A joint hydrodynamics-particle method for efficient hypersonic simulation in all flow regimes

The development of a multiscale method is essential for resolving cross-regime numerical simulations with precision, particularly in hypersonic flow scenarios. Traditional approaches, such as continuum fluid dynamics equations and stochastic particle methods, encounter considerable computational accuracy or efficiency limitations under extreme flow conditions. Here, we present a joint hydrodynamics-particle (JHP) method specifically designed for multi-regime hypersonic simulations, incorporating advancements in the discrete velocity method. In this framework, the main transport fluxes computed via the collision-free discrete velocity method are replaced by stochastic particle representations, while the continuum Navier-Stokes equations are seamlessly coupled with the particle method through an integral solution strategy. Adaptive weighting factors for these methodologies are determined dynamically at each spatial cell and timestep through a competition mechanism coupling model, ensuring multiscale consistency and computational efficiency. Analysis of the flux iteration formulation reveals that the JHP method exhibits strong asymptotic-preserving properties, naturally transitioning to macroscopic solvers in the continuum regime while accurately resolving particle-dominated fluxes in rarefied flows. Validation through benchmark cases, including shock wave structures and hypersonic flow around a cylinder, demonstrates the method’s ability to capture flow physics across continuum and rarefied regimes with high accuracy and computational efficiency. These results highlight the JHP method as a robust and versatile multiscale framework with significant potential for extending its applicability to complex physical phenomena.