KDI: Unsteady Flows with Dynamic Boundaries: Experiment and Computation Interacting in the Virtual Environment

佩斯金9980069 由动态边界驱动的非定常流体流动是最难模拟和可视化的流动。 无论是从聚合物流变学，微飞行，或心脏流体动力学，这些问题涉及许多长度和时间尺度上的结构，流体和变形边界之间的强耦合，以及复杂的几何形状。 这位研究者和他的同事们将昆虫飞行和心脏功能问题作为多学科合作的焦点，寻求一种理解边界流体动力学的新范式。这种新范式包括数值模拟和实验研究，并通过新兴的虚拟现实技术结合在一起。 在数值方面，他们开发了新的自适应和分层数值技术，并改进了现有的方法（浸入边界和自适应网格），以实现交互式模拟实验和可操纵的计算。 该实验计划的重点是方法，可用于验证和补充的结果ofnumerical模拟，并在新的技术研究ofunsteady流动与动态边界。 计算和实验方法集成在一个虚拟环境中，使研究人员能够交互地修改模拟系统的参数和几何形状，引导计算过程，灵活地可视化实验数据，并使用实验数据来指导计算。 当非定常三维流动与动态边界（如心脏瓣膜和昆虫翅膀）相互作用时，产生的流体动力学不容易表示和常规分析。 边界和流体之间的紧密耦合，不同的和相互作用的长度和时间尺度，以及湍流运动的复杂性，使这些问题成为一个可怕的理论和计算挑战。 对这类问题的突破性理解将使医学、生物学、航空学和化学工程等领域取得重要进展。 实现这样的突破是来自纽约大学柯朗数学科学研究所（CIMS）和华盛顿大学（UW）的研究人员合作的目标，他们结合了数学和计算、实验室调查和科学可视化方面的专业知识。 心脏瓣膜功能和昆虫飞行不能用基于稳定流动的经典论点来解释。 数百万年的演化已经产生了形状，反馈机制和边界特性，以应对边界-流体相互作用的复杂性。 更好地理解边界和流动之间的相互作用将为新一代人工心脏瓣膜、小型高效飞行器和其他精心设计的设备打开大门，这些设备可以与边界主导的流体流动的复杂但可重复的行为相互作用。 该项目的一个关键目标是在虚拟环境中整合实验和计算，以促进人类调查员的参与。 该项目致力于改变这一领域的研究范式。 研究人员应该能够在模拟运行时修改模拟系统的参数和几何形状;对于给定的模拟系统，操纵计算过程本身;使用实验数据来指导计算;处理实验数据并与之交互，同时在三维和时间上可视化它。 虽然重点是对昆虫飞行和心脏功能的核心研究，但从这些核心例子中推断，无论流体（包括气体）与复杂的和可能的动态几何结构相互作用，都应该能够取得突破。 该KDI项目由数学科学部、综合生物学和神经科学部以及化学和运输系统部支持。

Peskin9980069 Unsteady fluid flows driven by dynamic boundaries are amongthe most difficult flows to simulate and visualize. Whetherdrawn from polymer rheology, microflight, or cardiac fluiddynamics, these problems involve structures on many length andtime scales, strong coupling between the fluid and a deformableboundary, and complex geometry. The investigator and hiscolleagues, taking the problems of insect flight and heartfunction as focal points for a multidisciplinary collaboration,seek a new paradigm for understanding boundary-fluid dynamics.This new paradigm involves both numerical simulation andexperimental investigation, brought together through the emergingtechnology of virtual reality. On the numerical side, theydevelop new adaptive and hierarchical numerical techniques, aswell as improve existing methods (immersed boundary and adaptivegrid), to enable interactive simulation experiments and steerablecomputation. The experimental program focuses both on methodsthat can be used to validate and complement the results ofnumerical simulations, and on novel techniques for the study ofunsteady flows with dynamic boundaries. Computational andexperimental approaches are integrated within a virtualenvironment that enables a researcher to modify interactively theparameters and geometry of the simulated system, steercomputational processes, flexibly visualize experimental data,and use experimental data to guide computation. When unsteady three-dimensional flows interact with dynamicboundaries such as heart valves and insect wings, the resultingfluid dynamics defy easy representation and conventionalanalysis. The tight coupling between boundary and fluid, thediffering and interacting length and time scales, and thecomplexity of turbulent motions make these problems a formidabletheoretical and computational challenge. Breakthroughs inunderstanding this class of problems will enable importantadvances in fields such as medicine, biology, aeronautics, andchemical engineering. Achieving such breakthroughs is the goal ofa collaboration between researchers from NYU's Courant Instituteof Mathematical Sciences (CIMS) and the University of Washington(UW), with combined expertise in mathematics and computation,experimental laboratory investigation, and scientificvisualization. Heart valve function and insect flight cannot beexplained by classical arguments based on steady flow. Millionsof years of evolution have produced shapes, feedback mechanisms,and boundary properties in response to the complexity of theboundary-fluid interaction. A greater understanding of theseinteractions between boundary and flow will open the door to newgenerations of artificial heart valves, small and highlyefficient flying machines, and other devices carefully designedto interact with the complex but repeatable behaviors of boundarydominated fluid flows. A key goal of this project is theintegration of experiment and computation in a virtualenvironment that facilitates the involvement of the humaninvestigator. The project strives to change the paradigm ofresearch in this area. A researcher should be able to modify theparameters and geometry of a simulated system while thesimulation is running; to steer, for a given simulated system,the computational process itself; to use experimental data toguide the computation; and to process and interact with theexperimental data, while visualizing it in three dimensions aswell as over time. While the focus is on the core studies ofinsect flight and heart function, extrapolation from these coreexamples should enable breakthroughs wherever fluids (includinggases) interact with structures of complicated and possiblydynamic geometry. This KDI project is supported by the Divisionof Mathematical Sciences, the Division of Integrative Biology andNeuroscience, and the Division of Chemical and Transport Systems.