Acceleration of three-dimensional free-surface flow simulations using super-resolution convolutional neural network

We propose a super-resolution framework for accelerating three-dimensional free-surface flow simulations, termed the free-surface flow super-resolution convolutional neural network (FSFlow-SRCNN), by integrating a 3D U-Net-based CNN with an advanced free-surface flow solver. The free-surface flow solver is based on the coupled level-set and volume-of-fluid (CLSVOF) method and the full-variable Cartesian grid (FVCG) method. Numerical experiments show substantial acceleration while maintaining close agreement with high-resolution reference solutions and satisfying mass conservation to a comparatively high standard; a speed-up factor of approximately 139 is achieved in one computational environment. FSFlow-SRCNN also demonstrates generalization to nearby unseen conditions, remaining stable and maintaining robust super-resolution performance. Among the three tested loss functions, Loss3 combining an L1 term with divergence and gradient terms provides the best overall balance: the divergence term improves mass conservation, whereas the gradient term enhances the reconstruction of the density field across gas–liquid density discontinuities. Finally, training on mixed one- and two-droplet datasets yields reliable performance in both cases, indicating the potential of FSFlow-SRCNN as a versatile model for a range of free-surface flows.