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

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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.