High-gradient-aware wavelet-aligned U-Net for airfoil Reynolds-averaged Navier–Stokes flow-field prediction
Abstract
Near-field flow prediction around airfoils is essential for aerodynamic analysis and design, yet Reynolds-averaged Navier–Stokes simulations remain computationally expensive. Although data-driven surrogate models can substantially accelerate flow-field evaluation, accurately reconstructing localized high-gradient structures around the airfoil surface, leading and trailing edges, and wake remains challenging. This study proposes the wavelet-aligned U-Net with coefficient-domain cross-attention (WAX-UNet) for predicting airfoil velocity, pressure, and density fields. WAX-UNet combines a U-Net backbone with selective wavelet-domain refinement. The wavelet-bottleneck cross-attention refinement module couples low-resolution global context with wavelet detail coefficients through linear cross-attention, while the hierarchical cross-attention refinement module introduces high-frequency encoder sub-bands into decoder-side feature fusion through sub-band-specific modulation. A dynamically weighted high-gradient-region-of-interest (HG-ROI)-aware root mean square error objective further emphasizes physically sensitive regions during training. Experiments on the University of Illinois Urbana–Champaign airfoil dataset show that WAX-UNet achieves the lowest component-wise relative L2 errors and overall root mean square error among representative convolutional, neural-operator, and transformer-based baselines. It also achieves the lowest HG-ROI errors for streamwise velocity and pressure and the lowest errors in the near-wall, trailing-edge, and wake regions. Physical-consistency diagnostics indicate lower continuity-residual and wall-normal-velocity errors, while WAX-UNet achieves the lowest errors for all four variables on the geometry-extreme out-of-distribution test set. Ablation studies confirm the complementary contributions of the proposed modules and training objective. Averaged over three independent runs on the geometry-balanced test set, WAX-UNet achieves relative L2 errors of 0.499%, 2.089%, 0.109%, and 0.008% for u, v, p, and ρ, respectively, with moderate computational cost.