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Speaker: Yue Yu, Department of Mathematics, Lehigh University
Abstract: In this work, we consider the partitioned approach for fluid-structure interactions, and we develop new stabilized algorithms. 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. In particular, in vascular blood flow 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 a new numerical method to handle this added-mass effect, by relaxing the exact no-slip boundary condition and introducing proper penalty terms on the fluid-structure interface, which enables the possibility of stable explicit coupling procedure. The optimal parameters are obtained via theoretical analysis, and we numerically verify that stability can be achieved irrespective of the fluid-structure mass ratio. To demonstrate the effectiveness of the proposed techniques in practical computations, I will also discuss two vascular blood flow applications in three-dimensional large scale simulations. The first application is obtained for patient-specific cerebral aneurysms. The 3D fractional-order PDEs (FPDEs) are investigated which better describe the viscoelastic behavior of cerebral arterial walls. In the second application, we apply the stabilized FSI method to heart valves, and simulate the coupling of the bioprosthetic heart valve and the surrounding blood flow under physiological conditions. Lastly, I will present the progress of our ongoing project on the multiscale coupling of the peridynamic and the classical elastic theories, with an application on simulating the material damage in arterial simulations, say, the aneurysm rupture or the heart valve failure problems.
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