Hybrid Adaptive Numerical Methods and Computational Software for Biological Fluid-Structure Interaction

University Of North Carolina At Chapel Hill, Chapel Hill NC

Investigators

Abstract

Building upon his earlier work in developing parallel and adaptive immersed boundary (IB) methods for simulating fluid-structure interaction (FSI), in this project, the investigator aims to construct a new hybrid FSI methodology which incorporates features of both the IB method and the immersed interface (II) method. The IB method is a broadly-useful approach to FSI which has been applied to diverse problems in biological fluid dynamics. Although the IB method has been demonstrated to be a useful approach to such problems, it is generally only first-order accurate, and fine spatial grids are therefore required to obtain resolved numerical simulations. The II method is an IB-like approach to FSI which yields second-order accuracy for certain problems, but which is currently limited to thin elastic interfaces which are closed (i.e., which do not have free edges). The hybrid FSI methodology of this project will incorporate features of both the IB and II methods to obtain high-order accuracy for both "thick" and "thin" elastic bodies, including thin elastic interfaces with free edges. We believe that the basic version of the methodology will be the first IB-like method to achieve full second-order accuracy for thick elastic bodies such as the muscular walls of the heart, and that the extended version of the methodology will be the first II-like method to treat interfaces with free edges, such as the thin leaflets of the cardiac valves. These new methods will be used to simulate cardiovascular flows, especially the fluid dynamics of the aortic heart valve. Problems in which a fluid flow interacts with an elastic structure, such as the writhing and coiling of DNA or, as addressed within this project, blood flow in the heart and vessels, are ubiquitous in engineering, biology, and medicine. The immersed boundary (IB) method is a broadly-useful approach to such problems which was introduced to enable the computer simulation of the fluid dynamics of the heart and its valves. Indeed, cardiovascular applications have motivated much work to develop mathematical and computational methods for FSI, and the large and growing number of patients suffering from cardiovascular diseases (80 million people in the United States, approximately 30% of the population), such as coronary heart disease (16.8 million people) or heart failure (5.7 million people), make such applications increasingly important. This project aims to develop an improved version of the IB method which will improve the accuracy of the methodology, possibly leading to significantly more realistic simulations of cardiovascular dynamics. Because the IB approach is widely useful, and because the software implementing the methods of this project will be freely distributed, the potential impact of this work is quite broad, possibly affecting studies which aim to address basic scientific questions (e.g., the fluid-structure interactions which result in the beating of cilia within the oviduct or respiratory tract) to studies which aim to improve the design of medical therapies and devices (e.g., prosthetic cardiac valves or treatments for heart failure).