Functional Correction to Spalart–Allmaras Model for Adverse Pressure Gradient and Low-Reynolds Number

Turbulence modeling remains a critical challenge in computational fluid dynamics, particularly when simulating complex flow regimes. While the Spalart–Allmaras (S-A) turbulence model is widely regarded for its computational efficiency and robustness in attached flows with favorable pressure gradients, its predictive accuracy deteriorates under adverse pressure gradient (APG) conditions—such as flow separation and stall—and at low Reynolds numbers (Re), where skin friction coefficient predictions exhibit significant discrepancies in regions of low turbulent Reynolds number, [Formula: see text], within the developing boundary layer. In prior work, we introduced an adverse pressure gradient correction (APGC) that substantially improved lift coefficient predictions in APG-dominated flows without compromising drag coefficient accuracy. Concurrently, an existing low-Reynolds-number correction (LRe) demonstrated enhanced fidelity in skin friction predictions at low Re. Building upon these findings, the present study proposes a unified framework integrating both APGC and LRe corrections into the S-A model. This synergistic modification aims to extend the model’s applicability, improving predictions of lift, drag, and incipient angle of attack across a broader range of flow conditions with negligible computational overhead. The outcome is a refined S-A model capable of addressing key limitations in APG and low-Re regimes while nearly maintaining the original formulation’s efficiency.