A physics-informed diffusion model for super-resolution reconstruction of airfoil flow field data

High-fidelity flow field data are essential for accurate evaluation of the aerodynamic performance of airfoils, as they directly affect the prediction accuracy of lift, drag, and flow separation characteristics. However, traditional methods are either computationally expensive, e.g., computational fluid dynamics (CFD) solvers, or struggle to achieve sufficient reconstruction fidelity and physical consistency, e.g., data-driven super-resolution approaches. In this paper, we propose a novel super-resolution reconstruction method based on the denoising diffusion probabilistic model (DDPM). It incorporates deformable convolutional layers and attention modules into the U-Net denoising network to enhance the extraction of airfoil features. Meanwhile, residual networks are also integrated to improve data reconstruction performance. To embed physical information, we introduce pointwise physics-informed loss functions based on the continuity and momentum residuals to enforce physical consistency. We select various airfoils from the public University of Illinois at Urbana-Champaign (UIUC) airfoil database, generate computational grids using Gmsh, and obtain high-fidelity flow field data through OpenFOAM simulations for model training and validation. Experimental results demonstrate that our proposed method can accurately predict characteristics of the flow field data around the airfoils, with computation time being only 23% of that required by traditional computational fluid dynamics software. Moreover, our method outperforms other deep learning models in terms of generation accuracy and generalization ability. This indicates that the proposed method offers significant advantages in computational efficiency and generation accuracy, providing a new solution for airfoil flow field data reconstruction.