Fluid-structure interaction algorithms for vascular dynamics based on Robin interface conditions

In this talk we focus on the modeling and numerical simulation of the fluid structure interaction mechanism in vascular dynamics. We will first present a simplified coupled fluid-structure problem where the artery is modeled as an elastic membrane deforming only in the normal direction. This model generalizes the well known "independent rings" model to an arbitrary geometry and can be embedded into the fluid equations as a Robin boundary condition, thus leading to "cheap" algorithms to simulate the blood/artery interaction. We will then consider the more complex case of a thick structure, modeled by 3D elasticity equations and explore the possibility to use the reduced model as a preconditioner of the full one. In particular we propose partitioned fluid-structure algorithms based on Robin transmission conditions. We will present some theoretical results obtained on a linear model problem as well as numerical tests, showing the robustness of the new approach with respect to the added mass effect and its superiority with respect to more traditional partitioned procedures.