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

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.

Keywords:

• Newtonian effects
• Arterial graft geometry
• Navier–Stokes equations
• Non-Newtonian fluid

Acknowledgements

The authors gratefully acknowledge computing resources provided by the NSF MRI award EIA-0116289. This work was supported by the National Science Foundation under award ACI-0121360, CTS-ITR-0312764, and by Texas ATP grant 003604-0011-2001.