Development and analysis of high-order partitioned schemes for fluid-structure interaction problems

University Of Notre Dame, Notre Dame IN

Investigators

Abstract

Fluid-structure interaction (FSI) problems arise in many applications, such as aerodynamics, geomechanics and biomedical engineering. In hemodynamics, FSI models have been used to describe the interaction between blood and arterial walls. More precisely, numerical algorithms for fluid-structure interaction problems can provide predictions in many cardiovascular diseases, such as aneurysms or atherosclerosis. Since combining state-of-the-art algorithms with non-invasive clinical measurement tools provides an innovative approach to medical diagnosis and surgical decision making, there is an increasing demand for fast and efficient numerical schemes to solve FSI problems. The PI will develop and analyze a class of stable and robust high-order partitioned numerical methods for FSI problems. The development of stable and efficient algorithms for fluid-structure problems is crucial for performing patient specific diagnostic tests, and this work will make a major contribution in biomedical research. The goal of this research is a development and analysis of a class of higher-order partitioned numerical methods for interactions between an incompressible, viscous fluid and a thin, elastic structure. The discretization in space will be performed using the finite element method, and different partitioned methods will be proposed based on the time discretization. In particular, algorithms will be developed based on the kinematically coupled scheme (Project 1), the Strang operator splitting approach (Project 2) and the Crank-Nicolson and Leapfrog method (Project 3). Energy estimates and convergence rates will be derived for each proposed algorithm. A comparison of all the proposed methods based on their performance, stability and convergence properties will be made, allowing other researchers to identify optimal algorithms for specific choices of parameter values. The proposed algorithms, numerical analysis and simulation results will be published and made available to the community. In that way, they will serve as a set of reference data that can be used for model validation by other researchers.