The goals of this project are to create analytical and computational tools, coupled with experiments, to investigate biological propulsion in fluids at intermediate scales. These problems typically involve the movement of a flexible appendage in a fluid where both inertia and viscosity are important. The fundamental computational challenge associated with these problems is the accurate and efficient simulation of the moving, flexible structure in the surrounding fluid. One aim is to extend numerical methods for Stokes flow to Reynolds numbers on the order of 1 to 10. These methods will then be applied to aerodynamics problems involving flow through bristled wings. Another aim is to incorporate viscous effects into vortex sheet methods, in order to more accurately simulate flows over a wider range of scales. These tools will then be used to understand the importance of active control of fish fin rays and other instances of fluid interactions with organisms. Finally, this work will allow for comparisons of propulsion mechanisms and numerical methods across a wide range of Reynolds numbers.

The numerical methods and models developed in this research project can be applied to numerous and diverse biological fluid-structure interactions problems. Some examples beyond those specific to the proposal include the pumping of blood by the heart, the flow of air in the lungs, drag reduction in flexible materials such as leaves and sessile organisms, and the dispersal of seeds in air and larvae in water. The broader impacts of this work include the improved understanding of propulsion mechanics that can be used for the design of micro air and water vehicles; the development of computational tools which are useful to study optimization questions in biology; rich examples of nonlinear dynamics for physics; research mentoring to undergraduates in experimental and modeling work and graduate students in computational and modeling research. The outreach component will help more students achieve autonomy in research and critical thinking through independent research projects. This project also addresses one of the seven questions posed by the National Academy of Sciences on the role of theory in advancing 21st century biology: ``what are the engineering principles of life?''

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Mary Ann Horn
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Regents of the University of Michigan - Ann Arbor
Ann Arbor
United States
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