Friday March 18th, at 11:00AM Math Conference room

March 17, 2016 by Duan Chen
Categories: Spring 2022
Yue Yu, Department of Mathematics, Lehigh University
Title: Stabilized numerical methods for fluid-structure interactions with application in cerebral aneurysm simulations
Abstract: Cerebral aneurysm is a diseased dilatation of the arterial walls in brain, and its rupture can lead to intracranial hemorrage and subsequent death. While the current clinical technology could not provide detailed in vivo measurements for intra-aneurysm flow patterns, fluid (blood) structure (arterial wall) interaction simulations then appear as an effective alternative approach for un- derstanding the mechanisms behind aneurysm growth and rupture. There are two approaches in formulating the discrete systems in simulating fluid-structure interaction (FSI) problems: the monolithic approach, and the partitioned approach. The former is efficient for small problems but does not scale up to realistic sizes, whereas the latter suffers from numerical stability issues. Here we consider the partitioned approach and we develop new stabilized algorithms. In par- ticular, in cerebral aneurysm simulations where the mass ratio between the structure and the fluid is relatively small, the partitioned approach gives rise to the so-called added-mass effect which renders the simulation unstable. I will present two new numerical methods to handle this added-mass effect: (1) by introducing fictitious pressure (acceleration) terms in the fluid (structure) equations to balance the added-mass effect, which stabilizes the coupled formulation and reduces drastically the number of subiterations in each time step; (2) by relaxing the exact no-slip boundary condition and introducing proper penalty terms on the fluid-structure inter- face, which enables the possibility of stable explicit coupling procedure. For both methods we obtained the optimal parameters via theoretical analysis, and numerically verified that stability can be achieved irrespective of the fluid-structure mass ratio. Moreover, I will also discuss an application in three-dimensional large scale simulations which were obtained for patient- specific cerebral aneurysms. With stabilized FSI method applied, the 3D fractional-order PDEs (FPDEs) were investigated which better describe the viscoelastic behavior of cerebral arterial walls.