On the validity of the Boltzmann-BGK model

The Boltzmann-BGK model is investigated for its validity on the collision term approximation through relaxation evaluation. The evaluation is based on theoretical analysis and numerical comparison between BGK and DSMC results for three designed relaxation problems. In order to isolate model-induced error, the BGK results are derived theoretically whereas numerical error in DSMC results is well controlled. It is analyzed that the relaxation time in BGK model does not equal to molecular mean collision time. Relaxation of 1D-space distribution fails to involve enough contribution from distributions in other dimensions, which makes the BGK model unable to capture details of velocity distribution, especially when discontinuity exists in distribution. The BGK model, however, predicts satisfactory history of velocity distribution function during relaxation when the flow is not far from Maxwellian. Particularly, the model-induced error in BGK depends on the degree of nonequilibirum, thus the model is more applicable for low-speed flows than for hypersonic flows. Because relaxation problem has no direct connection to Knudsen number, the BGK model can be applied to high rarefied flow as long as degree of nonequilibrium is not strong