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multiscale models.

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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On the stability of the coupling of 3D and 1D fluid-structure interaction modelsfor blood flow simulations
Luca Formaggia, Alexandra Moura, Fabio Nobile
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 41 / Issue 4 / July 2007

Published online by Cambridge University Press:

04 October 2007, pp. 743-769

Print publication:

July 2007
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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 hyperbolicsystem of partial differential equations.The 3D model consists of the Navier-Stokes equationsfor incompressible Newtonian fluids coupled with a model for the vessel wall dynamics. A non standard formulationfor the Navier-Stokes equations is adopted tohave suitable boundary conditions for the couplingof the models. With this we derive an energy estimatefor the fully 3D-1D FSI coupling. We consider several possiblemodels for the mechanics of the vessel wall in the 3D problemand show how the 3D-1D coupling depends on them.Several comparative numerical tests illustrating the coupling are presented.