A divergence-free synthetic inflow turbulence generator for large eddy simulation of compressible turbulent boundary layers

We propose the Compressible Discretizing and Synthesizing Random Flow Generation (C-DSRFG) method, a divergence-free inflow turbulence generator for large eddy simulations (LES) of compressible boundary layers. As an extension of the incompressible DSRFG framework by Huang et al. [“A general inflow turbulence generator for large eddy simulation,” J. Wind Eng. Ind. Aerodyn. 98(10), 600–617 (2010)], C-DSRFG explicitly enforces the divergence-free condition on velocity fluctuations (∇·u′=0), a constraint whose significance is theoretically analyzed herein and has been largely overlooked in conventional compressible inflow generators. Validation through LES of a supersonic (M∞=2.33) flat-plate turbulent boundary layer demonstrates that enforcing this condition reduces the required turbulence adjustment length by over 40% compared to its non-divergence-free counterpart. Furthermore, the method's robustness and applicability are confirmed through simulations of a weakly compressible (M∞=0.5) boundary layer and a typical engineering problem—a shock-wave/turbulent boundary-layer interaction on a compression ramp. For all cases, key turbulence statistics—including velocity fluctuations, mean velocity profiles, friction coefficient, and spectral distribution—are compared with available datasets. The results reveal a consistent agreement with properties established in the literature, which fully validates the proposed method's physical realizability and its applicability to complex compressible flow engineering scenarios.