Sensitivity of shear rate in artificial grafts using automatic differentiation.

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.