Low-Resolution Vortex Simulation Enhanced by Data-Driven Fine-Scale Reconstruction

Vortex methods offer a natural framework for capturing coherent structures in turbulent flows, but resolving small-scale features at high Reynolds numbers typically requires fine discretization or subgrid-scale (SGS) modeling. While classical LES approaches (such as Variational Multiscale Smagorinsky and Spectral Vanishing Viscosity models) have been successfully integrated into remeshed vortex methods, we propose an alternative: a data-driven, low-resolution approach leveraging deep learning. Neural networks are trained to map coarse vorticity fields to high-resolution counterparts using DNS data, enabling the reconstruction of fine-scale features without explicit SGS models. Inspired by super-resolution strategies, we explore U-Nets and graph neural networks (GNNs), trained across varying initial and boundary conditions but fixed Reynolds number. The learned mapping captures the effects of vortex stretching and folding and acts as a surrogate for SGS closure by providing fine-scale corrections that are incorporated into the coarse solver. We present initial results toward hybrid vortex–ML methods for efficient simulation of unsteady turbulent flows.