On a constrained minimization problem arising in hemodynamics

João Janela, and Adélia Sequeira. "On a constrained minimization problem arising in hemodynamics." Banach Center Publications 81.1 (2008): 227-241. <http://eudml.org/doc/282314>.

@article{JoãoJanela2008,
abstract = {Experimental evidence collected over the years shows that blood exhibits non-Newtonian characteristics such as shear-thinning, viscoelasticity, yield stress and thixotropic behaviour. Under certain conditions these characteristics become relevant and must be taken into consideration when modelling blood flow. In this work we deal with incompressible generalized Newtonian fluids, that account for the non-constant viscosity of blood, and present a new numerical method to handle fluid-rigid body interaction problems. The work is motivated by the investigation of interaction problems occurring in the human cardiovascular system, where the rigid bodies may be blood particles, clots, valves or any structure that we may assume to move rigidly. This method is based on a variational formulation of the fully coupled problem in the whole fluid/solid domain, in which constraints are introduced to enforce the rigid motion of the body and the equilibria of forces and stresses at the interface. The main feature of the method consists in introducing a penalty parameter that relaxes the constraints and allows for the solution of an associated unconstrained problem. The convergence of the solution of the relaxed problem is established and some numerical simulations are performed using common benchmarks for this type of problems.},
author = {João Janela, Adélia Sequeira},
journal = {Banach Center Publications},
keywords = {constrained minimization; hyper-viscosity method; fluid-rigid body interactions; shear-thinning fluids},
language = {eng},
number = {1},
pages = {227-241},
title = {On a constrained minimization problem arising in hemodynamics},
url = {http://eudml.org/doc/282314},
volume = {81},
year = {2008},
}

TY - JOUR
AU - João Janela
AU - Adélia Sequeira
TI - On a constrained minimization problem arising in hemodynamics
JO - Banach Center Publications
PY - 2008
VL - 81
IS - 1
SP - 227
EP - 241
AB - Experimental evidence collected over the years shows that blood exhibits non-Newtonian characteristics such as shear-thinning, viscoelasticity, yield stress and thixotropic behaviour. Under certain conditions these characteristics become relevant and must be taken into consideration when modelling blood flow. In this work we deal with incompressible generalized Newtonian fluids, that account for the non-constant viscosity of blood, and present a new numerical method to handle fluid-rigid body interaction problems. The work is motivated by the investigation of interaction problems occurring in the human cardiovascular system, where the rigid bodies may be blood particles, clots, valves or any structure that we may assume to move rigidly. This method is based on a variational formulation of the fully coupled problem in the whole fluid/solid domain, in which constraints are introduced to enforce the rigid motion of the body and the equilibria of forces and stresses at the interface. The main feature of the method consists in introducing a penalty parameter that relaxes the constraints and allows for the solution of an associated unconstrained problem. The convergence of the solution of the relaxed problem is established and some numerical simulations are performed using common benchmarks for this type of problems.
LA - eng
KW - constrained minimization; hyper-viscosity method; fluid-rigid body interactions; shear-thinning fluids
UR - http://eudml.org/doc/282314
ER -