Numerical simulation of across multiple flow vegimes over high-speed vehicles based on the multiscale discrete velocity method

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.