The first part of the thesis presents the surface representation of blood vessel walls extracted from medical images, sensitivity to the inlet/outlet boundary conditions, and a hp-refinement study. Our study shows that flow instability in supraclinoid aneurysms is not affected by flow division at downstream branches. However, inlet boundary condition is recommended to be specified upstream of the cavernous segment. The hp-refinement study shows that our spectral element code captures velocity and wall shear stress (WSS) fluctuations.

The second part describes the development and implementation of new fluid solvers with better stability properties than the standard NEKTAR. Due to the strict CFL condition in semi-implicit scheme, the standard NEKTAR over-resolves solutions in time. The semi-implicit scheme is stabilized by sub-iterations with relaxation at each time step. The stability and accuracy of the scheme has been tested with analytic steady solutions, unsteady flows past a cylinder, and pulsatile flows in straight/bend pipes. We also develop a high-order spectral/hp element method for fluid-structure interaction which couples solvers in a partitioned way. Fictitious mass and damping terms introduced to the elastodynamics equation are shown to enhance the stability and reduce the number of sub-iterations. A new boundary condition with spring supports is proposed and its effect on the displacement and stability is investigated.

In the last part of the thesis, we report on flow instabilities and WSS distributions in funnel-shaped bifurcations and aneurysms. Our simulations also show that pulsatile flows in aneurysms are subject to a hydrodynamic instability during the decelerating systolic phase, resulting in high-frequency oscillations in the range of 20–50 Hz. When the aneurysmal flow becomes unstable, both the magnitude and the directions of WSS vectors fluctuate at the aforementioned high frequencies. Impingement regions coincide with the locations of the rupture of infundibulae or progression to aneurysms.