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.

Issue Section:
Technical Briefs
Topics:
Computational fluid dynamics, Sensitivity analysis, Turbulence, FORTRAN, Laminar flow, Errors, Approximation, Fluids

References

1.
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.
2.
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
.10.1108/09615530410544292
Google Scholar
Crossref
Search ADS
 
3.
Giles
,
M. B.
, and
Pierce
,
N. A.
,
2000
, “
An Introduction to the Adjoint Approach to Design
,”
Flow Turbulence Combust.
,
65
, pp.
393
–
415
.10.1023/A:1011430410075
Google Scholar
Crossref
Search ADS
 
4.
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.
5.
Griewank
,
A.
,
2000
,
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
,
SIAM
,
Philadelphia, PA
.
6.
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
.10.1115/1.2720475
Google Scholar
Crossref
Search ADS
 
7.
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
.
8.
Wilcox
,
D. C.
,
2006
,
Turbulence Modeling for CFD
, DCW Industries, Inc., La Canada, CA, Chap. 4.
9.
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.
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