Computational Methods for Simulating Flows and Structures with Complex Dynamic Geometry

复杂动态几何结构的流动和结构仿真计算方法

• 批准号: RGPIN-2021-02524
• 负责人: Batty, Christopher
• 金额: $ 3.5万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=750179
• 关键词: Computational; Methods; Simulating; Flows; Structures

The intricate splashing of water and the kneading of bread dough are familiar examples of severe deformations undergone by liquids and solids. The ubiquity of such processes, involving rapid, dramatic, and frequent changes in a material's shape, has led to tremendous demand for computer simulation techniques that can seamlessly reproduce them. Such algorithms will be necessary for the creation of truly immersive, physically realistic virtual environments, a longstanding grand challenge of computer graphics research. To be practically useful, these algorithms must be at once robust to difficult inputs, physically accurate, and computationally efficient. Computational meshes, sometimes called wireframe models, are concise representations of digital objects and materials that have been prevalent in computer graphics for decades. Despite their many well-studied benefits, limitations of existing algorithms have prevented their widespread use in animating materials undergoing radical shape changes (i.e., changing geometry and especially topology). For example, mesh-based approaches have often failed to completely handle key sources of error, such as numerical imprecision, tangled intersections, poor quality meshes, and complex mesh edits; this dearth of strong mathematical guarantees leads inevitably to fragile algorithms that can crash unpredictably. Fortunately, recent advances have brought practical mesh-based animation of severe, geometrically complex deformations closer to being realized. The three themes of this research capitalize on this opportunity by: (I) developing improved methods for dynamically evolving triangulated surfaces; (II) investigating fluid and solid simulation techniques that exploit new tools for generating arbitrary polyhedral cut-cell meshes, and (III) deriving novel mesh-based techniques to animate materials composed of complex branching structures or mixed-dimensional components (solids, surfaces, curves), known as non-manifold geometry. Through this research a diverse student team will receive interdisciplinary training spanning fluid and solid mechanics, computational mathematics, and computer graphics. This unique skill set is highly valuable both in digital media (i.e., virtual and augmented reality, visual effects, game development, advertising, etc.) and many areas of engineering and applied mathematics. The proposed agenda will yield open-source software tools to simulate important fluid and solid phenomena with greater accuracy, robustness, and efficiency than is currently available, immediately providing faster and more realistic animation capabilities to the digital media sector in Canada and globally. Furthermore, because of the fundamental nature of the geometric and physical techniques to be developed, it will also provide a firm foundation for future computational investigations in the countless disciplines where highly deforming materials arise, from biophysics to 3D printing to geophysics and more.

复杂的水花飞溅和揉面团是液体和固体剧烈变形的常见例子。这种过程无处不在，涉及材料形状的快速、剧烈和频繁的变化，导致了对能够无缝地再现它们的计算机模拟技术的巨大需求。这样的算法对于创造真正身临其境的、物理逼真的虚拟环境是必要的，这是计算机图形学研究的一个长期的重大挑战。为了在实践中发挥作用，这些算法必须对困难的输入具有鲁棒性，物理上准确，并且计算效率高。计算网格，有时被称为线框模型，是几十年来在计算机图形学中流行的数字对象和材料的简明表示。尽管它们有许多经过充分研究的优点，但现有算法的局限性阻碍了它们在动画材料中广泛使用，这些材料经历了激进的形状变化（即改变几何形状，特别是拓扑结构）。例如，基于网格的方法往往不能完全处理关键的误差来源，如数值不精确、纠结的交叉点、质量差的网格和复杂的网格编辑；缺乏强大的数学保证不可避免地导致脆弱的算法不可预测地崩溃。幸运的是，最近的进展已经带来了实用的基于网格的动画严重，几何复杂的变形更接近实现。本研究的三个主题利用这一机会：(1)开发改进的动态演化三角曲面的方法；（II）研究流体和固体模拟技术，利用新工具生成任意多面体切割单元网格；（III）推导出新的基于网格的技术，对由复杂分支结构或混合维度组件（固体、表面、曲线）组成的材料进行动画处理，称为非流形几何。通过这项研究，一个多元化的学生团队将接受跨学科的训练，包括流体和固体力学、计算数学和计算机图形学。这种独特的技能在数字媒体（即虚拟和增强现实，视觉效果，游戏开发，广告等）以及工程和应用数学的许多领域都非常有价值。拟议的议程将产生开源软件工具，以比目前更高的准确性、稳健性和效率模拟重要的流体和固体现象，立即为加拿大和全球的数字媒体部门提供更快、更真实的动画能力。此外，由于要开发的几何和物理技术的基本性质，它还将为未来在高度变形材料出现的无数学科（从生物物理学到3D打印到地球物理学等）的计算研究提供坚实的基础。