Article

Shape optimization in unsteady blood flow: a numerical study of non-Newtonian effects.

University of Pennsylvania, Mechanical Engineering and Applied Mechanics, Philadelphia, PA 19104, USA.
Computer Methods in Biomechanics and Biomedical Engineering (impact factor: 0.85). 07/2005; 8(3):201-12. DOI:10.1080/10255840512331388957
Source: PubMed

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 modified Cross 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 modified Cross model. By varying a geometric parameter in our test case, we investigate the influence of the shear rate on the solution.

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Keywords

computations
 
computed optimal shape
 
generalized Newtonian constitutive equations
 
geometric parameter
 
modified Cross model
 
Navier-Stokes equations generalized
 
Newtonian constitutive equation
 
non-Newtonian fluid
 
numerical study
 
optimal shapes
 
paper presents
 
shear rate
 
shear rate prevalent
 
shear-thinning behavior
 
unsteady pulsatile blood flow
 
varying