We develop a numerical method for fluid-structure interaction. Our emphasis is on strong, monolithic coupling between fluid and structure and on developing scalable parallel algorithms and preconditioning techniques. The work developed in this thesis is the first to carefully consider parallel performance and scalability for monolithic coupling in fluid-structure interaction.
Although our fluid-structure algorithm is robust and flexible and could be used for several applications, the target application considered here is the simulation of blood flow in compliant arteries. In this setting, the incompressible Navier-Stokes equations are used to model the fluid and these are coupled to an incompressible linear visco-elastic model for the blood vessel walls. Our fluid-structure interaction method features an unstructured, dynamically moving fluid mesh in the arbitrary Lagrangian-Eulerian framework. We use a finite element discretization in space and fully implicit methods for the time discretization. Simulations are based on blood vessel geometries derived from patient-specific clinical data.
For the parallel implementation, we develop a scalable Newton-Krylov algorithms preconditioned with a two-level overlapping restricted additive Schwarz method. This preconditioner works on the entire fluid-structure system, with subdomain boundaries having no necessary correspondence to the fluid-structure interface. Our parallel algorithm is shown to be robust to many physical parameters and scalable to millions of unknowns and thousands of processor cores.
|Commitee:||Bortz, David, Hunter, Kendall, Manteuffel, Thomas, McCormick, Steve|
|School:||University of Colorado at Boulder|
|School Location:||United States -- Colorado|
|Source:||DAI-B 70/04, Dissertation Abstracts International|
|Subjects:||Mathematics, Biophysics, Computer science|
|Keywords:||Blood flow, Domain decomposition, Fluid-structure interaction, Parallel computing, Preconditioning|
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