Unsteady nonlinear coupled constitutive relations model based on the PHengLEI framework

To enable efficient prediction of rarefied nonequilibrium effects, a nonlinear coupled constitutive relations (NCCR) solver and an unsteady NCCR solver (ALE-NCCR) were developed within the open source PHengLEI framework of the National Numerical Wind Tunnel project. The proposed models substantially extend the capability and applicability of PHengLEI for continuum–rarefied cross-regime flows, and their accuracy has been systematically validated through a series of representative test cases. The governing equations, non-dimensionalization procedures, and inner iteration strategies adopted in the PHengLEI-NCCR solver are first presented. The dual-time stepping ALE-NCCR model is then applied to compute the static and dynamic derivatives of the HBS configuration undergoing pitching oscillations. Numerical results show that the NCCR model exhibits strong agreement with experimental data in continuum regimes and provides substantially improved accuracy compared with the Navier–Stokes–Fourier (NSF) equations in rarefied nonequilibrium regimes, approaching the fidelity of DSMC simulations. Furthermore, the ALE-NCCR model recovers the accuracy of the ALE-NSF equations for unsteady continuum flows. These results demonstrate the robustness, accuracy, and broad applicability of the proposed NCCR based solvers.