The improvement of adverse-pressure-gradient eddy viscosity based on the wall law

Building upon recent theoretical advancements in adverse pressure gradient (APG) turbulent boundary layer (TBL) dynamics, this study proposes a novel modification to the Menter shear-stress transport (SST) turbulence model through the introduction of a pressure gradient influence factor. This enhancement enables systematic adjustment of the eddy viscosity coefficient to account for pressure gradient effects in turbulent flow simulations. Through analysis of the logarithmic decay law and logarithmic pressure law, the eddy viscosity coefficient in APG TBLs overlapping regions is shown to scale with v s + —a dimensionless velocity parameter quantifying momentum-transport-dominant eddy velocity. This parameter, analytically expressed via the logarithmic decay law, intrinsically incorporates both pressure gradient and Reynolds number effects. A pressure gradient influence factor is rigorously integrated into the Menter-SST model's eddy viscosity formulation to address this limitation. Comprehensive validation through canonical APG cases demonstrates significant improvements in flow separation prediction accuracy, with enhanced agreement against high-fidelity reference solutions. The proposed modification effectively rectifies the model's premature flow separation tendency while retaining its baseline computational efficiency, advancing predictive capabilities for pressure gradient-dominated turbulent flows.