Semi-Differential Reynolds-Stress Model and Field Inversion Symbolic Regression Optimization

The Reynolds-averaged Navier–Stokes (RANS) framework incorporates two approaches for obtaining turbulent stresses: the algebraic eddy-viscosity model and the full transport-equation model. The latter is generally considered to have more potential than the former when applied to complex flows but still displays limitations in predicting streamwise separation flows, including overprediction of the recirculation length and irregular streamlines near reattachment points. Based on the fact that streamwise separated flows are primarily associated with turbulent shear effect, a new algebraic model of turbulent shear stresses is proposed based on the moving equilibrium assumption and symbolic regression optimization with field inversion. This algebraic model extends the well-known isotropic eddy viscosity to an anisotropic form, which is proven to be related to the Reynolds normal stress components. Subsequently, by establishing transport models for both the Reynolds normal stresses and the scale-providing variable, the entire equation system is closed and called the semi-differential Reynolds-stress model (Semi-RSM). Many separation cases, involving periodic hill, wall-mounted hump, cavity-ramp structure, and sharp leading-edge delta wing, are carried out for validation. It is indicated that the Semi-RSM driven by data successfully predicts the recirculation length and improves velocity and turbulent stress distributions compared to the non-data-driven version, as well as the Shear-Stress Transport (SST) [Formula: see text] and Speziale–Sarkar–Gatski/Launder–Reece–Rodi-[Formula: see text] (SSG/LRR-[Formula: see text]) RSM. Furthermore, it demonstrates strong generalization capability in three-dimensional complex flow and reduces computational cost compared to traditional RSM.