An efficient approach to optimal aerodynamic design. I - Analytic geometry and aerodynamic sensitivities

Verhoff, A.; Stookesberry, D.; Cain, Alan B.

doi:10.2514/6.1993-99

Cited by 15 publications

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“…The orthogonality property is important since it gives completeness of the design space. This parameterization can be defined as a series of basis functions [42,36],…”

Section: Shape Parameterization By Means Of Chebyshev Polynomialsmentioning

confidence: 99%

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Adjoint-based aerodynamic shape optimization on unstructured meshes

Carpentieri

Koren

Tooren

2007

Journal of Computational Physics

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In this paper, the exact discrete adjoint of an unstructured finite-volume formulation of the Euler equations in two dimensions is derived and implemented. The adjoint equations are solved with the same implicit scheme as used for the flow equations. The scheme is modified to efficiently account for multiple functionals simultaneously. An optimization framework, which couples an analytical shape parameterization to the flow/adjoint solver and to algorithms for constrained optimization, is tested on airfoil design cases involving transonic as well as supersonic flows. The effect of some approximations in the discrete adjoint, which aim at reducing the complexity of the implementation, is shown in terms of optimization results rather than only in terms of gradient accuracy. The shape-optimization method appears to be very efficient and robust.

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“…The orthogonality property is important since it gives completeness of the design space. This parameterization can be defined as a series of basis functions [42,36],…”

Section: Shape Parameterization By Means Of Chebyshev Polynomialsmentioning

confidence: 99%

“…The shape parameterization used here is based upon orthogonal Chebyshev polynomials [42]. This parameterization is relatively unexplored in the literature [34] in spite of its interesting features.…”

Section: Introductionmentioning

confidence: 99%

Adjoint-based aerodynamic shape optimization on unstructured meshes

Carpentieri

Koren

Tooren

2007

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…The shape parameterization used here is based upon orthogonal Chebyshev polynomials. 10 This parameterization gives completeness in the design space and behaves smoothly during the optimization process even in case of large shape deformations. Shape optimization is performed by means of two algorithms.…”

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confidence: 99%