Sensitivity Derivatives for Advanced CFD Algorithm and Viscous Modeling Parameters via Automatic Differentiation
✍ Scribed by Lawrence L Green; Perry A Newman; Kara J Haigler
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 337 KB
- Volume
- 125
- Category
- Article
- ISSN
- 0021-9991
No coin nor oath required. For personal study only.
✦ Synopsis
The computational technique of automatic differentiation (AD) is applied to a complicated computer program to illustrate the simplicto achieve some optimal or constrained condition. Numerity, efficiency, and versatility of AD with complex algorithms for ous examples with SA used in such a context can be found use within a sensitivity analysis. Many algorithmic and physics mod-[1-9], including several examples of multidisciplinary deeling coefficients appear in computer programs that are routinely sign optimization (MDO). The current study is relevant set in an ad hoc manner; AD can be used to enhance computer programs with derivative information suitable for guiding formal to SA used in the former context as an aid in improving sensitivity analyses, which allows these coefficient values to be the accuracy of physical approximations and numerical alchosen in a rigorous manner to achieve particular program propergorithms.
ties such as an improved convergence rate or improved accuracy.
The use of SA depends upon the SD matrix that has
In this paper, AD is applied to a three-dimensional thin-layer Navier-Stokes multigrid flow solver to assess the feasibility and computabeen computed in the past by divided differences (DD), tional impact of obtaining exact sensitivity derivatives with respect direct differentiation (handcoding), or symbolic manipulato algorithmic and physics modeling parameters typical of those tion; the method used depends upon the complexity of the needed for sensitivity analyses. Calculations are performed for an system to be modeled. However, when the system includes ONERA M6 wing in transonic flow with both the Baldwin-Lomax and Johnson-King turbulence models. The wing lift, drag, and an advanced three-dimensional (3D) computational fluid pitching moment coefficients are differentiated with respect to two dynamics (CFD) model, all of these differentiation methdifferent groups of input parameters. The first group consists of the ods have serious drawbacks, and few SA's for advanced second-and fourth-order damping coefficients of the computational 3D CFD models have been attempted until recently. Realgorithm, whereas the second group consists of two parameters sults from the first application of automatic differentiation in the viscous turbulent flow physics modeling. Results obtained via AD are compared for both accuracy and computational efficiency (AD) to advanced CFD codes to obtain SD's have been with the results obtained with divided differences (DD). The AD reported recently [10]. That work demonstrated the feasiresults are accurate, extremely simple to obtain, and show signifibility of obtaining the exact nongeometric SD's of the wing cant computational advantage over those obtained by DD for C L , C D , and C M with respect to M, Ͱ, and Re from a some cases.
complex state-of-the-art 3D thin-layer Navier-Stokes flow code (TLNS3D, ). The emphasis and direction of that initial work continues in order to demonstrate that SD's 313