Direct numerical simulation of supersonic turbulence with non-equilibrium multi-temperature model

In this paper, a multi-temperature high-order gas-kinetic scheme (HGKS) is developed for the direct numerical simulation (DNS) of supersonic turbulent boundary layers. The multi-temperature model based on the Bhatnagar–Gross–Krook (BGK) equation coupled with the Landau–Teller–Jeans relaxation model is adopted for the computation of thermal non-equilibrium flows. The seventh-order weighted essentially non-oscillatory (WENO) reconstruction is used for spatial accuracy. To resolve the stiff source terms for the relaxation model, a two-stage third-order semi-implicit scheme is proposed to ensure temporal accuracy and robustness. To accelerate the computation, HGKS is implemented with multiple graphics processing units (GPU) using the compute unified device architecture (CUDA). The supersonic turbulent boundary layers with Ma_∞=2.25 and Ma_∞=6 are tested with the single-temperature HGKS. Numerical results are presented to validate the single-temperature HGKS and analyze the effects of compressibility and wall-temperature. Subsequently, the turbulent boundary layer with Ma_∞=6 is simulated with the multi-temperature HGKS. According to the properties of nitrogen, the current simulation ensures the excitation of vibrational modes and the chemically frozen state for the analysis of thermal non-equilibrium effects. Compared with the single-temperature case, the dynamic variables have negligible differences, while the thermodynamic parameters and wall heat flux exhibit considerable deviations. The current work validates the multi-temperature HGKS as a powerful tool for thermal non-equilibrium supersonic turbulence simulation.