Design Sensitivity Analysis

We investigate the influence of the fluid constitutive model on the outcome of shape optimization tasks, motivated by optimal design problems in biomedical engineering. 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. The generalized Newtonian treatment exhibits striking differences in the velocity field for smaller shear rates. We apply sensitivity-based optimization procedure to a flow through an idealized arterial graft. For this problem we study the influence of the inflow velocity, and thus the shear rate. Furthermore, we introduce an additional factor in the form of a geometric parameter, and study its effect on the optimal shape obtained.

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“…Other approaches are possible. We refer to (Stanley and Stewart 2002, Gunzburger 2003) for more details.…”

Section: Gradient Computationmentioning

confidence: 99%

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

Abraham

Behr

Heinkenschloss

2005

Computer Methods in Biomechanics and Biomedical Engineering

150

132

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“…The SEM requires that the original governing equation(s) of a given system, as well as the boundary and initial conditions, be differentiated with respect to the design parameters prior to discretization [2,6,33]. The new set of equations for the sensitivity parameters may be solved by implementing the same numeric algorithms and techniques as used with the original governing equations.…”

Section: Sensitivity Equation Methodsmentioning

confidence: 99%

“…In this study, the numerical method used to solve (6) and (7) is a projection method, also known as a fractional-step or time-splitting method, first proposed by Harlow and Welch [35] and Chorin [36], and applied to canonical CFD problems using finite volumes by Kim and Moin [37].…”

Section: Cfd Methodsmentioning

confidence: 99%

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Sensitivity analysis of low Reynolds number channel flow using the finite volume method

Kirkman

Metzger

2007

Numerical Methods in Fluids

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SUMMARYAn unsteady finite volume-based fractional step algorithm solved on a staggered grid has been developed for computing design sensitivity parameters in two-dimensional flows. Verification of the numerical code is performed for the case of low Reynolds number, pressure-driven flow through a straight channel, which has an exact steady-state solution to the Navier-Stokes equations. Sensitivity of the flow to the channel height, fluid viscosity, and imposed pressure gradient is considered. Three different numerical techniques for computing the design sensitivity parameters: finite difference, complex-step differentiation, and sensitivity equation method (SEM), are compared in terms of numerical error (relative to the exact solution), computational expense, and ease of implementation. Results indicate that, of all the three methods, complex step is the most accurate and requires the least computational time. In addition, treatment of the boundary conditions in SEM is addressed, within the framework of the present finite volume approach, with special attention given to parameter dependence in the boundary conditions. Error estimation based on the Grid Convergence Index provides a good indication of the exact error in the SEM solutions. An example of application of the use of sensitivity parameters to estimate the propagation of input uncertainty through the numerical simulation is also provided.

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“…Indeed, textbooks have been written on sensitivity analysis of structures (Kleiber et al, 1997;Haug et al, 1986). To our knowledge there is only one book on sensitivity analysis of flow problems (Stanley et al, 2001). It is recent and more specialized than structural mechanics books.…”

Section: Introductionmentioning

confidence: 99%

The sensitivity equation method in fluid mechanics

Pelletier

Hay

Étienne

et al. 2008

TECM

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We present the sensitivity Equation Method (SEM) as a complementary tool to adjoint based optimisation methods. Flow sensitivities exist independently of a design problem and can be used in several non-optimization ways: characterization of complex flows, fast evaluation of flows on nearby geometries, and input data uncertainties cascade through the CFD code to yield uncertainty estimates of the flow field. The Navier-Stokes and sensitivity equationssensitivity are solved by an adaptive finite element method.

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Design Sensitivity Analysis

Cited by 46 publications

References 0 publications

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

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

Sensitivity analysis of low Reynolds number channel flow using the finite volume method

The sensitivity equation method in fluid mechanics

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