Description
- Abstract:
- In recent years, there has been great interest in fluid-structure interaction (FSI) problems due to their relevance in structural engineering and biomedical applications. However, several difficulties have hindered the development of partitioned FSI algorithms in large-scale simulations: the relatively small values of the mass ratio between the arterial wall and the blood causes instabilities in solvers; the arterial wall responses are very complicated therefore difficult to be described by classical structural models; accurate simulations in patient-specific geometries require large CPU time; and so on. To resolve these difficulties, design and analysis of efficient and stable numerical schemes for structure solver, fluid solver, and FSI procedure are considered in this thesis, with contributions on: developing and accelerating the spectral element method structure solvers for linear elastic, hyperelastic and viscoelastic models; validating the spectral element method fluid solver in image-based computational biofluid mechanics; stabilizing the partitioned fluid-structure interaction procedure and resolving the added-mass effect; developing and employing fractional PDEs solvers to model the complex biomechanical viscoelastic properties of patient-specific arteries. Specifically, on the structure side firstly a mixed formulation for nearly incompressible nonlinear elasticity is investigated, which has superior accuracy and efficiency compared with the displacement-only formulation. Moreover, a semi-local solver is developed for spectral element discretization of the linear elasticity equations, from which we obtain good scalability in large scale parallel computing. To better capture the complex biomechanical viscoelastic properties of soft tissue in arteries, the governing equations for structure are extended to fractional viscoelasticity models, and their sensitivities to the patient-specific parameters are numerically investigated. On the fluid side, the spectral element method solver is validated by comparing the simulation results with clinical angiographic images and with numerical solutions from other research groups. Lastly, two new schemes for FSI are designed to stabilize and accelerate the communications between fluid and structure solvers, with analysis for choosing the optimal coefficients provided. To validate the analysis, the FSI framework is applied to patient-specific aneurysms and also to deepwater offshore risers covered with fairings, hence demonstrating the general applicability of the methodology.
- Notes:
- Thesis (Ph.D. -- Brown University (2014)
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Citation
Yu, Yue,
"Numerical Methods for Fluid-Structure Interaction: Analysis and Simulations"
(2014).
Applied Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.7301/Z0GM85PP
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Applied Mathematics Theses and Dissertations
Theses and Dissertations for the Applied Mathematics department....