CGV: Small: Mesh-based Simulation of Thin Liquid Structures

在这项研究中，PI将开发高效的基于网格的算法来模拟薄液结构的动力学和相互作用，如薄片、射流、气泡和薄膜。这些液体现象的薄几何形状给传统技术带来了巨大的困难，导致运行时间长和内存消耗过大。PI认为，需要一种根本不同的方法来识别和利用稀薄液体的独特几何形状，以便有效和准确地模拟它们(通过类比于特殊处理薄弹性体，如杆、板、壳)。该项目由三个推进部分组成。首先，PI将开发由高粘度螺纹和薄板组成的液体的动态模拟算法，包括物理建模、碰撞处理、拓扑变化和混合维度重新划分网格。其次，他将解决低粘度射流和薄片的具体挑战，特别是考虑到表面张力、薄片破碎的增强影响，以及欧拉和拉格朗日演化的选择。最后，他将研究薄膜、气泡和泡沫的变形，使用一种新的基于网格的表示法来变形多区域界面，并结合周围空气的流体动力学。在每一次推力中，所开发的技术的预测能力都将与实验观察和文献中的理论结果进行验证。为此，PI将从薄弹性力学中引入几种几何和计算技术来研究薄流体的动力学。PI认为，这种思想的交叉授粉有可能在效率和精度方面提供戏剧性的改进，同时产生补充稀薄流体现象研究理论和实验的计算工具。通过将薄材料视为具有相关厚度的低维对象(曲线或曲面)，可以降低问题的维度，从而产生更好的数值特性和更好的自由度分配。这一观点以前从未被应用于开发三维稀薄液体的计算技术。使用非流形网格来表示稀薄液体的混合体，也开启了混合维度网格划分和拓扑转换处理方面的未知挑战。此外，提出的曲面跟踪表示建立在最初应用于布料动画的稳健碰撞处理技术的基础上，并将为多材质界面的演化提供第一个基于曲面网格的技术。与最先进的隐式曲面方法相比，这将允许更准确地跟踪气泡和一般的多相流。流畅的动画在视觉效果驱动的电影中越来越普遍，但薄薄的飞溅仍然是最难制作动画的效果之一。粘性液体的细丝和薄片出现在从食品加工到化妆品的应用中，从地壳的地球物理到精密玻璃艺术品的形成和吹制。它们是大量同时进行的实验和理论研究的主题，针对这些问题的补充计算工具可以提供至关重要的新见解。低粘度液体和泡沫的潜在应用同样广泛。项目成果将在包括SIGGRAPH会议在内的主要国际会议上报告，相关的计算工具将公之于众。还计划开展各种教育和宣传活动，其中一些活动专门针对少数族裔中学生。

In this research the PI will develop efficient mesh-based algorithms to simulate the dynamics and interactions of thin liquid structures such as sheets, jets, bubbles, and films. The thin geometry of these liquid phenomena poses tremendous difficulties for traditional techniques, leading to long runtimes and excessive memory consumption. The PI argues that a fundamentally different approach that recognizes and exploits the unique geometry of thin liquids is needed in order to simulate them efficiently and accurately (by analogy with the special treatment of thin elastic bodies such as rods, plates, shells). The project is comprised of three thrusts. First, the PI will develop algorithms for the dynamic simulation of liquid bodies composed of high viscosity threads and sheets, including physical modeling, collision processing, topology changes, and mixed dimensional remeshing. Second, he will address the specific challenges of low viscosity jets and sheets, considering in particular the enhanced influence of surface tension, sheet breakup, and the choice of Eulerian vs. Lagrangian evolution. Finally, he will examine the deformations of films, bubbles, and foams, using a new mesh-based representation for deforming multi-region interfaces, coupled to the fluid dynamics of the surrounding air. In each thrust, the predictive power of the techniques developed will be validated against both experimental observations and theoretical results from the literature.To these ends, the PI will bring several geometric and computational techniques from the dynamics of thin elastica to bear on the dynamics of thin fluids. The PI believes this cross-pollination of ideas has the potential to provide dramatic improvements in efficiency and accuracy, while yielding computational tools that complement theory and experiment in the study of thin fluid phenomena. By considering a thin material as a lower dimensional object (curve or surface) with an associated thickness, the dimension of the problem can be reduced, yielding improved numerical properties and better allocation of degrees of freedom. This perspective has never before been applied to develop computational techniques for three-dimensional thin liquids. The use of non-manifold meshes to represent mixed bodies of thin liquids also opens up previously unexplored challenges in mixed dimensional remeshing and the handling of topological transitions. Furthermore, the proposed surface tracking representation builds on robust collision-processing techniques originally applied to cloth animation, and will offer the first surface mesh-based technique for the evolution of multi-material interfaces. This will allow for more accurate tracking of bubbles and general multiphase flows than can be achieved with state-of-the-art implicit surface approaches.Broader Impacts: Thin liquids are crucial to a broad class of problems in computer graphics, engineering, and scientific applications. Liquid animations are increasingly prevalent in visual effects-driven films, yet thin splashes remain among the most difficult effects to animate. Thin threads and sheets of viscous liquids arise in applications from food processing to cosmetics, from the geophysics of the earth's crust to the forming and blowing of elaborate glass artwork. They are the subject of substantial concurrent experimental and theoretical investigation, and complementary computational tools for these problems could offer vital new insights. The potential applications for low viscosity liquids and foams are equally wide-ranging. Project outcomes will be reported at major international venues including the SIGGRAPH conferences, and the associated computational tools will be made publicly available. A variety of education and outreach efforts, some of which specifically target minority middle school students, are also planned.