Multi-scale implicit scheme for steady flows of diatomic molecular gases in all flow regimes

The application of unified gas kinetic scheme is greatly hindered by the huge requirements of computing resources. Based on Boltzmann-Rykov model equation, a conservative implicit scheme for steady flows in all flow regimes was developed by adopting macroscopic prediction technique, and the macroscopic equation and microscopic equation were solved collaboratively to accelerate the convergence. At the cell interface, a simplified and efficient multi-scale numerical flux was directly constructed from the characteristic difference solution of kinetic model equation. The adoption of non-uniform, unstructured velocity space and velocity space adaptive technology further reduce the requirement of computation and improve computational efficiency. The applications of unstructured discrete velocity space and adaptive discrete velocity space reduced the number of velocity mesh significantly and made the present method be rather efficient. The accuracy and effectiveness of the proposed method were confirmed by the simulations of rarefied supersonic and hypersonic flows over a flat plate, supersonic and hypersonic flows over a sphere. Numerical results indicate that the proposed method can accurately solve two-dimensional and three-dimensional diatomic gas multi-scale flow problems, and it is about one orders of magnitude faster than the explicit discrete unified gas kinetic scheme method.