Momentum and Energy Transport in rarefied cavity flow Across Compressibility and Knudsen Number Ranges

The present study investigates the energy and momentum transport of Argon (Ar) in a lid-driven cavity setup across a range of compressibility (0.16 < Ma < 3.0) and rarefaction (10^-4 < Kn < 10²) conditions. We explore the behavior in different flow regimes using the Gas Kinetic Scheme (GKS), which calculates fluxes based on higher-order moments of the distribution function, and the Unified Gas Kinetic Scheme (UGKS), which employs multiple equi-variant distribution functions and is applicable across the entire Knudsen spectrum. We define breakdown parameters to characterize the rarefaction regimes captured by both GKS and UGKS. Our study examines Fourier and anti-Fourier (co-gradient) heat transport, as well as the misalignment between the deviatoric stress tensor (derived from higher-order statistics of peculiar velocity) and the constitutive strain tensor. We also analyze pressure anisotropy in the compressible (Ma = 3) and highly rarefied (Kn ~10) regimes, noting that the maximum contribution arises in the direction of the external forcing, i.e., the lid velocity direction. Furthermore, we compare various slip velocity models with UGKS cases for both stationary and moving walls, assessing the degree of departure from equilibrium. This comprehensive examination provides deeper insights into the complex behavior of gases under varying flow conditions and enhances our understanding of kinetic schemes in predicting fluid behavior in non-equilibrium states.