Premium
Sensitivity of shear rate in artificial grafts using automatic differentiation
Author(s) -
Probst M.,
Lülfesmann M.,
Bücker H. M.,
Behr M.,
Bischof C. H.
Publication year - 2009
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2061
Subject(s) - solver , compressibility , sensitivity (control systems) , truncation (statistics) , truncation error , mathematics , shear rate , shear thinning , newtonian fluid , partial differential equation , generalized newtonian fluid , shear (geology) , non newtonian fluid , viscosity , mechanics , mathematical analysis , mathematical optimization , physics , materials science , engineering , thermodynamics , statistics , electronic engineering , composite material
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. Copyright © 2009 John Wiley & Sons, Ltd.