Discrete unified gas kinetic scheme for flows of binary gas mixture based on the McCormack model

Abstract

The discrete unified gas kinetic scheme (DUGKS) was originally developed for single-species flows covering all the regimes, whereas the gas mixtures are more frequently encountered in engineering applications. Recently, the DUGKS has been extended to binary gas mixtures of Maxwell molecules on the basis of the Andries–Aoki–Perthame kinetic (AAP) model [P. Andries et al., “A consistent BGK-type model for gas mixtures,” J. Stat. Phys. 106, 993–1018 (2002)]. However, the AAP model cannot recover a correct Prandtl number. In this work, we extend the DUGKS to gas mixture flows based on the McCormack model [F. J. McCormack, “Construction of linearized kinetic models for gaseous mixtures and molecular gases,” Phys. Fluids 16, 2095–2105 (1973)], which can give all the transport coefficients correctly. The proposed method is validated by several standard tests, including the plane Couette flow, the Fourier flow, and the lid-driven cavity flow under different mass ratios and molar concentrations. Good agreement between results of the DUGKS and the other well-established numerical methods shows that the proposed DUGKS is effective and reliable for binary gas mixtures in all flow regimes. In addition, the DUGKS is about two orders of magnitude faster than the direct simulation Monte Carlo for low-speed flows in terms of the wall time and convergent iteration steps.