We propose unified data structures and algorithms for free-surface fluid simulations based on partial optimal transport, such as the Power Particles method or Gallouët-Mérigot's scheme. 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, we propose to analytically construct the generalized Laguerre cells characterized by intersections between Laguerre cells and spheres. This makes it possible to accurately compute the differential quantities used by the Newton algorithm, that is, the areas of the (curved) facets and the volumes of the (generalized) Laguerre cells. This significantly improves the convergence of the Newton algorithm, hence the robustness of the simulations, even in challenging scenarios with high velocities and chocs. Moreover, this drastically reduces the computational cost as compared to previous works. Based on our data structure, we propose a framework that combines (1) the numerical solution mechanism for partial optimal transport, (2) the fluid simulation scheme and (3) the rendering. The aforementioned three components are implemented on the GPU, providing further speedup and avoiding data transfers. This is made possible by the compactness of our data structure combined with a massively parallel implementation. We report the result of numerical experiments featuring highly detailed, large-scale simulations and high variations of physical properties within the same simulation.

翻译：我们提出了基于部分最优输运（如Power Particles方法或Gallouët-Mérigot方案）的自由表面流体模拟的统一数据结构与算法。此类方法以往依赖经典凸胞元裁剪算法对单元进行离散化，但这导致高昂的计算成本及对计算量的粗略近似。与之相对，我们提出通过解析方法构建以Laguerre胞元与球体相交为特征的广义Laguerre胞元。这使得能够精确计算牛顿算法所需的微分量，即（曲边）面的面积与（广义）Laguerre胞元的体积。这显著改善了牛顿算法的收敛性，从而提升了模拟的鲁棒性，即便在具有高速度与冲击的挑战性场景中亦然。此外，与先前工作相比，该方法大幅降低了计算成本。基于我们的数据结构，我们提出了一个整合（1）部分最优输运数值求解机制、（2）流体模拟方案及（3）渲染的框架。上述三个组件均在GPU上实现，进一步提升了速度并避免了数据传输。这得益于我们数据结构的紧凑性与大规模并行实现的结合。我们报告了数值实验的结果，展示了高细节度的大规模模拟以及同一模拟中物理属性的剧烈变化。