HCC: Small: Simulating and Animating Materials with Dynamic Geometry

抽象?O ?这个研究项目的重点是数值和几何方法的物理逼真模拟的物体和材料的形状是严重变形或变化。这些方法使用了几种动态网格生成技术，其中非结构化四面体体积网格和三角形表面网格随着时间的推移而演变或改变，以适应高度可变形材料的运动。这项研究将带来前所未有的模拟能力，以发展用于数值技术（如有限元方法和有限体积方法）的网格，同时保持高质量的四面体和三角形。这些新算法将使以前由于难以模拟形状急剧变化的材料而无法很好地模拟的现象成为可能，例如手术中的身体组织或高速撞击的弹道学。本研究的技术贡献可分为两类。第一个贡献是使用动态网格生成的数值方法，为弹塑性固体和粘性流体在塑性流动、切削和断裂过程中的模拟提供了更好的精度。模拟和动态网格是耦合的，因此它们在局部保存质量、能量和动量，随着网格的发展，网格的细化和各向异性是针对物理问题量身定制的。第二个贡献是研究人员开发的动态几何算法的扩展，该算法可以更准确地模拟表面演化，实现比体积分辨率更精细的表面分辨率，并且易于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.