Numerical comparison between the Boltzmann and ES-BGK models for rarefied gases

Rarefied gas flows obey the Boltzmann equation, but numerical simulations of this equation are not always possible, so that simpler models have been introduced. The ES-BGK equation is one of these models. It gives the correct transport coefficients for the Navier-Stokes approximation, so that Boltzmann or ES-BGK simulations are expected to give the same results for dense gases, but in the case of a rarefied flow, complete numerical comparisons are needed. In this paper we present numerical comparisons between the two models in transitional regimes (where the ES-BGK model is expected to be useful) for reentry flows around a compression ramp and a plate. We also emphasize that the ES-BGK model gives flow predictions closer to the Boltzmann result than the simpler BGK model.