Geodesic
On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations
Formaggia, Luca1  ; Moura, Alexandra ; Nobile, Fabio
1 Politecnico di Milano, MOX, Piazza L. da Vinci 32, 20133 Milano, Italy.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 41 (2007) no. 4, pp. 743-769

Voir la notice de l'article provenant de la source 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.

DOI : 10.1051/m2an:2007039
Classification : 65M12, 65M60, 92C50, 74F10, 76Z05
Keywords: fluid-structure interaction, 3D-1D FSI coupling, energy estimate, multiscale models

Formaggia, Luca 1 ; Moura, Alexandra  ; Nobile, Fabio 

1 Politecnico di Milano, MOX, Piazza L. da Vinci 32, 20133 Milano, Italy. 
@article{M2AN_2007__41_4_743_0,
     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 },
     pages = {743--769},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {4},
     year = {2007},
     doi = {10.1051/m2an:2007039},
     mrnumber = {2362913},
     zbl = {1139.92009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007039/}
}
TY  - JOUR
AU  - Formaggia, Luca
AU  - Moura, Alexandra
AU  - Nobile, Fabio
TI  - On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 2007
SP  - 743
EP  - 769
VL  - 41
IS  - 4
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007039/
DO  - 10.1051/m2an:2007039
LA  - en
ID  - M2AN_2007__41_4_743_0
ER  - 
%0 Journal Article
%A Formaggia, Luca
%A Moura, Alexandra
%A Nobile, Fabio
%T On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2007
%P 743-769
%V 41
%N 4
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007039/
%R 10.1051/m2an:2007039
%G en
%F 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 , Tome 41 (2007) no. 4, pp. 743-769. doi: 10.1051/m2an:2007039

Cité par Sources :