Document Type : Original Article
Authors
1 University of Bonab
2 University of Tabriz
Abstract
Direct Numerical Simulation (DNS) of turbulent flows is computationally prohibitive for most practical engineering applications. Instead, reduced-order models such as Reynolds-Averaged Navier–Stokes (RANS) equations are widely used, but they suffer from inherent structural errors, particularly in flows with separation and adverse pressure gradients. Quantifying the uncertainty of these models is essential for assessing the reliability of their predictions. This study presents a physics-informed deep learning framework for the direct quantification of structural model-form uncertainty in RANS simulations. The proposed approach employs a deep neural network (specifically, a Physics-Informed Neural Network—PINN) trained on high-fidelity wavy-wall flow data to learn the discrepancy between the RANS-predicted and reference Reynolds stress tensors in the form of perturbations to the eigenvalues and eigenvectors of the turbulence anisotropy tensor. Unlike common methods that focus on parametric uncertainty, this technique corrects the intrinsic model form error while preserving the physical realizability constraints of the Reynolds stress. The trained model is then rigorously validated on two geometrically and physically distinct, unseen flow configurations: an asymmetric planar diffuser and a periodic hill. Results demonstrate that the neural-network-based model significantly improves the accuracy of baseline RANS predictions. This improvement is evident in velocity profiles, turbulent kinetic energy, shear stress, and, most notably, in the prediction of flow separation and lift and drag coefficients. This work establishes that learning perturbations in eigenspace provides an effective, generalizable, and physics-constrained approach for assessing and reducing model uncertainty in engineering turbulence simulations.
Keywords
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