The high-speed flow around aerospace vehicles is characterized by regions with strong thermodynamic non-equilibrium effects, in particular at higher altitudes when rarefaction becomes more prominent. Modeling the flow at the kinetic level, i.e. governed by Boltzmann or kinetic model equations, provides the required level of physical detail. The formulation of numerical methods governing the flow at kinetic level with a computational efficiency suitable for demanding aerospace applications still presents a significant challenge. In addition to numerical methods, the development of kinetic models accurately describing a mixture of gases still presents a major research challenge. In this work, we contribute 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 as well as species diffusion. The model accounts for separate species-mean velocity such that the species diffusion and velocity drift are accurately represented. The resulting model is implemented in a parallel multi-block discrete-velocity solver and applied to a range of test cases. The discrete velocity method (DVM) is known to provide accuracy, but at high computational cost. To reduce computational cost, a gas kinetic scheme (GKS) is developed based on the described kinetic model and a comparative study with the discrete velocity method is conducted. The main goal is to derive a numerically efficient GKS method which 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. A detailed formulation of this GKS method is presented. The paper compares the solutions of the underlying kinetic model obtained using the GKS method and the discrete-velocity method. Using the DVM results as benchmark solutions for the GKS method, the limitations of the GKS for different flows and different levels of thermodynamic non-equilibrium are examined. The profile of a shock wave and the rarefied supersonic flow over a flat plate under different flow conditions are considered, with varying species mass ratios, concentrations and Knudsen number. 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 DVM is shown to be very significant.
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