An improved slip boundary condition for wall-modeled large-eddy simulation of flow separation using high-order finite-difference method

Simulating flow separation in turbulent flows at high Reynolds numbers remains a significant challenge for high-order finite-difference methods. This study introduces a non-equilibrium slip boundary condition, integrated into a wall-modeled large-eddy simulation framework, to address this issue. By explicitly incorporating the tangential pressure gradient and a consistent eddy-viscosity closure, the proposed model effectively mitigates a key limitation of conventional equilibrium wall models (EQWMs) in separated flow regimes. Initial validation in an equilibrium channel flow demonstrates that the non-equilibrium wall model (NEQWM) achieves accuracy comparable to that of the EQWM. In contrast, for separated flow over periodic hills, the EQWM fails to capture the separation bubble, while the NEQWM provides substantially improved predictions of both the mean flow and turbulence statistics. Grid-resolution studies at Reh = 10 600 reveal that mean velocity profiles exhibit weak dependence on grid resolution. In comparison, predictions of the pressure coefficient and turbulent fluctuations improve notably with mesh refinement, particularly near the separation point and within the recirculation region. Velocity spectra in the shear layer confirm that the resolved turbulence in the outer layer is physically consistent and that the wall model does not artificially suppress large-scale turbulent dynamics. Simulations at higher Reynolds numbers confirm the robustness of the model in capturing correct scaling behavior for mean and fluctuating quantities, including the upstream shift of the reattachment location with increasing Reynolds number.