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Research Papers: Fundamental Issues and Canonical Flows

The Use of Dual-Number-Automatic-Differentiation With Sensitivity Analysis to Investigate Physical Models

[+] Author and Article Information
Malcolm J. Andrews

Los Alamos National Laboratory,
Los Alamos, NM 87545
e-mail: mandrews@lanl.gov

Manuscript received December 10, 2012; final manuscript received February 20, 2013; published online April 12, 2013. Assoc. Editor: Z. C. Zheng.

J. Fluids Eng 135(6), 061206 (Apr 12, 2013) (10 pages) Paper No: FE-12-1613; doi: 10.1115/1.4023788 History: Received December 10, 2012; Revised February 20, 2013

Local sensitivities are explored using dual-number-automatic-differentiation (DNAD) across three mathematical models of physical systems that have increasing complexity. The models are: (1) a model for the approach of a sphere to free fall; (2) the Taylor-analogy-breakup (TAB) model for liquid droplet atomization; and, (3) an evaluation of the BHR model of turbulence for the development of one-dimensional Rayleigh–Taylor driven material mixing. Sensitivity and functional shape parameters are developed that permit a relative study to be quickly performed for each model. Furthermore, compensating errors, measurement parameter sensitivity, and feature sensitivities are investigated. The test problems consider transient (initial condition effects), steady state (final functional forms), and measures of functional shape. Reduced model forms are explored and selected according to sensitivity. Aside from the local sensitivity studies of the models and associated results, DNAD is shown to be one of several useful, quickly implemented tools to investigate a variety of sensitivity effects in models and together with the present results may serve as a means to simplify a model or focus future model developments and associated experiments.

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References

Figures

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Fig. 1

Velocity and normalized sensitivities for case 2 of the particle drag problem

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Fig. 7

α-sensitivities using top-hat initial profiles and equilibrium initial condition coefficients (Cb,Caz,Ck,CS). Top shows the sensitivity to initial condition coefficients, and bottom shows sensitivity to BHR model coefficients (C2,C4,Ca1,Cb2,Cμ).

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Fig. 8

Execution time as a function of the number of DNAD parameters

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Fig. 2

1D Rayleigh–Taylor mixing

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Fig. 5

α-sensitivities using parabolic initial profiles and two-fluid initial condition coefficients. Top shows the sensitivity to initial condition coefficients (Cb,Caz,Ck,CS), and bottom shows sensitivity to BHR model coefficients (C2,C4,Ca1,Cb2,Cμ).

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Fig. 4

Normalized sensitivity of the length scale initial condition as a function of the initial width of the mixing zone

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Fig. 3

BHR profiles at t = 3 s using grids Nz = 1001, Nt = 1000 on the left and Nz = 2001, Nt = 2000 on the right

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Fig. 6

α-sensitivities using parabolic initial profiles and equilibrium initial condition coefficients (Cb,Caz,Ck,CS). Top shows the sensitivity to initial condition coefficients, and bottom shows sensitivity to BHR model coefficients (C2,C4,Ca1,Cb2,Cμ).

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