Fluid-Structure Interaction in the Cardiovascular System. Numerical Analysis and Simulation

In this thesis we focus on the numerical analysis and the development of efficient partitioned algorithms for fluid-structure interaction (FSI) problems arising in hemodynamics. In particular we consider the mechanical interaction of the blood with the large arteries, with the cardiac valves and with the myocardium. In partitioned FSI procedures the coupling between the fluid and the structure can be enforced in different ways: implicit, semi-implicit or explicit. In the first part of this thesis, the convergence properties of a projection semi-implicit coupling scheme are investigated from the theoretical and numerical viewpoints. Then, for the same scheme, we propose a modification that aims at improving its stability properties. This modification relies on the reinterpretation of the Nitsche's interface coupling as a particular Robin-Robin coupling. In the second part fluid-structure interaction problems with cardiac valves are addressed. For these problems we devise a modular partitioned strategy for the numerical simulation of 3D FSI problems where contact among multiple elastic solids can occur. For the analysis of the computational results, we also investigate the use of an advanced post-processing technique based on the notion of Lagrangian coherent structures. Finally, in the last part, a new reduced model for cardiac valves simulations is presented. This new model offers a compromise between standard lumped parameter models and fully 3D FSI problems. Various numerical experiments are presented to validate its efficiency and robustness. With this model, numerical simulations of the cardiac hemodynamics can be performed with a reduced computational cost.