Abstract

An aneurysm is a pathological condition whereby a weakened artery wall may dilates up to dangerous proportions. One of the most common treatments consists of the insertion of a stent graft, which is a medical device introduced into the artery lumen in order to diminish the pressure on the aneurysm wall and so avoiding its rupture. In this article we perform the simulation of the fluid-structure interaction between the blood, the artery wall and the stent. We consider the blood modeled by incompressible Navier-Stokes equations in ALE formulation, while the solid parts are modeled using nonlinear shells in a Lagrangian framework. We suppose the stent being perfectly matched with the artery, i.e., with no filtrations or endoleaks, such that we obtain two disconnected regions of fluid by the stent wall. The main difficulty in this problem is the numerical solution for the isolated portion of fluid, where the explicit coupling with standard Dirichlet-Neumann boundary conditions may lead to non uniqueness for the intra-aneurysm pressure and also to violate the divergence-free condition. To address this issue we use Robin-Neumann conditions for the coupling, which allow us not only to obtain successful numerical simulations but also a less sensitive scheme to the added-mass effect and a more stable and robust iterative technique than the Dirichlet-Neumann procedure. We present numerical evidence of the well-posedeness of this technique and examples showing the effect of the stent on the aneurysm wall.