Shock wave kinetics: Multiscale hydrodynamic and thermodynamic non-equilibrium via the discrete Boltzmann method

Shock waves are typical multiscale phenomena in nature and engineering, inherently driven by both hydrodynamic and thermodynamic non-equilibrium (HNE and TNE) effects. However, the underlying mechanisms governing these non-equilibrium processes remain incompletely understood. In this study, we advance the discrete Boltzmann method (DBM) to adequately capture higher-order non-equilibrium. To reveal the dominant mechanism and offer mutual interpretation between macroscopic and TNE quantities, we derive analytical solutions for distribution functions and TNE measures of various orders via Chapman−Enskog analysis. Using argon shock structures as a case study, the DBM results show agreement with experimental, direct simulation Monte Carlo, and analytical data across two levels: (i) macroscopic interface profiles and thickness, and (ii) mesoscopic-level distribution functions and TNE indicators. Key findings include: (i) a Mach-number-induced two-stage behavior that manifests not only in shock width and smoothness but also in the peak of the distribution function, and (ii) a shift in the compressibility-dominated region from the outflow to inflow side with increasing Mach number. Beyond classical hydrodynamics, we analyze the dominant TNE mechanisms with analysis perspectives including the distribution function, types of TNE quantities, and TNE at different non-equilibrium orders. This study reveals how various orders and types of non-equilibrium effects govern shock wave structure, offering mesoscopic insight into kinetic behavior and laying a theoretical foundation for constructing physically robust non-equilibrium models.