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Graph."],"published-print":{"date-parts":[[2025,8,1]]},"abstract":"<jats:p>\n                    We propose the\n                    <jats:italic toggle=\"yes\">adaptive hybrid particle-grid flow map<\/jats:italic>\n                    method, a novel flow-map approach that leverages Lagrangian particles to simultaneously transport impulse and guide grid adaptation, introducing a fully adaptive flow map-based fluid simulation framework. The core idea of our method is to maintain flow-map trajectories separately on grid nodes and particles: the grid-based representation tracks long-range flow maps at a coarse spatial resolution, while the particle-based representation tracks both long and short-range flow maps, enhanced by their gradients, at a fine resolution. This hybrid Eulerian-Lagrangian flow-map representation naturally enables adaptivity for both advection and projection steps. We implement this method in\n                    <jats:italic toggle=\"yes\">Cirrus<\/jats:italic>\n                    , a GPU-based fluid simulation framework designed for octree-like adaptive grids enhanced with particle trackers. The efficacy of our system is demonstrated through numerical tests and various simulation examples, achieving up to 512 \u00d7 512 \u00d7 2048 effective resolution on an RTX 4090 GPU. We achieve a 1.5 to 2\u00d7 speedup with our GPU optimization over the Particle Flow Map method on the same hardware, while the adaptive grid implementation offers efficiency gains of one to two orders of magnitude by reducing computational resource requirements. 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