Isogeometric analysis of turbulence and fluid-structure interaction

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Bazilevs, Jurijs

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This work puts Isogeometric Analysis, a new analysis framework for computational engineering and sciences, on a firm mathematical foundation. FEM-like theory is developed in which optimal in h approximation properties for NURBS spaces with boundary conditions and inverse estimates are shown. This, in turn, grants straightforward extensions of the theory to stabilized formulations of incompressible and advection dominated phenomena. This work also continues the development of residual-based turbulence models for incompressible fluid flow based on the multiscale paradigm. Novel turbulent closures, inspired by wellknown stabilized methods, are derived and tested within the unsteady parallel isogeometric incompressible flow solver that was written as a part of this work. The latter part of this dissertation focuses on the fluid-structure interaction (FSI) problem. A fully-coupled FSI formulation is proposed and a methodology for deriving shape derivative jacobian matrices is presented, allowing for a monolithic solution of the FSI system at the discrete level, and rendering the fluid and structural computations more robust. These ideas are implemented in the form of an isogeometric parallel fluid-structure interaction solver. This technology is used to perform computations of contemporary interest and importance in patient-specific vascular simulation and modeling.