  The particle-based ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK)
model is extended to diatomic molecules and compared with the Direct Simulation
Monte Carlo (DSMC) method. For this an efficient method is developed that
optionally allows the handling of quantized vibrational energies. The proposed
method is verified with a gas in an adiabatic box relaxing from a
non-equilibrium state to an equilibrium. It is shown that the analytical
Landau-Teller expression as well as DSMC results agree very well with the new
method. Furthermore, the method is compared with DSMC results and experimental
measurements of a hypersonic flow around a 70$^\circ$ blunted cone. It is shown
that the ellipsoidal statistical BGK compares very well with the DSMC results
while saving up to a factor of $\approx 35.8$ CPU time for this low Knudsen
number case.
