Shape Optimization in Stationary Blood Flow:
A Numerical Study of Non-Newtonian Effects
Feby Abraham
Department of Mechanical Engineering and Materials Science
Marek Behr
Computational Analysis of Technical Systems (CATS)
RWTH Aachen, Germany
Matthias Heinkenschloss
Department of Computational and Applied Mathematics
Rice University
Computer Methods in Biomechanics and Biomedical Engineering,
Vol 8 (2005), pp. 201-212.
Abstract
This paper presents a numerical study of non-Newtonian effects on the
solution of shape optimization problems involving unsteady pulsatile
blood flow.
We consider an idealized two-dimensional arterial graft geometry.
Our computations are based on the Navier-Stokes equations generalized
to non-Newtonian fluid, with the Carreau-Yasuda model employed to
account for
the shear-thinning behavior of blood.
Using a gradient-based optimization algorithm,
we compare the optimal shapes obtained using both the Newtonian and
generalized Newtonian
constitutive equations.
Depending on the shear rate prevalent in the domain,
substantial differences in the flow as well as in the computed
optimal shape are observed when the Newtonian constitutive equation
is replaced by the Carreau-Yasuda model.
By varying a geometric parameter in our test case,
we investigate the influence of the shear rate on the solution.
This paper complements
Shape Optimization in Stationary Blood Flow:
A Numerical Study of Non-Newtonian Effects.