On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations
Formaggia, Luca ; Moura, Alexandra ; Nobile, Fabio
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 41 (2007), p. 743-769 / Harvested from Numdam

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.

Publié le : 2007-01-01
DOI : https://doi.org/10.1051/m2an:2007039
Classification:  65M12,  65M60,  92C50,  74F10,  76Z05
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     author = {Formaggia, Luca and Moura, Alexandra and Nobile, Fabio},
     title = {On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {41},
     year = {2007},
     pages = {743-769},
     doi = {10.1051/m2an:2007039},
     mrnumber = {2362913},
     zbl = {1139.92009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_2007__41_4_743_0}
}
Formaggia, Luca; Moura, Alexandra; Nobile, Fabio. On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 41 (2007) pp. 743-769. doi : 10.1051/m2an:2007039. http://gdmltest.u-ga.fr/item/M2AN_2007__41_4_743_0/

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