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

在这项研究中，PI将开发有效的基于网格的算法来模拟薄液体结构，如片材，射流，气泡和薄膜的动力学和相互作用。 这些液体现象的薄的几何形状对传统技术造成了巨大的困难，导致长的运行时间和过多的内存消耗。 PI认为，需要一种根本不同的方法来识别和利用薄液体的独特几何形状，以便有效和准确地模拟它们（通过类比薄弹性体的特殊处理，如杆，板，壳）。 该项目包括三个重点。 首先，PI将开发用于高粘度线和片组成的液体体的动态模拟的算法，包括物理建模、碰撞处理、拓扑变化和混合维网格重新划分。 其次，他将解决低粘度射流和片材的具体挑战，特别是考虑表面张力，片材破碎的增强影响，以及欧拉与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方法来变形多区域界面，再加上周围空气的流体动力学。 在每一个推力，预测能力的技术开发将验证对实验观察和理论结果从literary.To这些目的，PI将带来几个几何和计算技术，从薄弹性体的动力学承担薄流体的动力学。 PI认为，这种思想的交叉授粉有可能在效率和准确性方面提供显着的改进，同时产生计算工具，补充薄流体现象研究中的理论和实验。 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，从而改善数值特性并更好地分配自由度。 这种观点以前从未被应用于开发三维薄液体的计算技术。 使用非流形网格来表示稀薄液体的混合体，也开辟了以前未探索的挑战，在混合维重新划分网格和处理拓扑转换。 此外，所提出的表面跟踪表示建立在鲁棒的碰撞处理技术最初应用于布料动画，并将提供第一个表面网格为基础的多材料界面的演变技术。 这将允许更准确地跟踪气泡和一般的多相流比可以实现与国家的最先进的隐式表面approaches.Broader影响：薄液体是至关重要的，在计算机图形学，工程和科学应用中的广泛的一类问题。 液体动画在视觉效果驱动的电影中越来越普遍，但薄飞溅仍然是最难制作的效果之一。 从食品加工到化妆品，从地壳的地球物理学到精致玻璃艺术品的成型和吹制，粘性液体的细线和薄片都有应用。 它们是大量并行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，相关的计算工具将向公众提供。 还计划开展各种教育和外联活动，其中一些活动专门针对少数民族中学生。

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.