On the validity of the Boltzmann–BGK model through relaxation evaluation

The Boltzmann-Bhatnagar-Gross-Krook（BGK）model is investigated for its validity regarding the collision term approximation through relaxation evaluation. The evaluation is based on theoretical analysis and numerical comparison between the BGK and direct simulation Monte Carlo（DSMC） results for three specifically designed relaxation problems. In these problems, one or half component of the velocity distribution is characterized by another Maxwellian distribution with a different temperature. It is analyzed that the relaxation time in the BGK model is unequal to the molecular mean collision time. Relaxation of component distribution fails to involve enough contribution from other component distributions, which makes the BGK model unable to capture details of velocity distribution, especially when discontinuity exists in distribution. The BGK model,however, predicts satisfactory results including fluxes during relaxation when the temperature difference is small. Particularly, the model-induced error in the BGK model increases with the temperature difference, thus the model is more reliable for low-speed rarefied flows than for hypersonic flows.