To address the challenge of predicting flow characteristics of vehicles in rarefied gas environments at high altitudes across multiple flow regimes, the multiscale discrete velocity method coupled with a steady implicit algorithm was employed to conduct numerical simulations of transitional flows over high-speed vehicles. Numerical simulations were performed for typical three-dimensional geometries, including $9{}^{\circ }$ blunt cone, $70{}^{\circ }$ blunted cone, Apollo 6 reentry capsule, and X-38 vehicle, across multiple flow regimes. Results show that the present method accurately captures non-equilibrium effects and primary flow features across these regimes. Comparisons with reference data from the direct simulation Monte Carlo (DSMC) method and relevant experimental measurements show good agreement for key aerodynamic parameters, including lift and drag coefficients, surface pressure coefficient, and heat flux coefficient. For the X-38 vehicle case, the relative errors of lift and drag coefficients are 1.31% and 2.69%, respectively. A comparative analysis for the X-38 vehicle case indicates that, under the conditions considered in this study, the MDVM with the steady implicit algorithm produces results comparable to those of the DSMC method, while showing certain advantages in computational efficiency: the total core-hours are reduced from 4281 (DSMC) to 3072 (MDVM), representing a saving of approximately 28% , and potential for engineering applications. These results validate the effectiveness and accuracy of the multiscale discrete velocity method, providing methodological support for aerodynamic characteristic prediction and design of vehicles operating across multiple 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.