Efficient partitioned algorithms for the solution of fluid-structure interaction problems in haemodynamics
Monday 26th March 2012
Nobile, F.; Vergara, C.
The purpose of this thesis is the description, study and numerical approximation of the fluid-structure interaction (FSI) problem applied to hemodynamics. The blood is modelled as an incompressible Newtonian fluid on moving domains and the vessel as isotropic materials. The fluid equations are written in an arbitrary Lagrangian-Eulerian (ALE) frame of reference. The principal goals of this work are • The development of efficient ways to build high-order temporal schemes for the solution of the FSI problem. • The study of different methods for the treatment of fluid-structure inter- face position, focusing on partitioned algorithms for the prescription of the continuity conditions at the fluid-structure interface. We consider some preconditioners of the FSI problem determinate some explicit and implicit algorithms and propose new hybrid methods. We investigate the performances and the accuracy of these schemes. • The extention of these algorithms to FSI problem with non linear isotropic materials; • The patient-specific numerical simulations, the comparison of the fluid- dynamics in the same patient before and after the removal of the artherosclerotic plaque. The geometrical data are obtained by means of Magnetic Resonance Imaging acquisitions, and the conditions to be imposed at the inlet by means of Doppler Ultrasound measurements. Keywords: Fluid-structure interaction, blood flow, time advancing schemes, time accuracy, linear and non linear structure, partitioned schemes.