Data-Driven Reconstruction of Vorticity Fields in Lid-Driven Cavity Flow Using a U-Net Convolutional Neural Network Based on the Streamfunction–Vorticity Formulation

This work provides a deep learning approach to predicting the non-dimensional vorticity field for two-dimensional lid-driven cavity flow from a U-Net convolutional neural network. The simulation data were generated according to the streamfunction–vorticity formulation of the incompressible Navier–Stokes equations and varied over Reynolds numbers (Re = ۱۰۰ to ۱۰۰۰) and spatial resolutions (۶۴ × ۶۴ and ۱۲۸ × ۱۲۸). Normalized velocity components (u*, v*) and the divergence field were utilized as input features, whereas the vorticity field (ω*) was the prediction target. The results show that the suggested U-Net model reconstructs the principal as well as secondary vortical structures of laminar flow regimes accurately, with an average root mean square error (RMSE) below ۶% on the Re = ۱۰۰ coarse grid. As the Reynolds number and spatial resolution are increased, the model reveals increased prediction error predominantly by the growth of small-scale flow structures and powerful shear layers that strain the networks receptive field. Even so, the U-Net predictions maintain qualitative agreement with the reference numerical data, capturing the global flow dynamics adeptly. The work presents the promise of convolutional neural networks as effective surrogates for the flow field reconstruction and points out the possibility that future enhancements, like multiscale training or physics-informed loss functions, may be able to augment the prediction of fine-scale vortical dynamics even better in the case of the flow regimes around transition.

کلیدواژه ها:

U-Net ، Lid-driven cavity flow ، Data-driven modeling ، Vorticity prediction