Fluid-structure interaction (FSI) problems arise in many applications, such as geomechanics, aerodynamics, and blood flow dynamics (hemodynamics). In hemodynamic applications, mathematical models must capture the non-linear coupling between blood and the elastic structural dynamics of vessel walls, soft tissue, or cardiac muscles. These structural dynamics create 'moving domain' FSI problems that are challenging to numerically solve and analyze. Fast and efficient FSI solvers are valuable for bioengineering applications since the combination of numerical algorithms with experimental and clinical measurements provides an innovative approach to understanding the basic function of many components of the cardiovascular system and their mutual interaction. The PI will develop a class of numerical methods and underlying theory for non-linear FSI problems with large displacements. The research aims at making fundamental contributions to development of algorithms and numerical analysis of such problems. The proposed research will push the boundaries of our ability to model FSI problems in hemodynamics, including fracture propagation in soft tissue.

The goal of this project is the development of a class of numerical methods and underlying theory for solving non-linear FSI problems with large displacements. Proposed methods will be specially designed for problems arising from hemodynamics. We will consider elastic and poroelastic structures where solid mechanics are described by hyperelastic constitutive models. Both partitioned and monolithic methods will be developed. Special attention will be given to numerical analysis of the proposed methods. The research goals will be achieved through the following specific aims: Aim 1: Development of noniterative, domain decomposition methods for FSI problems with porohyperelastic structures using secondorder Backward Differentiation Formula time discretization and the Crank-Nicolson Leapfrog time discretization; Aim 2: Development of non-iterative, domain decomposition methods for FSI problems with thick, hyperelastic structures; and Aim 3: Development and analysis of a monolithic, phase-field approach for FSI problems with hyperelastic structures.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Leland Jameson
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University of Notre Dame
Notre Dame
United States
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