The optimal control of unsteady flows with a discrete adjoint method

Rumpfkeil, Markus P.; Zingg, David W.

doi:10.1007/s11081-008-9035-5

Cited by 57 publications

(33 citation statements)

References 36 publications

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“…Because the adjoint equations depend on the states themselves, we must store the complete time history of the states when the time-dependent solution of the states is obtained. More details on the time-dependent adjoint method and proposed solutions to handle the memory requirements have been presented by various authors [58,81,96].…”

Section: Derivation From Unifying Chain Rulementioning

confidence: 99%

Review and Unification of Methods for Computing Derivatives of Multidisciplinary Computational Models

2013

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. Review and unification of methods for computing derivatives of multidisciplinary computational models. AIAA Journal, 51(11):2582-2599. doi:10.2514 Abstract This paper presents a review of all existing discrete methods for computing the derivatives of computational models within a unified mathematical framework. This framework hinges on a new equationthe unifying chain rule-from which all the methods can be derived. The computation of derivatives is described as a two-step process: the evaluation of the partial derivatives and the computation of the total derivatives, which are dependent on the partial derivatives. Finite differences, the complex-step method, and symbolic differentiation are discussed as options for computing the partial derivatives. It is shown that these are building blocks with which the total derivatives can be assembled using algorithmic differentiation, the direct and adjoint methods, and coupled analytic methods for multidisciplinary systems. Each of these methods is presented and applied to a common numerical example to demonstrate and compare the various approaches. The paper ends with a discussion of current challenges and possible future research directions in this field.

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Section: Derivation From Unifying Chain Rulementioning

confidence: 99%

Review and Unification of Methods for Computing Derivatives of Multidisciplinary Computational Models

2013

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“…Unfortunately, computing the stability derivatives with a full time-dependent solution in order to include that information would be extremely expensive. Several authors have examined the use of adjoint methods in time-dependent optimizations, both in two dimensions [33,34,35] and three dimensions [36,37]. While the timedependent adjoint method is certainly an improvement over finite-difference sensitivity methods, it still incurs a high computational cost.…”

Section: Considerations For Optimizationmentioning

confidence: 99%

Computing Stability Derivatives and Their Gradients for Aerodynamic Shape Optimization

Mader

Martins

2014

AIAA Journal

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“…Nadarajah and Jameson [15] and Nadarajah et al [16] developed a continuous adjoint approach for control and design optimization of unsteady and periodic phenomena. Rumpfkeil and Zingg [17] developed a discrete adjoint approach for time-dependent aerodynamic flows. They later applied their framework to minimize noise from the blunt trailing edge of an airfoil [18].…”

Section: Literature Reviewmentioning

confidence: 99%

An Adjoint-based Derivative Evaluation Method for Time-dependent Aeroelastic Optimization of Flexible Aircraft

Kennedy

Martins²

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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The goal of this paper is to develop techniques to enable the use of aeroelastic constraints within a high-fidelity design optimization framework. As a first-step towards this goal we have developed a fully-coupled aeroelastic analysis tool that includes a coupled structural and aerodynamic analysis as well as rigid-body degrees of freedom. This work departs from previous efforts in two important ways: first, we use solution techniques that are tailored for high-performance parallel computing; second, we implement a fully-coupled adjoint method using a coupled-Krylov approach for the evaluation of derivatives of time-dependent functions of interest. The coupled Newton-Krylov approach enables us to perform simulations in the full structural space without modal reduction. The timedependent adjoint approach enables us to evaluate the gradient of functions of interest for cases with hundreds or thousands of design variables in a cost similar to the time-dependent simulation. In order to demonstrate our framework, we verify the gradient accuracy of some preliminary simulations of three transport aircraft wings with increasing span subject to gust loads.

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The optimal control of unsteady flows with a discrete adjoint method

Cited by 57 publications

References 36 publications

Review and Unification of Methods for Computing Derivatives of Multidisciplinary Computational Models

Review and Unification of Methods for Computing Derivatives of Multidisciplinary Computational Models

Computing Stability Derivatives and Their Gradients for Aerodynamic Shape Optimization

An Adjoint-based Derivative Evaluation Method for Time-dependent Aeroelastic Optimization of Flexible Aircraft

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