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Technical Briefs

Imbedded Dual-Number Automatic Differentiation for Computational Fluid Dynamics Sensitivity Analysis

[+] Author and Article Information
Robert E. Spall

e-mail: robert.spall@usu.edu

Wenbin Yu

e-mail: wenbin.yu@usu.edu
Department of Mechanical and
Aerospace Engineering,
Utah State University,
Logan, UT 84322-4130

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 3, 2012; final manuscript received July 30, 2012; published online December 21, 2012. Editor: Malcolm J. Andrews.

J. Fluids Eng 135(1), 014501 (Dec 21, 2012) (4 pages) Paper No: FE-12-1055; doi: 10.1115/1.4023074 History: Received February 03, 2012; Revised July 30, 2012

Dual number automatic differentiation was applied to two computational fluid dynamics codes, one written specifically for this purpose and one “legacy” fortran code. Results for the simple case of a fully developed laminar flow in a channel validated the approach in computing derivatives with respect to both a fluid property and a geometric dimension. DNAD was also implemented into the JET fortran program which is available with a popular turbulence modeling textbook. Mean centerline velocity derivatives for a self-similar round jet with respect to all applicable turbulence model closure coefficients for k-ω and k-ε models were obtained.

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References

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Yu, W., and Blair, M., 2010, “DNAD: A Simple Tool for Automatic Differentiation of Fortran Codes Using Dual Numbers,” Proc. 35th Annual Dayton-Cincinnati Aerospace Science Symposium, Dayton, OH.
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Rubel, A., and Melnik, R. E., 1984, “Jet, Wake and Wall Jet Solutions Using a k-ε Turbulence Model,” AIAA, Paper No. AIAA-84-1523.

Figures

Grahic Jump Location
Fig. 1

Sensitivity of streamwise velocity to dynamic viscosity for fully developed laminar flow in a two-dimensional channel

Grahic Jump Location
Fig. 2

Sensitivity of streamwise velocity to channel height

Grahic Jump Location
Fig. 3

Compute time as a function of the number of design variables

Grahic Jump Location
Fig. 4

Percent relative errors (with respect to DNAD) using finite-difference approximations for different values of the difference perturbation parameter (k-ω model results)

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