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

Luca Formaggia; Alexandra Moura; Fabio Nobile

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

- Volume: 41, Issue: 4, page 743-769
- ISSN: 0764-583X

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topFormaggia, Luca, Moura, Alexandra, and 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 41.4 (2007): 743-769. <http://eudml.org/doc/250040>.

@article{Formaggia2007,

abstract = {
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.
},

author = {Formaggia, Luca, Moura, Alexandra, Nobile, Fabio},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Fluid-structure interaction; 3D-1D FSI coupling;
energy estimate; multiscale models.},

language = {eng},

month = {10},

number = {4},

pages = {743-769},

publisher = {EDP Sciences},

title = {On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations},

url = {http://eudml.org/doc/250040},

volume = {41},

year = {2007},

}

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

DA - 2007/10//

PB - EDP Sciences

VL - 41

IS - 4

SP - 743

EP - 769

AB -
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.

LA - eng

KW - Fluid-structure interaction; 3D-1D FSI coupling;
energy estimate; multiscale models.

UR - http://eudml.org/doc/250040

ER -

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