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Immersed Methods for Fluid-Structure Interaction: The Immersed Boundary Method and Some Extensions
This talk will provide an introduction to immersed boundary (IB) methods for simulating fluid-structure interaction (FSI) along with several extensions of the IB method for a variety of different types of models. The fundamental IB approach to FSI describes the structural kinematics in Lagrangian form, and describes the momentum and incompressibility of the fluid-structure system in Eulerian form. Lagrangian and Eulerian variables are connected through integral equations with Dirac delta function kernels, and classical IB methods discretize these interaction operators by replacing the singular delta function with a regularized version of the delta function. I will discuss several extensions or generalizations of the IB approach, including: 1) (hyper-)elastic structural models that are simulated using conventional finite element methods; 2) flexible structures that can experience damage and rupture that are modeled using peridynamics; 3) FSI schemes based on the immersed interface method (IIM) that allow volumetric structures to be coupled to the fluid only along fluid-structure interfaces; 4) methods for treating interactions with polymeric (viscoelastic) fluids; 5) methods for treating multiphase fluid models; and 6) methods for treating interactions between fluid-phase chemical species and surface-bound species. All of the approaches are implemented in the IBAMR software (https://ibamr.github.io) and will be demonstrated using that software.
Research Areas: Computational Biophysics
Research Interests: Mathematical modeling and computer simulation in physiology, especially cardiovascular mechanics, fluid dynamics, and fluid-structure interaction and cardiac electrophysiology.
Place: Math, 402 and Zoom https://arizona.zoom.us/j/83758253931Password: applied