EDGE: Epsilon-Difference Gradient Evolution for Buffer-Free Flow Maps

Zhiqi Li*1, Ruicheng Wang*1, Junlin Li*1, Duowen Chen1, Sinan Wang1, Bo Zhu1(* Co-first Authors)
1Georgia Institute of Technology
ACM Transactions on Graphics (SIGGRAPH 2025)
Paper arXiv
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Dye drift simulation using flow map methods. Our novel strategy for flow map evolution, Epsilon-Difference Gradient Evolution (EDGE) (blue dye) and Four-Point Epsilon Difference (ED4) (purple dye), achieves vorticity conservation on par with the original Eulerian Flow Map (EFM) method (red dye), but with significantly reduced memory usage. While EFM requires 37.89 GB of overall simulation memory, EDGE cuts this down to 10.79 GB, and ED4 further reduces it to 8.54 GB—a performance leap without compromising accuracy.

Abstract

We propose the Epsilon Difference Gradient Evolution (EDGE) method for accurate flow-map calculation on grids via Hermite interpolation without using velocity buffers. Our key idea is to integrate Gradient Evolution for accurate first-order derivatives and a tetrahedron-based Epsilon Difference scheme to compute higher-order derivatives with reduced memory consumption. EDGE achieves O(1) memory usage, independent of flow map length, while maintaining vorticity preservation comparable to buffer-based methods. We validate our methods across diverse vortical flow scenarios, demonstrating up to 90% backward map memory reduction and significant computational efficiency, broadening the applicability of flow-map methods to large-scale and complex fluid simulations.

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BibTeX

@inproceedings{li2025edge,
        title = {EDGE: Epsilon-Difference Gradient Evolution for Buffer-Free Flow Maps},
        author = {Li, Zhiqi and Wang, Ruicheng and Li, Junlin and Chen, Duowen and Wang, Sinan and Zhu, Bo},
        journal={ACM Transactions on Graphics (TOG)},
        volume={44},
        number={4},
        pages={1--11},
        year={2025},
        publisher={ACM New York, NY, USA}
      }