Discrete shape sensitivity equations for aerodynamic problems

Hou, Gene; Taylor, Arthur C.; Korivi, Vamshi

doi:10.1002/nme.1620371307

Cited by 33 publications

(2 citation statements)

References 16 publications

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“…A description of these techniques can be found in Refs. [6,16,17], and in the references contained therein. Of particular interest in the present context are adjoint methods.…”

Section: Introductionmentioning

confidence: 99%

Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations

1999

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A continuous adjoint approach for obtaining sensitivity derivatives on unstructured grids is developed and analyzed. The derivation of the costate equations is presented, and a second-order accurate discretization method is described. The relationship between the continuous formulation and a discrete formulation is explored for inviscid, as well as for viscous¯ow. Several limitations in a strict adherence to the continuous approach are uncovered, and an approach that circumvents these diculties is presented. The issue of grid sensitivities, which do not arise naturally in the continuous formulation, is investigated and is observed to be of importance when dealing with geometric singularities. A method is described for modifying inviscid and viscous meshes during the design cycle to accommodate changes in the surface shape. The accuracy of the sensitivity derivatives is established by comparing with ®nite-dierence gradients and several design examples are presented. #

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“…A description of these techniques can be found in Refs. [6,16,17], and in the references contained therein. Of particular interest in the present context are adjoint methods.…”

Section: Introductionmentioning

confidence: 99%

Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations

1999

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“…In order to evaluate the constraints and objective function in 10, we first solve for U 1 , U 2 individually from the equations W1(Xv, X12; Ui) = 0 W2(XD, X21; U2) = 0. (11) Note that this formulation allows us to use existing individual discipline solvers for W; because Xv and X;j are the normal inputs and U; is the normal output of such codes. The number of optimization variables is nv + L n, 1 , which would be the same number as the i,j#,i AAO method if every variable from a given discipline were communicated to every other discipline.…”

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confidence: 99%

On alternative problem formulations for multidisciplinary design optimization

Cramer¹,

Frank²,

Shubin³

et al. 1992

4th Symposium on Multidisciplinary Analysis and Optimization

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In this paper we introduce a perspective on multidisciplinary design optimization (MOO) problem formulation that provides a basis for choosing among existing formulations and suggests provocative, new ones. MOO problems offer a richer spectrum of possibilities for problem formulation than do single discipline design optimization problems, or multidisciplinary analysis problems. This is because the variables and the equations that characterize the MOO problem can be "partitioned" in some interesting ways between what we traditionally think of as the "analysis code(s)" and the "optimization code." An MOO approach can be characterized by what part of the overall computation is done in each code, how that computation is done, and what information is communicated between the codes.The key issue in the three fundamental approaches to MOO formulation that we discuss is the kind of feasibility that is maintained at each optimization iteration. In the most familiar "multidisciplinary feasible" approach, the multidisciplinary analysis problem is solved at each optimization iteration. At the other end of the spectrum is the "all-at-once" approach where feasibility happens only at optimization convergence. Between these extremes lie other, new, possibilities that amount to maintaining feasibility of the individual analysis disciplines at each optimization iteration, while allowing the optimizer to drive the computation toward multidisciplinary feasibility as convergence is approached.There are further considerations completing the classification such as how the optimization is actually done,• Senior Member AIAA 518 how sensitivity information is computed from each discipline, and how, if necessary, individual gradients are combined to obtain overall problem gradients. This view of MOO problem formulation highlights the trade-offs between reuse of existing software, computing resources required, and probability of success.

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Optimal design of paper machine headboxes

Hämäläinen

Mäkinen

Tarvainen

2000

Int. J. Numer. Meth. Fluids

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A shape optimization problem for incompressible flows within a stabilized finite element framework is studied. The goal is to develop and test numerical realizations of optimal shape design problems that could be applied to non‐trivial industrial problems. The resulting algorithm is applied to the optimization of the geometry of a tapered header in a paper machine headbox. Copyright © 2000 John Wiley & Sons, Ltd.

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Discrete shape sensitivity equations for aerodynamic problems

Cited by 33 publications

References 16 publications

Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations

Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations

On alternative problem formulations for multidisciplinary design optimization

Optimal design of paper machine headboxes

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