Development of a Particle Bhatnagar-Gross-Krook Method for Rarefied Monatomic Gas Mixtures

Abstract

The Direct Simulation Monte Carlo (DSMC) method has long served as a reliable numerical approach for simulating rarefied and non-equilibrium gas flows. Its computational cost, however, increases rapidly as the flow approaches the near-continuum regime. This limitation has motivated the development of kinetic model equations that replace binary collisions with simplified relaxation processes. This paper presents a particle multi-relaxation unified BGK (UBGK) model for monatomic gas mixtures. The model retains pairwise species relaxation and determines the target velocity, temperature, shear stress, and heat flux by matching the corresponding production terms to those of the Boltzmann equation. A stochastic particle algorithm is developed. The model is implemented in SPARTA, and two validation problems are considered: homogeneous relaxation and a Mach 3 flow over a cylinder. In both cases, the UBGK solution reproduces the DSMC reference behavior, including species-dependent relaxation and non-equilibrium shock structure.