Ab initio simulation of planar shock waves

The structure of planar shock wave is calculated for helium, neon and argon, applying the direct simulation Monte Carlo method based on ab initio potentials in the range of the Mach number varying from 1.5 to 10. To characterize the density and temperature variations along the shock wave, the dimensionless slopes of these quantities, defined through their maximum derivative with respect to the spatial coordinate, are calculated. The parameters of the numerical scheme were chosen to provide numerical error of the slopes less than 0.5%. The slopes for helium, neon and argon are qualitatively the same, but they are quantitatively different from each other. The largest difference is observed for the high value of Mach number and reaches 20% that means that the shock wave structure is strongly sensitive to the intermolecular potential. The obtained results can be used as benchmark data to test new mathematical models and new numerical methods in rarefied gas dynamics.