Abstract

The immersed boundary (IB) method is a general mathematical framework and a particular numerical approach to problems of fluid-structure interaction. Over the last several years, we have developed an adaptive version of the IB method which uses Cartesian grid adaptive mesh refinement (AMR), thereby allowing us to deploy locally high spatial resolution where it is most needed (e.g., in the vicinity of the heart valve leaflets and the vorticies shed from those leaflets), and to use comparatively coarse resolution where it suffices. In this talk, we shall describe our adaptive version of the IB method, along with recent extensions of this method which enable the specification of physical boundary conditions for the fluid, thereby allowing us to connect three-dimensional immersed boundary models to reduced flow models (e.g., Windkessel models) via fluid boundary conditions. (Earlier versions of the IB method generally imposed periodic boundary conditions on the fluid, and for such methods, connections to reduced flow models were mediated by internal fluid sources and sinks.) Three-dimensional computational results will be presented to demonstrate the application of this methodology to simulating the fluid mechanics of isolated models of heart valves, as well as a new whole heart model derived from cardiac computed tomography (CT) data from a healthy human heart.