A slip boundary condition for wall-modeled large eddy simulation with synthetic turbulence generator using high-order finite difference method

High-fidelity computational aeroacoustics simulations encounter significant challenges in industrial applications, especially in high Reynolds number flow regimes. These difficulties arise primarily from stringent requirements imposed by the Courant–Friedrichs–Lewy condition and the near-wall grid spacing, leading to prohibitively high computational costs. To address this limitation, this study presents a novel slip boundary condition for wall-modeled large eddy simulation that employs high-order finite-difference methods based on the dispersion-relation-preserving scheme. The slip boundary condition prescribes the tangential velocity at solid walls while enforcing zero normal penetration. The slip velocity is derived from a linearized near-wall velocity profile approximation at the sample point, significantly reducing grid resolution requirements. The slip boundary condition is first validated in turbulent channel flows at Reτ=2000 with optimized grid spacings (δ/Δx=20, δ/Δz=30, δ/Δy=20–30, δ: boundary-layer thickness), yielding mean velocity profiles and Reynolds stresses that closely match direct numerical simulation (DNS) benchmarks. Additionally, errors in the low-to-mid frequency components of the power spectral density remain within 3–6 dB. The optimized grid spacings are further validated over a range of friction Reynolds numbers (Reτ=576–5100). Besides, a synthetic turbulence inflow method is developed by superimposing divergence-free, spatially correlated steady jet structures onto the mean flow, integrated with the radiation nonreflective boundary conditions. The time-invariant source terms maintain computational efficiency while effectively suppressing spurious numerical oscillations. The synthesized velocity profiles and Reynolds stresses show excellent agreement with DNS data. While the spectra exhibit overprediction in amplitude, the characteristic shape maintain consistency with Goody's empirical model.