Numerical Treatment of Defective Boundary Conditions for the Navier--Stokes Equations
SIAM Journal on Numerical Analysis
Parallel Algorithms for Fluid-Structure Interaction Problems in Haemodynamics
SIAM Journal on Scientific Computing
On the continuity of mean total normal stress in geometrical multiscale cardiovascular problems
Journal of Computational Physics
High resolution methods for scalar transport problems in compliant systems of arteries
Applied Numerical Mathematics
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In this work we discuss the reliability of the coupling among three-dimensional (3D) and one-dimensional (1D) models that describe blood flowing into the circulatory tree. In particular, we study the physical consistency of the 1D model with respect to the 3D one. To this aim, we introduce a general criterion based on energy balance for the proper choice of coupling conditions between models. We also propose a way to include in the 1D model the effect of the external tissue surrounding the vessel and we discuss its importance whenever this effect is considered in the 3D model. Finally, we propose several numerical results in real human carotids, studying different configurations for the 1D model and highlighting the best one in view of the physical consistency.