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The paper develops a solver based on a conforming finite element method for a3D--1D coupled incompressible flow problem. New coupling conditions areintroduced to ensure a suitable bound for the cumulative energy of the model.We study the stability and accuracy of the discretization method, and theperformance of some state-of-the-art linear algebraic solvers for such flowconfigurations. 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 modelposed in a domain with anisotropic inclusions. The relevance of our approach torealistic cardiovascular simulations is demonstrated by computing a blood flowover a model IVC filter.

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