Mimetic Immersed Boundary Methods for Fluid-Structure Interaction

Fluid-structure interaction occurs when moving fluids act on structures and the resulting structural motion or deformation changes the fluid flow. It plays a central role when blood flows through heart valves, organisms swim or fly, bio-inspired vehicles move through water or air, energy devices convert flow into power, aircraft and turbine components respond to aerodynamic loads, and medical devices interact with the body. Immersed boundary methods are mathematical and computational tools for simulating systems in which fluids and structures influence each other. These simulations can support scientific discovery, engineering design, and medical innovation, but current methods can sometimes fail to preserve volume, produce unrealistic fluid motion near pressurized surfaces, or give inaccurate estimates of local forces. This project will create more reliable simulation methods for fluid-structure interaction. By improving general-purpose tools that can impact cardiovascular modeling, medical device design, energy technology, aircraft and turbine analysis, and other engineered systems, the work will help advance national health, economic competitiveness, public welfare, and national defense. The project will also strengthen open-source software used by scientists and engineers, train students in computational mathematics and scientific computing, and support areas of Federal strategic interest, including biotechnology, advanced manufacturing, medical device design, energy technology, and artificial intelligence workflows that depend on high-quality simulation data for training, testing, and validation. This project will develop new mimetic immersed boundary (IB) methods for fluid-structure interaction. These methods use anisotropic regularized delta functions based on composite B-splines to preserve mathematical structures that are lost by conventional IB coupling methods based on isotropic regularized delta functions. The work has three connected goals. First, grid-adapted quadrature rules will be developed to align discrete integration with the polynomial structure of the composite B-spline coupling kernels, improving the accuracy of force spreading and velocity interpolation in both two- and three-dimensional settings. Second, stabilization strategies based on surface regularization and normal and tangential force decompositions will be developed and analyzed, with the goal of obtaining accurate, nonoscillatory pointwise interfacial forces. The effects of these stabilization strategies on energy conservation, volume conservation, and the suppression of spurious currents will also be quantified. Third, these tools will be integrated into an interfacial coupling strategy for volumetric fluid-structure interaction. The resulting methods will be implemented in the open-source IBAMR software library and assessed on a wide range of thin-interface and volumetric benchmark cases. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria. NSF Award ID: 2608488 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Boyce Griffith | Institution: University of North Carolina at Chapel Hill, CHAPEL HILL, NC | Award Amount: $350,000 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2608488 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2608488.html