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The particle-based ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK)model is extended to diatomic molecules and compared with the Direct SimulationMonte Carlo (DSMC) method. For this an efficient method is developed thatoptionally allows the handling of quantized vibrational energies. The proposedmethod is verified with a gas in an adiabatic box relaxing from anon-equilibrium state to an equilibrium. It is shown that the analyticalLandau-Teller expression as well as DSMC results agree very well with the newmethod. Furthermore, the method is compared with DSMC results and experimentalmeasurements of a hypersonic flow around a 70$^\circ$ blunted cone. It is shownthat the ellipsoidal statistical BGK compares very well with the DSMC resultswhile saving up to a factor of $\approx 35.8$ CPU time for this low Knudsennumber case.

Extending the Particle ESBGK Method to Diatomic Molecules including Quantized Vibrational Energies