A Shakhov-based Bhatnagar-Gross-Krook model for polyatomic molecules and for atomic as well as polyatomic mixtures

TL;DR

This paper extends the Shakhov Bhatnagar-Gross-Krook (SBGK) model within the PICLas code to simulate polyatomic molecules and mixtures, demonstrating its accuracy in non-equilibrium flow scenarios compared to DSMC and ESBGK methods.

Contribution

The paper introduces a new SBGK model implementation for polyatomic molecules and mixtures, including a derivation of the Prandtl number parameter and validation against benchmark flows.

Findings

The SBGK model accurately predicts shock structures in hypersonic flows.

Good agreement with DSMC and ESBGK methods in test cases.

The model captures non-equilibrium effects in complex gas mixtures.

Abstract

The implementation of the Shakhov Bhatnagar-Gross-Krook (SBGK) method in the open-source particle code PICLas is extended for modeling of polyatomic molecules, as well as mixtures including atoms and molecules, while accounting for non-equilibrium in the internal degrees of freedom. The conservation properties of the model are shown and the model parameter for the Prandtl number is derived. In order to determine the viscosity and thermal conductivity of gas mixtures, the first approximation of the transport properties using collision integrals is employed. The model is verified with simulation test cases of a supersonic Couette flow and a hypersonic flow around a 70{\deg} blunted cone with different flow parameters and gas compositions. The results are compared to the Direct Simulation Monte Carlo (DSMC) method as well as the Ellipsoidal Statistical BGK (ESBGK) method to assess the accuracy of the model, where overall good agreement is achieved. In particular, the proposed SBGK model captures the shock in front of the 70{\deg} blunted cone more precisely than the ESBGK model.