Analytical {Geometry} for fluid simulations based on {Partial} {Optimal} {Transport}

@inproceedings{Plateau-Holleville2025RM,
 abstract = {We propose an analytical construction of the geometry required for free-surface fluid simulations and deformation mechanics based on Partial Optimal Transport such as the Gallouët-Mérigot's scheme or the Power Pinproceedingss method. Such methods previously relied on a discretization of the cells by leveraging a classical convex cell clipping algorithm. However, this results in a heavy computational cost and a coarse approximation of the evaluated quantities. In contrast, our algorithm efficiently computes the intersection between Voronoï cells and their bounding shells shaped as spheres. This allows a more precise computation of the volume and the area of the facets as well as strongly reducing the number of operations required to obtain the geometry. Finally, we show that our method supports the efficiency and robustness of the fluid simulations. We conclude with possible applications besides fluid dynamics, in deformation mechanics and shape optimization.},
 author = {Plateau-Holleville, Cyprien and Lévy, Bruno},
 booktitle = {2025 {RING} meeting},
 language = {en},
 pages = {316--329},
 publisher = {ASGA},
 title = {Analytical {Geometry} for fluid simulations based on {Partial} {Optimal} {Transport}},
 year = {2025}
}