Publication: Sensitivity of Shear Rate in Artificial Grafts Using Automatic Differentiation
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Sensitivity of Shear Rate in Artificial Grafts Using Automatic Differentiation

- Article in a journal -
 

Author(s)
M. Probst , M. Lülfesmann , H. M. Bücker , M. Behr , C. H. Bischof

Published in
International Journal for Numerical Methods in Fluids

Year
2010

Abstract
An accurate numerical simulation of blood requires the solution of incompressible Navier-Stokes equations coupled with specific constitutive models. We consider a generalized Newtonian fluid model in which viscosity depends on shear rate, accounting for the shear-thinning behavior of blood. Previous work on the design of an artificial graft indicated that there is an influence of the fluid model on the solution of the partial differential equation-constrained shape optimization problem. Therefore, we carry out a sensitivity analysis of the actual implementation of the flow solver using automatic differentiation (ad). We compare the sensitivities of shear rate with respect to viscosity for different configurations and validate the truncation-error-free sensitivities obtained from ad with those based on divided differencing and, if available, with analytic derivatives.

AD Tools
ADIFOR

AD Theory and Techniques
Hierarchical Approach

BibTeX
@ARTICLE{
         Probst2010SoS,
       author = "M. Probst and M. L{\"u}lfesmann and H. M. B{\"u}cker and M. Behr
         and C. H. Bischof",
       title = "Sensitivity of Shear Rate in Artificial Grafts Using Automatic Differentiation",
       journal = "International Journal for Numerical Methods in Fluids",
       pages = "1047--1062",
       doi = "10.1002/fld.2061",
       abstract = "An accurate numerical simulation of blood requires the solution of incompressible
         Navier-Stokes equations coupled with specific constitutive models. We consider a generalized
         Newtonian fluid model in which viscosity depends on shear rate, accounting for the shear-thinning
         behavior of blood. Previous work on the design of an artificial graft indicated that there is an
         influence of the fluid model on the solution of the partial differential equation-constrained shape
         optimization problem. Therefore, we carry out a sensitivity analysis of the actual implementation of
         the flow solver using automatic differentiation (AD). We compare the sensitivities of shear rate
         with respect to viscosity for different configurations and validate the truncation-error-free
         sensitivities obtained from AD with those based on divided differencing and, if available, with
         analytic derivatives.",
       year = "2010",
       volume = "62",
       number = "9",
       ad_tools = "ADIFOR",
       ad_theotech = "Hierarchical Approach"
}


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