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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Adams, B. M., Bohnhoff, W. J., Dalbey, K. R., Eddy, J. P., Eldred, M. S., Gay, D. M., Haskell, K., Hough, P. D., and Swiler, L. P., 2010, “DAKOTA, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 5.0 User's Manual,” Sandia Technical Report No. SAND2010-2183.
Soto, O., Lohner, R., and Yang, C., 2004, “An Adjoint-Based Design Methodology for CFD Problems,” Int. J. Numer. Methods Heat Fluid Flow, 14, pp. 734–759. [CrossRef]
Giles, M. B., and Pierce, N. A., 2000, “An Introduction to the Adjoint Approach to Design,” Flow Turbulence Combust., 65, pp. 393–415. [CrossRef]
Martins, J., Sturdza, P., and Alonso, J., 2001, “The Connection Between the Complex-Step Derivative Approximation and Algorithmic Differentiation,” AIAA, Paper No. AIAA-2001-0921.
Griewank, A., 2000, Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, SIAM, Philadelphia, PA.
Bischof, C. H., Bucker, H. M., Rasch, A., Slusanschi, E., and Lang, B., 2007, “Automatic Differentiation if the General-Purpose Computational Fluid Dynamics Package FLUENT,” ASME J. Fluids Eng., 129(5), pp. 652–658. [CrossRef]
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.
Wilcox, D. C., 2006, Turbulence Modeling for CFD, DCW Industries, Inc., La Canada, CA, Chap. 4.
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.


Grahic Jump Location
Fig. 2

Sensitivity of streamwise velocity to channel height

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. 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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