A stochastic particle method based on the Fokker-Planck Master equation for rarefied gas flows of diatomic mixtures

Abstract

The direct simulation Monte Carlo (DSMC) method has become a standard numerical technique for rarefied gas flows. However, its computational cost becomes prohibitive in the near-continuum regime. To enable efficient simulation of multiscale rarefied gas flows, the particle-based Fokker-Planck (FP) method has been studied. While several monatomic and diatomic FP models have been proposed, the extension to gas mixtures has received little attention. This paper aims to construct a Fokker-Planck Master (FPM) equation for diatomic mixtures, including energy exchange between translational, rotational, and vibrational modes as well as momentum and energy transfer between species. Two new kinetic models are proposed by combining the monatomic mixture FP model [S. Kim and E. Jun, Phys. Fluids 37, 016104 (2025)] and the diatomic single-gas FPM model [S. Kim and E, Jun, J. Comput. Phys. 506, 112940 (2024)]: the ESFPM mixture model, which is based on the ellipsoidal-statistical FP (ESFP) framework, and the ESFPM+ mixture model, which includes nonlinear drift coefficients to improve predictions of translational heat flux relaxation rates. Numerical studies include the relaxation problem, Couette flow, hypersonic flow over a vertical flat plate, and hypersonic flow around a cylinder. The results demonstrate that both the ESFPM and ESFPM+ mixture models agree well with DSMC near equilibrium. Furthermore, the ESFPM+ mixture model better captures shock structures than the ESFPM mixture model at high Knudsen numbers.