Adverse-pressure-gradient turbulence model improvement via mixing-length and symbolic regression

A novel theoretical formulation for the mixing length (luv+) in the logarithmic region under adverse pressure gradient (APG) conditions is developed, based on the logarithmic decay law of the total shear stress. Utilizing a symbolic regression (SR)-based machine learning algorithm, we establish a transition function for luv+ in the buffer layer under APG. The synergistic combination of these developments yields a comprehensive mathematical expression for the near-wall luv+, designated as luv_SR+. Extensive validation against multiple high-fidelity datasets demonstrates excellent agreement, confirming the universal applicability of luv_SR+. Subsequently, we derive a formulation for the turbulent eddy viscosity coefficient (νt+) under APG conditions building upon luv_SR+, which reveals inherent limitations in the νt+ calculation of the Menter shear stress transport (SST) turbulence model. To address these limitations, we propose the LSR SST model. Extensive validation through six flow separation cases demonstrates that the LSR SST model significantly improves the prediction accuracy of the wall friction coefficient (Cf) distribution and the separation point compared to the original Menter SST model. The results conclusively show that the LSR SST model effectively resolves the premature separation issue inherent in the original Menter SST model.