A unified stochastic particle method based on the Bhatnagar-Gross-Krook model for polyatomic gases and its combination with DSMC

TL;DR

This paper introduces a hybrid stochastic particle method based on the BGK model for simulating multiscale hypersonic flows of polyatomic gases, combining accuracy and efficiency improvements over traditional methods.

Contribution

It extends the unified stochastic particle BGK scheme to polyatomic gases with vibrational and rotational energies and combines it with DSMC for enhanced hypersonic flow simulation.

Findings

Achieves second-order accuracy in fluid limit

Validates with shock and hypersonic flow tests

Reduces computational cost compared to traditional methods

Abstract

Simulating hypersonic flow around a space vehicle is challenging because of the multiscale and nonequilibrium nature inherent in these flows. To effectively deal with such flows, a novel particle particle hybrid scheme combining the stochastic particle Bhatnagar-Gross-Krook (BGK) method with Direct Simulation Monte Carlo (DSMC) was developed recently, but only for monatomic gases [Fei et. al., J. Comput. Phys. 2021]. Here this work is extended to the particle-particle hybrid method for polyatomic gases. In the near continuum regime, employing the Ellipsoidal Statistical BGK model proposed by Y. Dauvois, et. al. [Eur. J. Mech. B Fluids, 2021] with discrete levels of vibrational energy, the stochastic particle BGK method is first established following the idea of the unified stochastic particle BGK (USPBGK) scheme. In the fluid limit, it has been proven to be of second order temporal and spatial accuracy. Then, the USPBGK scheme with rotational and vibrational energies is combined with DSMC to construct a hybrid method for polyatomic gases. The present hybrid scheme is validated with numerical tests of homogenous relaxation, 1D shock structure and 2D hypersonic flows past a wedge and a cylinder. Compared to traditional stochastic particle methods, the proposed hybrid method can achieve higher accuracy at a much lower computational cost. Therefore, it is a more efficient tool to study multiscale hypersonic flows.