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

Peskin9980069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之一。无论是来自聚合物流变学、微飞行还是心脏流体动力学，这些问题都涉及许多长度和时间尺度上的结构、流体和可变形边界之间的强耦合以及复杂的几何形状。这位研究人员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调查，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的数值技术，并改进了现有的方法(浸没边界和自适应网格)，以实现交互式模拟实验和可控计算。该实验计划侧重于可用于验证和补充数值模拟结果的方法，以及用于研究具有动态边界的定常流动的新技术。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结构，指导计算过程，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心脏瓣膜和昆虫翅膀等动态边界相互作用时，所产生的流体动力学很难表示和常规分析。边界和流体的紧密耦合、不同的长度和时间尺度以及复杂的湍流运动使得这些问题成为一个巨大的理论和计算挑战。对这类问题认识的突破将使医学、生物、航空和化学工程等领域取得重大进展。实现这样的突破是纽约大学库兰特数学科学研究所(CIMS)和华盛顿大学(UW)的研究人员合作的目标，他们拥有数学和计算、实验实验室调查和科学可视化方面的综合专业知识。心脏瓣膜功能和昆虫飞行不能用基于恒定流动的经典论点来解释。数百万年的进化已经产生了形状、反馈机制和边界属性，以响应边界-流体相互作用的复杂性。更好地了解边界和流动之间的这些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，这些设备旨在与边界主导的流体流动复杂但可重复的行为进行交互。该项目的一个关键目标是在便于人类研究人员参与的虚拟环境中整合实验和计算。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结构；对于给定的模拟系统，控制计算过程本身；使用实验数据指导计算；处理实验数据并与实验数据交互，同时将其可视化为三维和随时间变化。虽然重点放在部分飞行和心脏功能的核心研究上，但从这些核心例子推断应该能够在流体(包括气体)与复杂和可能的动态几何结构相互作用的地方取得突破。这个KDI项目得到了数学科学部、综合生物学和神经科学部以及化学和运输系统部的支持。

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.