HCC: Small: Simulating and Animating Materials with Dynamic Geometry

抽象？O？Brien(0915462)本研究项目致力于数值和几何方法，用于对形状发生巨大变形或变化的对象和材料进行物理真实感模拟。这些方法使用几种动态网格生成技术，其中非结构化四面体网格和三角形曲面网格随时间演变或改变，以适应高度变形材料的移动。这项研究带来了前所未有的模拟能力，可以在保持高质量四面体和三角形的同时，进化用于数值技术的网格，如有限元方法和有限体积方法。这些新的算法将使以前无法很好地模拟的现象得以模拟，因为模拟形状发生根本变化的材料是困难的，例如手术中的身体组织或经历高速撞击的弹道。这项研究的技术贡献分为两类。第一个贡献是数值方法，它使用动态网格生成来提高弹塑性固体和粘性流体在塑性流动、切割和断裂过程中的模拟精度。模拟和动力学网格器是耦合的，以便随着网格的发展，它们在本地守恒质量、能量和动量，从而使网格的精细化和各向异性适合于物理问题。第二个贡献是研究人员开发的动态几何算法的扩展，这些算法可以更准确地模拟曲面演化，实现比体积分辨率更精细的曲面分辨率，并且可以轻松处理拓扑变化和自碰撞。

Abstract ? O?Brien (0915462) This research project focuses on numerical and geometric methods for physically realistic simulation of objects and materials whose shapes are grossly deforming or changing. These methods use several techniques for dynamic mesh generation, wherein unstructured tetrahedral volume meshes and triangular surface meshes evolve or change through time to accommodate the movement of a highly deformable material. This research is leading to unprecedented simulation capabilities to evolve the meshes used for numerical techniques such as finite element methods and finite volume methods, while maintaining high-quality tetrahedra and triangles. These new algorithms will enable the simulation of phenomena that could not previously be modeled well because of the difficulty of simulating materials whose shapes change radically, such as body tissues during surgery or ballistics undergoing high-speed impacts. The technical contributions of this research fall into two classes. The first contribution is numerical methods that use dynamic mesh generation to bring better accuracy to simulations of elastoplastic solids and viscous fluids undergoing plastic flow, cutting, and fracture. The simulation and dynamic mesher are being coupled so that they locally conserve mass, energy, and momentum as a mesh evolves, and so that the refinement and anisotropy of the mesh are tailored to the physical problem. The second contribution is extensions of dynamic geometry algorithms developed by the researchers that more accurately model surface evolution, that enable a finer surface resolution than volume resolution, and that easily handle topological changes and self-collisions.