Targeting the pronounced non-equilibrium characteristics of high-speed flows, this study conducted numerical simulations of typical high-speed flows based on the joint hydrodynamics–particle (JHP) method. The method employed stochastic particles to describe collisionless transport, and a competition mechanism was introduced within an integral solution framework through the coupling of the cell-averaged collision time and the global time step. This enabled a unified coupling between the macroscopic Navier–Stokes (N-S) equations and mesoscopic particle transport, allowing accurate resolution of locally strong non-equilibrium features. To validate the applicability of the method for high-speed non-equilibrium flows, three benchmark cases were selected: a one-dimensional shock structure and a high-speed flow over a circular cylinder at Mach 20, as well as a high-speed blunt-wedge flow at Mach 5. Comparisons with the unified gas-kinetic scheme (UGKS) and the unified gas-kinetic wave–particle (UGKWP) method demonstrated that the JHP method achieves high accuracy in predicting macroscopic quantities, including temperature and velocity distributions, as well as overall flow structures. Further comparisons with N-S solutions, combined with local Knudsen number analysis, revealed the spatial distribution of non-equilibrium regions within the flow field. Compared with conventional macroscopic approaches, the JHP method more accurately captures flow features in regions with strong non-equilibrium effects, such as the shock layer, near-wall region, and wake. These results indicate that non-equilibrium effects in high-speed flows exhibit pronounced spatial heterogeneity and significantly influence flow evolution. In the blunt wedge flow case, the computational time of the JHP method is approximately 37.9% of that of the reference method (IUGKS), and its memory consumption is about 2.5%, indicating that the method provides an efficient and high-fidelity approach for the simulation of hypersonic non-equilibrium flows.

To enable efficient prediction of rarefied nonequilibrium effects, a nonlinear coupled constitutive relations (NCCR) solver and an unsteady NCCR solver (ALE-NCCR) were developed within the open source PHengLEI framework of the National Numerical Wind Tunnel project. The proposed models substantially extend the capability and applicability of PHengLEI for continuum–rarefied cross-regime flows, and their accuracy has been systematically validated through a series of representative test cases. The governing equations, non-dimensionalization procedures, and inner iteration strategies adopted in the PHengLEI-NCCR solver are first presented. The dual-time stepping ALE-NCCR model is then applied to compute the static and dynamic derivatives of the HBS configuration undergoing pitching oscillations. Numerical results show that the NCCR model exhibits strong agreement with experimental data in continuum regimes and provides substantially improved accuracy compared with the Navier–Stokes–Fourier (NSF) equations in rarefied nonequilibrium regimes, approaching the fidelity of DSMC simulations. Furthermore, the ALE-NCCR model recovers the accuracy of the ALE-NSF equations for unsteady continuum flows. These results demonstrate the robustness, accuracy, and broad applicability of the proposed NCCR based solvers.

The increasingly complex and dynamic design requirements of future hypersonic vehicle have heightened the call for enhanced flexibility and efficacy in aerodynamic shape parameterization methods. This research addresses the constraints imposed by conventional geometric parameterization methods in hypersonic vehicle design, which tend to confine aerodynamic shapes excessively, limiting design optimization and culminating in the “dimensional disaster”. To tackle these challenges, the study introduces a novel approach centered on generative models to generalize the depiction of three-dimensional hypersonic vehicle aerodynamic profiles. This innovative method entails extracting geometric attributes from aerodynamic profile images and imposing constraints on global and local point cloud diffusion models to facilitate the creation of three-dimensional point cloud representations, catering to the intricate demands of three-dimensional shape reduction and adaptable design in engineering contexts. The method achieves a comprehensive multi-view generalized representation pipeline from cross-sectional images to point cloud geometry and surface meshes through three core modules: a geometric feature extraction and dimensionality reduction reconstruction model for cross-sectional images based on Variational Autoencoder (VAE) and residual networks; a 3D geometric point cloud generation model integrating point cloud variational autoencoder networks with conditionally controllable generative diffusion models; a surface mesh reconstruction model employing a differentiable Poisson solver. In the context of the three-dimensional blended wing-body configuration, manipulating generalized shape parameters within latent variable spaces enables rapid generation of single profile images in 3 s and three-dimensional aerodynamic mesh files in 80 s. The reconstructed shapes maintain an average geometric error within 1 mm compared to the initial design, demonstrating efficient and accurate generalization of complex aircraft shapes. Furthermore, the generated surface meshes were directly imported into Computational Fluid Dynamics (CFD) software to predict flow fields and aerodynamic characteristics under different angles of attack. The results highlight the potential of this method as an intelligent and flexible aerodynamic shape generalization tool for optimizing complex aircraft designs.

To predict aeroheating performance of hypersonic vehicles accurately in thermochemical nonequilibrium flows accompanied by rarefaction effect, a Nonlinear Coupled Constitutive Relations (NCCR) model coupled with Gupta’s chemical models and Park’s two-temperature model is firstly proposed in this paper. Three typical cases are intensively investigated for further validation, including hypersonic flows over a two-dimensional cylinder, a RAM-C Ⅱ flight vehicle and a type HTV-2 flight vehicle. The results predicted by NCCR solution, such as heat flux coefficient and electron number densities, are in better agreement with those of direct simulation Monte Carlo or flight data than Navier-Stokes equations, especially in the extremely nonequilibrium regions, which indicates the potential of the newly-developed solution to capture both thermochemical and rarefied nonequilibrium effects. The comparisons between the present solver and NCCR model without a two-temperature model are also conducted to demonstrate the significance of vibrational energy source term in the accurate simulation of high-Mach flows.