Simulation of high-speed non-equilibrium flows via the joint hydrodynamics-particle method

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.