A test of equivalence of the variable-hard-sphere and inverse-power-law models in the direct-simulation Monte Carlo method

Abstract

A test of the equivalence of the variable-hard-sphere (VHS) and inverse-power-law (IPL) models in rarefied gas flows is made for the molecular diffusion in a heat-bath gas and the two-dimensional rarefied gas flow around a circular cylinder using the null-collision Monte Carlo method. For the most severe test, the softest practical model corresponding to the Maxwell molecule is chosen. It is shown that the VHS diffusion is slower than the IPL one in the viscosity mean-free-path (mean-collision-time) scale but agrees with the IPL one in the diffusion scale. The VHS and IPL flow fields around a circular cylinder reveal a small but appreciable discrepancy in the usual viscosity scale. These facts should call attention to the equivalence of the VHS and IPL models especially when the molecular diffusion may play an important role in a (gas mixture) flow, where the diffusion scale may be preferable to the viscosity scale.