Physics-Informed Adversarial Network for prediction of turbulent flow over rough surfaces

Surface roughness usually develops on degraded flow-related equipment, leading to various roughness characteristics that significantly alter surface drag. Predicting roughness-induced drag has been the focus of extensive research for decades. In this study, a Physics-Informed Adversarial Network (PIAN) is proposed to predict Reynolds-averaged 2D turbulent flow over irregular rough surfaces at $Re_\tau = 800$. PIAN is trained to deliver predictions that comply with Reynolds-Averaged Navier-Stokes (RANS) equations combined with a critic convolutional neural network (CNN). The critic CNN is trained based on direct numerical simulation (DNS) data. Stability and convergence of the training process are ensured using the Wasserstein distance. Additionally, a Fourier feature extraction technique is implemented to capture multi-scale roughness and turbulence interactions. The PIAN model achieves an average prediction error below $10\%$ for local Reynolds stresses and velocities, with roughness function deviations under $4\%$ compared to DNS data, demonstrating its effectiveness in integrating physics-based constraints with machine learning for roughness-induced flow predictions.