# Robust numerical approximation of coupled Stokes' and Darcy's flows applied to vascular hemodynamics and biochemical transport*

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

- Volume: 45, Issue: 3, page 447-476
- ISSN: 0764-583X

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topD'Angelo, Carlo, and Zunino, Paolo. "Robust numerical approximation of coupled Stokes' and Darcy's flows applied to vascular hemodynamics and biochemical transport*." ESAIM: Mathematical Modelling and Numerical Analysis 45.3 (2011): 447-476. <http://eudml.org/doc/276343>.

@article{DAngelo2011,

abstract = {
The fully coupled description of blood flow and mass transport in
blood vessels requires extremely robust numerical methods. In order
to handle the heterogeneous coupling between blood flow and plasma filtration,
addressed by means of Navier-Stokes and Darcy's equations,
we need to develop a numerical scheme capable to deal with
extremely variable parameters, such as the blood viscosity and
Darcy's permeability of the arterial walls. In this paper, we describe a finite element method for the
approximation of incompressible flow coupled problems. We exploit
stabilized mixed finite elements together with Nitsche's type matching
conditions that automatically adapt to the coupling of different
combinations of coefficients. We study in details the stability of
the method using weighted norms, emphasizing the robustness of the
stability estimate with respect to the coefficients. We also
consider an iterative method to split the coupled heterogeneous
problem in possibly homogeneous local problems, and we
investigate the spectral properties of suitable preconditioners for
the solution of the global as well as local problems. Finally, we present the simulation of the fully coupled blood flow
and plasma filtration problems on a realistic geometry of a
cardiovascular artery after the implantation of a drug eluting stent
(DES). A similar finite element method for mass transport is then
employed to study the evolution of the drug released by the DES in
the blood stream and in the arterial walls, and the role of plasma
filtration on the drug deposition is investigated.
},

author = {D'Angelo, Carlo, Zunino, Paolo},

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

keywords = {Coupled Stokes/Darcy's problem; biological flows and mass
transfer; cardiovascular applications; finite element approximation;
interior penalty method; iterative splitting strategy; optimal
preconditioning; coupled Stokes/Darcy's problem; biological flows and mass transfer; interior penalty method; optimal preconditioning},

language = {eng},

month = {1},

number = {3},

pages = {447-476},

publisher = {EDP Sciences},

title = {Robust numerical approximation of coupled Stokes' and Darcy's flows applied to vascular hemodynamics and biochemical transport*},

url = {http://eudml.org/doc/276343},

volume = {45},

year = {2011},

}

TY - JOUR

AU - D'Angelo, Carlo

AU - Zunino, Paolo

TI - Robust numerical approximation of coupled Stokes' and Darcy's flows applied to vascular hemodynamics and biochemical transport*

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2011/1//

PB - EDP Sciences

VL - 45

IS - 3

SP - 447

EP - 476

AB -
The fully coupled description of blood flow and mass transport in
blood vessels requires extremely robust numerical methods. In order
to handle the heterogeneous coupling between blood flow and plasma filtration,
addressed by means of Navier-Stokes and Darcy's equations,
we need to develop a numerical scheme capable to deal with
extremely variable parameters, such as the blood viscosity and
Darcy's permeability of the arterial walls. In this paper, we describe a finite element method for the
approximation of incompressible flow coupled problems. We exploit
stabilized mixed finite elements together with Nitsche's type matching
conditions that automatically adapt to the coupling of different
combinations of coefficients. We study in details the stability of
the method using weighted norms, emphasizing the robustness of the
stability estimate with respect to the coefficients. We also
consider an iterative method to split the coupled heterogeneous
problem in possibly homogeneous local problems, and we
investigate the spectral properties of suitable preconditioners for
the solution of the global as well as local problems. Finally, we present the simulation of the fully coupled blood flow
and plasma filtration problems on a realistic geometry of a
cardiovascular artery after the implantation of a drug eluting stent
(DES). A similar finite element method for mass transport is then
employed to study the evolution of the drug released by the DES in
the blood stream and in the arterial walls, and the role of plasma
filtration on the drug deposition is investigated.

LA - eng

KW - Coupled Stokes/Darcy's problem; biological flows and mass
transfer; cardiovascular applications; finite element approximation;
interior penalty method; iterative splitting strategy; optimal
preconditioning; coupled Stokes/Darcy's problem; biological flows and mass transfer; interior penalty method; optimal preconditioning

UR - http://eudml.org/doc/276343

ER -

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