Data-Driven Modeling of Pressure Diffusion in Wall-Bounded Turbulent Flows

In Full Reynolds Stress Models (FRSM), the pressure diffusion term is often neglected or modeled implicitly by incorporating it into the turbulence diffusion term. However, DNS studies across various flow configurations have highlighted the importance of explicitly modeling pressure diffusion. Most existing models are based on Lumley's formulation and have been subsequently modified and calibrated using DNS data from channel flow at Re_τ = 180. These models, however, generally exhibit poor performance near the wall. In this work, we propose a data-driven approach to model the near-wall behavior of the pressure diffusion. Using DNS data from turbulent channel flows at Re_τ = 180, 550, 1000, 2000, and 5200, we develop a wall-corrected pressure diffusion model that accounts for both bulk and near-wall effects. Each component—bulk and wall—includes contributions from slow and rapid pressure fluctuations. A machine learning framework is employed to learn the damping function governing the wall correction. For a posteriori calibration, the proposed model is implemented within an FRSM framework alongside an existing wall-corrected pressure–strain model. The resultant pressure diffusion model is shown to retain accuracy for the unseen data of Channel flow DNS at Re_τ = 10000.