STABILIZATION OF THE HYBRID IMMERSED BOUNDARY METHOD

The immersed boundary method is a model of fluid-structure interaction that uses a single momentum equation to account for the dynamics of a fluid and an immersed solid. The momentum equation is solved in Eulerian form, and fluid-solid coupling operators with delta function kernels are used to communicate between the Eulerian and Lagrangian frames. Over the years many extensions to the immersed boundary method have been introduced, notably the hyper-elastic extension of Boffi et al which treats the structure as a finite volume. Subsequent to this work, Griffith and Luo introduced a hybrid numerical approach to Boffi's formulation, which used finite differences to approximate the Eulerian equations and C^0 finite elements to solve the Lagrangian equations. This new numerical method presents both more flexibility and more challenges. Specifically, questions arise as to how to adequately maintain incompressibility of the solid in the Lagrangian frame, how to choose the discrete set of points that most efficiently couples the fluid and solid, and how to model finitely-thin structures. In this work we leverage techniques of computational mechanics to offer solutions to these questions.Doctor of Philosoph