Thermodynamic nonequilibrium effects in three-dimensional high-speed compressible flows: Multiscale modeling and simulation via the discrete Boltzmann method.

This article focuses on the development and validation of a three-dimensional (3D) Burnett-level discrete Boltzmann model (DBM) for simulating high-speed compressible flows with significant thermodynamic nonequilibrium effects (TNEs). By employing Chapman–Enskog multiscale analysis, the study identifies essential kinetic moment relations that characterize second-order TNEs and constructs a discrete velocity set with 55 velocities (D3V55) to accurately capture these effects in 3D supersonic flows. The model derives nonlinear constitutive relations that extend traditional fluid dynamics by incorporating complex nonequilibrium driving forces and their couplings unique to three dimensions. Extensive numerical tests, including one-, two-, and three-dimensional Riemann problems, demonstrate the model's capability to accurately reproduce large-scale flow structures and mesoscopic nonequilibrium quantities such as viscous stress and heat flux, outperforming lower-order models especially in regimes beyond the continuum flow assumption. The study also discusses the limitations of the current DBM, such as its restriction to second-order TNEs and single relaxation time, and outlines future directions involving higher-order effects, multi-relaxation-time schemes, and stability analyses to enhance applicability in aerospace, energy, and defense engineering contexts.