High-fidelity simulations of turbulent incompressible flows remain computationally expensive, particularly for three-dimensional configurations and long time horizons. This work introduces a hybrid reduced-order modeling (ROM) framework for turbulent flows on collocated finite-volume grids, combining projection-based model reduction with data-driven closure modeling. The approach follows a discretize-then-project strategy using the consistent flux method, ensuring mass conservation and robust pressure–velocity coupling without the need for additional stabilization techniques at the reduced level.

While velocity and pressure fields are resolved intrusively via POD–Galerkin projection, the turbulent viscosity field is reconstructed using a non-intrusive data-driven closure, addressing the known physical inconsistency of directly projecting turbulence quantities. Three neural architectures, MLP, Transformer, and LSTM, are evaluated for modeling the temporal evolution of turbulent viscosity coefficients.

The methodology is validated on a three-dimensional turbulent lid-driven cavity simulated with Large Eddy Simulation (LES). Results show that the LSTM-based closure provides the most accurate and stable reconstruction, achieving relative errors of approximately 0.7% for velocity and 4% for turbulent viscosity, while preserving key flow dynamics. The proposed framework effectively bridges physics-based reduced modeling and data-driven learning, offering a reliable and efficient surrogate for complex turbulent flows.