphere (VS) molecular model is introduced to Monte Carlo simulation of rarefied gas flow. The VS model provides the consistency for diffusion and viscosity cross‐sections with those of any realistic intermolecular potential. The VS model has a much simpler scattering law than either the variable hard sphere (VHS) or variable soft sphere (VSS) models; also, it has the same computational efficiency as the VHS and VSS models. In this study, VS model is applied to the inverse power law (IPL) and Lennard‐Jones (LJ) potentials. Comparative simulations between the VS mode, IPL and LJ potentials are made for the molecular diffusion in a homogeneous heat‐bath gas, normal shock wave structure in a monatomic gas, and normal shock wave structure in binary gas mixture. The good agreement is shown in the molecular diffusion and shock wave structure between the VS model and the IPL and LJ potentials. The VS model is applied to the statistical inelastic cross‐section (SICS) model for the rotational inelastic collision of the diatomic molecule. Comparative simulation between the VS model with the SICS (VS‐SICS) model and VSS model with SICS (VSS‐SICS) model is made for rotational relaxation in a nitrogen normal shock wave. The agreement in the shock wave structure and rotational energy distribution function across the shock wave between the VS‐SICS model and the VSS‐SICS model are good. It is shown that the macroscopic transport phenomena are affected by the diffusion and viscosity cross‐sections rather than the scattering law of the each molecular collision.