Numerical sensitivity analysis for aerodynamic optimization

Review

Numerical sensitivity analysis for aerodynamic optimization:A survey of approaches

Jacques E.V.Peter a ,Richard P.Dwight b,*

a ONERA BP 72–29av.de la Division Leclerc,92322Chatillon Cedex,France b

Aerodynamics Group,TU Delft,P.O.Box 5058,2600GB Delft,The Netherlands

a r t i c l e i n f o Article history:

Received 19November 2007

Received in revised form 21July 2009Accepted 24September 2009Available online 6October 2009Keywords:

Sensitivity analysis

Linearized Navier–Stokes Flow solver linearization Adjoint method

Duality preserving iteration Krylov stabilization

Aerodynamic optimization

a b s t r a c t

The calculation of the derivatives of output quantities of aerodynamic ?ow codes,commonly known as numerical sensitivity analysis,has recently become of increased importance for a variety of applications in ?ow analysis,but the original motivation came from the ?eld of aerodynamic shape optimization.There the large numbers of design variables needed to parameterize surfaces in 3D necessitates the use of gradient-based optimization algorithms,and hence ef?cient and accurate evaluation of gradients.In this context over the last 20years a variety of approaches have been developed to supply these gradi-ents,raising particular challenges that have required novel algorithms.In this paper,we examine the his-torical development of these approaches,describe in some detail the theoretical background of each major method and the associated numerical techniques required to make them practical in an engineer-ing setting.We give examples from our own experience and describe what we consider to be the state-of-the-art in these methods,including their application to optimization of complex 3D aircraft con?gurations.

ó2009Elsevier Ltd.All rights reserved.

Contents 1.Introduction (374)

2.

Sensitivity evaluation methods ..........................................................................................3752.1.Finite differences................................................................................................3752.2.The discrete direct method........................................................................................3762.3.The discrete adjoint method.......................................................................................3762.4.Evaluation of discrete Jacobians....................................................................................3762.5.Derivation of the continuous adjoint equations .......................................................................3772.6.Spatial discretization of the continuous adjoint equations...............................................................3782.7.Discrete versus continuous adjoint .................................................................................3793.

Accuracy of sensitivity computations .....................................................................................3793.1.Fully linearized or frozen turbulence modeling .......................................................................3803.2.Other approximations............................................................................................3803.3.Impact on,and influence of gradient accuracy ........................................................................3814.

Solution strategies for the primal and adjoint equations .....................................................................3814.1.Duality preserving fixed-point iterations.............................................................................3824.2.Krylov stabilization ..............................................................................................3835.

Generalizations of gradient evaluation....................................................................................3845.1.Adjoint mesh deformation ........................................................................................3845.2.Higher-order derivatives using discrete methods ......................................................................

3845.2.1.DD.DD .................................................................................................3855.2.2.DD.AV .................................................................................................3855.2.3.AV.DD .................................................................................................3855.2.4.AV.AV .................................................................................................3855.2.5.Applications ............................................................................................

385

0045-7930/$-see front matter ó2009Elsevier Ltd.All rights reserved.doi:10.1016/0f9759e85ef7ba0d4a733b0ep?uid.2009.09.013

*Corresponding author.

E-mail addresses:jacques.peter@onera.fr (J.E.V.Peter),r.p.dwight@tudelft.nl (R.P.Dwight).Computers &Fluids 39(2010)

373–391

Contents lists available at ScienceDirect

Computers &Fluids

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5.3.Extension to aeroelasticity (386)

6.Examples of sensitivity applications (386)

6.1.Navier–Stokes optimization of a wing–fuselage configuration (387)

6.2.Multi-disciplinary optimization of an engine pylon (388)

7.Conclusion (389)

Acknowledgments (389)

References (389)

1.Introduction

In1987,Sobieszczanski-Sobieski,a specialist in multi-disciplin-ary optimization working at NASA,made a plea to the CFD commu-nity,to extend their codes from simple aerodynamic analysis to sensitivity analysis[1],by which he meant evaluation of the deriv-atives of aerodynamic quantities(typically depending on both geometry and?ow)with respect to some parameterization of the geometry.Such an evaluation is demanding bec …… 此处隐藏：86009字，全部文档内容请下载后查看。喜欢就下载吧 ……