Multi-species modeling in the particle-based ellipsoidal statistical Bhatnagar-Gross-Krook method including internal degrees of freedom

TL;DR

This paper extends the ESBGK particle method to multi-species polyatomic gases with internal degrees of freedom, compares models and collision rules, and validates accuracy and efficiency against DSMC in high-speed flows.

Contribution

It introduces a multi-species ESBGK implementation with internal energies, combining existing models, and evaluates transport coefficient determination methods for polyatomic gas mixtures.

Findings

Good agreement with DSMC in test cases.

Collision integrals outperform Wilke's mixing rules for accuracy.

ESBGK offers significant computational efficiency improvements.

Abstract

The implementation of the ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) method in the open-source particle code PICLas is extended for multi-species modeling of polyatomic molecules, including internal energies with multiple vibrational degrees of freedom. For this, the models of Mathiaud, Mieussens, Pfeiffer, and Brull are combined. In order to determine the transport coefficients of the gas mixture, Wilke's mixing rules and collision integrals are compared. The implementation is verified with simulation test cases of a supersonic Couette flow as well as a hypersonic flow around a 70{\deg} blunted cone. The solutions of the ESBGK method are compared to the Direct Simulation Monte Carlo (DSMC) method to assess the accuracy, where overall good agreement is achieved. In general, collision integrals should be preferred for the determination of the transport coefficients, since the results using Wilke's mixing rules show larger deviations in particular for large mass ratios. Considering the computational efficiency of the methods, a considerable reduction in computational time is possible with the ESBGK model.