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

Abstract: 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.