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

TL;DR

This paper extends the particle ESBGK model to diatomic molecules with quantized vibrational energies, demonstrating its accuracy and computational efficiency compared to DSMC and experimental data in gas relaxation and hypersonic flow scenarios.

Contribution

The paper introduces an efficient extension of the ESBGK method for diatomic molecules with quantized vibrational energies, validated against DSMC and experiments.

Findings

The new method agrees well with DSMC and Landau-Teller predictions.

It significantly reduces computational time by up to 35.8 times.

The method accurately simulates hypersonic flow around a blunted cone.

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.