Comparison of Discrete Velocity Method and Gas-Kinetic Method for Binary Gas Mixtures

Abstract

The formulation of computationally efficient methods describing gas mixtures at kinetic level suitable for demanding aerospace applications presents significant challenges. This work presents a gas-kinetic scheme for binary gas mixtures in which the kinetic model is capable of recovering, in the continuum limit, the correct heat transfer, mixture viscosity, and species diffusion. The model accounts for separate species-mean velocity such that the species diffusion and velocity drift are accurately represented. The main goal is to derive a numerically efficient gas kinetic scheme (GKS) method that has the ability to accurately model species diffusion and velocity drift, such that two-species Navier–Stokes equations are recovered with the correct Prandtl number. The paper compares the solutions of the underlying kinetic model obtained using the GKS method and the discrete velocity method. The limitations of the GKS for different flows and different levels of thermodynamic nonequilibrium are examined. Supersonic flows with varying species mass ratios, concentrations, and Knudsen number are investigated. For the cases considered a good agreement is observed, showing that the developed GKS method provides a valuable approach for modeling these challenging flows. Also, the reduction in required CPU time for the GKS relative to discrete velocity method is shown to be significant.