Non-equilibrium flow simulations based on Grad-14 and Grad-17 moment equations for polytropic gases

This study presents non-equilibrium flow simulations based on the Grad-14 and Grad-17 moment equations for polytropic gases, demonstrating their effectiveness in capturing complex flow phenomena in various shock dynamics scenarios. Detailed analyses of one-dimensional shock structure, shock tube, and two-dimensional shock-bubble interaction problems reveal that the Grad models, particularly the Grad-17 model, offer superior accuracy in predicting non-equilibrium effects compared to traditional Euler and Navier–Stokes–Fourier models. The results are validated through comparisons with direct simulation Monte Carlo (DSMC) data, showcasing the ability of the Grad models to resolve shock thickness, stress, and heat flux in high-speed flows where non-equilibrium effects are significant. Sensitivity studies on the Grad-17 model's source term coefficients indicate that modified coefficients enhance the accuracy of the model in capturing non-equilibrium behavior and energy transport. Furthermore, the study highlights the critical role of higher-order moment models in rarefied regimes, where non-equilibrium effects become more pronounced with increasing Knudsen numbers. The two-dimensional shock-bubble interaction problem further validates the Grad-17 model's performance, demonstrating its capability to accurately simulate shock wave interactions with bubbles in both near-continuum and rarefied gas regimes. The numerical simulations, validated by experimental data, confirm the reliability and robustness of the computational framework, making it a valuable tool for simulating complex non-equilibrium flows in high-speed applications.