A Hypocoercive LBM–PINN Framework for High-Mach Rotating Thermal-Hydraulics in Nuclear Reactor Components

Classical turbulence closures systematically fail in high-Mach rotating flows because they introduce excessive dissipation and cannot capture the non-equilibrium effects that govern the dynamics. This limitation severely compromises the predictive reliability of thermal-hydraulic simulations for gas-cooled nuclear reactors. To overcome this challenge, we develop a rigorous numerical framework that seamlessly integrates a structure-preserving Lattice Boltzmann Method with a Physics-Informed Neural Network correction, grounded in hypocoercive stability theory. At the heart of our approach lies the Santos-Andrade inequality, a novel stability criterion that explicitly quantifies the competing influences of rotation, compressibility, and neural-network corrections, thereby offering a mathematically certified threshold for stable data-driven closures. We derive second-order convergence estimates for the semi-discrete LBM–PINN scheme and validate the framework against the canonical Taylor-Couette flow at Mach numbers 5.0 and 10.0. At Ma=10.0, classical closures — Smagorinsky, RANS, and SAS — fail catastrophically, producing unphysical constant temperature and pressure fields. In striking contrast, the Smagorinsky+PINN scheme uniquely restores a realistic radial temperature gradient and delivers a physically plausible Nusselt number of 17.14. The observed Lipschitz constant Lθ≈2.96 lies comfortably below the stability limit, confirming the practical utility of the Santos-Andrade criterion for high-fidelity nuclear thermal-hydraulic simulations.