A finite element solver and energy stable coupling for 3D and 1D fluid models

The paper develops a solver based on a conforming finite element method for a 3D--1D coupled incompressible flow problem. New coupling conditions are introduced to ensure a suitable bound for the cumulative energy of the model. We study the stability and accuracy of the discretization method, and the performance of some state-of-the-art linear algebraic solvers for such flow configurations. Motivated by the simulation of the flow over inferior vena cava (IVC) filter, we consider the coupling of a 1D fluid model and a 3D fluid model posed in a domain with anisotropic inclusions. The relevance of our approach to realistic cardiovascular simulations is demonstrated by computing a blood flow over a model IVC filter.