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On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations

Published online by Cambridge University Press:  04 October 2007

Luca Formaggia
MOX - Modelling and Scientific Computing, Department of Mathematics, Politecnico di Milano, Italy.;;
Alexandra Moura
MOX - Modelling and Scientific Computing, Department of Mathematics, Politecnico di Milano, Italy.;;
Fabio Nobile
MOX - Modelling and Scientific Computing, Department of Mathematics, Politecnico di Milano, Italy.;;
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We consider the coupling between three-dimensional (3D) and one-dimensional (1D) fluid-structure interaction (FSI) models describing blood flow inside compliant vessels. The 1D model is a hyperbolic system of partial differential equations. The 3D model consists of the Navier-Stokes equations for incompressible Newtonian fluids coupled with a model for the vessel wall dynamics. A non standard formulation for the Navier-Stokes equations is adopted to have suitable boundary conditions for the coupling of the models. With this we derive an energy estimate for the fully 3D-1D FSI coupling. We consider several possible models for the mechanics of the vessel wall in the 3D problem and show how the 3D-1D coupling depends on them. Several comparative numerical tests illustrating the coupling are presented.

Research Article
© EDP Sciences, SMAI, 2007

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