Prof. Boyce Griffith
Department of Mathematics and Biomedical Engineering
University of North Carolina at Chapel Hill

Immersed Methods for Fluid-Structure Interaction

ABSTRACT: The immersed boundary (IB) method is a framework for modeling systems in which an elastic structure interacts with a viscous incompressible fluid. The fundamental feature of the IB approach to such fluid-structure interaction (FSI) problems is its combination of an Eulerian formulation of the momentum equation and incompressibility constraint with a Lagrangian description of the structural deformations and resultant forces. In conventional IB methods, Eulerian and Lagrangian variables are linked through integral equations with Dirac delta function kernels, and these singular kernels are replaced by regularized delta functions when the equations are discretized for computer simulation. This talk will focus on three related extensions of the IB method. I first detail an IB approach to structural models that use the framework of large-deformation nonlinear elasticity. I will focus on efficient numerical methods that enable finite element structural models in large-scale simulations, with examples focusing on models of the heart and its valves. Next, I will describe an extension of the IB framework to simulate soft material failure using peridynamics, which is a nonlocal structural mechanics formulation. Numerical examples demonstrate constitutive correspondence with classical mechanics for non-failure cases along with essentially grid-independent predictions of fluid-driven soft material failure. Finally, I will introduce a reformulation of the IB large-deformation elasticity framework that enables accurate and efficient fluid-structure coupling through a version of the immersed interface method, which is a sharp-interface IB-type method. Computational examples demonstrate the ability of this methodology to simulate a broad range of fluid-structure mass density ratios without suffering from artificial added mass instabilities, and to facilitate subgrid contact models. I will also present biomedical applications of the methodology, including models of clot capture by inferior vena cava filters.

BIOGRAPHY: Boyce Griffith is a Professor of Mathematics at the University of North Carolina at Chapel Hill (UNC-Chapel Hill). He also is a Professor in the Joint Department of Biomedical Engineering at UNC-Chapel Hill and North Carolina State University, and is an Adjunct Professor of Applied Physical Sciences at UNC-Chapel Hill. He received his PhD in Mathematics in 2005 from the Courant Institute of Mathematical Sciences at New York University. His interests include mathematical modeling and computer simulation of cardiac mechanics, fluid dynamics, and electrophysiology, with a focus on fluid-structure interaction and the fluid dynamics of native and prosthetic heart valves.