Improved Shear-Stress-Transport Model with Pressure Diffusion Term for Adverse Pressure Gradients

This work presents a method for enhancing the sensitivity of the shear-stress transport turbulence model to adverse pressure gradients (APGs). The approach is motivated by the mean-velocity profile in the overlap region of a turbulent boundary layer under APGs, which exhibits a half-power law behavior not adequately captured by standard models. To address this limitation, composite shear-stress and mean-velocity profiles are developed under APGs using localized variables, enabling turbulence model recalibration. A pressure-diffusion term is then introduced into the [Formula: see text] equation to improve the model’s response to APGs. Theoretical analysis of the [Formula: see text] equation in the overlap region yields compatibility conditions consistent with the target velocity profile, guiding the calibration of the pressure-diffusion term. Damping and transition functions are incorporated to appropriately modulate the pressure-diffusion coefficient across flow regions. The modified model is validated using four distinct test cases with APG, outperforming the baseline model in most scenarios and delivering improved predictions of mean-velocity profiles and skin-friction coefficients.