Nonlinear Elimination in Aerodynamic Analysis and Design Optimization

Young, David P.; Huffman, William P.; Melvin, Robin G.; Hilmes, Craig L.; Johnson, F. T.

doi:10.1007/978-3-642-55508-4_2

Cited by 20 publications

(21 citation statements)

References 17 publications

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“…However, neither thickness nor area constraints demonstrated the ability to control surface oscillations that appeared in some design cases. Young et al (2003) reported similar surface oscillations in some of their design cases and produced smoother airfoil shapes using design variables that directly parameterized the airfoil curvature. Sobieczky (1999) used mathematical functions and basic parameters such as leading-edge radius and curvature at upper and lower crest locations to address two-dimensional surface curvature in the development of the PARSEC airfoil.…”

Section: Introductionmentioning

confidence: 76%

Curvature constraints for airfoil shape optimization in turbulent flow

Kolla¹,

Yokota²,

Lassaline³

et al. 2008

Can. Aeronaut. Space J.

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Abstract. This paper illustrates how surface curvature constraints are incorporated within a two-dimensional optimization method to control geometric oscillations along aerodynamically optimized airfoils. Two treatments were developed; each bounds the surface curvature of an airfoil with upper and lower limits. The first treatment maintains the overall shape of the airfoil while minimizing the local oscillations by applying symmetric curvature bounding. The second treatment bounds an airfoil within a prescribed curvature space. It strongly controls the geometric surface oscillations; however, it does allow an airfoil to be significantly altered from its original shape versus the first method. Both treatments are effective in reducing geometric oscillations along the airfoil surface while maintaining the overall aerodynamic performance.Résumé. Dans cet article, on montre comment les contraintes de la courbure de la surface sont intégrées dans le contexte d'une méthode d'optimisation à deux dimensions pour contrôler les oscillations géométriques le long des surfaces portantes optimisées pour l'aérodynamisme. Deux traitements ont été développés, chacun fixant la courbure du profil d'aile portante dans des limites supérieures et inférieures. Le premier traitement conserve la forme de la surface portante dans son ensemble tout en minimisant les oscillations locales en appliquant une limite de courbure symétrique. Le second traitement fixe les limites de la surface portante à l'intérieur d'un espace de courbure prescrit. Ce dernier contrôle fortement les oscillations géométriques de surface, tout en permettant de transformer de façon significative la surface portante par rapport à sa forme initiale contrairement à la première méthode. Les deux traitements sont efficaces pour réduire les oscillations géométriques le long de la surface portante tout en maintenant la performance aérodynamique dans son ensemble. [Traduit par la Rédaction] 7

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Section: Introductionmentioning

confidence: 76%

Curvature constraints for airfoil shape optimization in turbulent flow

Kolla¹,

Yokota²,

Lassaline³

et al. 2008

Can. Aeronaut. Space J.

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“…The problem is a one-dimensional compressible-flow problem describing transonic flow in a duct that first narrows and then expands to form a nozzle; see Cai, Keyes, and Young [9] and Young et al [47] for more details. The PDE problem is where ρ(u) = 1 + γ−1…”

Section: A Transonic-flow Problemmentioning

confidence: 99%

“…The solution u is the potential and u x is the velocity of the flow. Following [9], [47], we take u R = 1.15 and γ = 1.4 and apply the finite-difference discretization described in those papers, using the firstorder density biasing stabilization outlined in [47]. The resulting discretized problem is very challenging for globalized Newton-like solvers, which tend to require many iterations to resolve the shock.…”

Section: A Transonic-flow Problemmentioning

confidence: 99%

Anderson Acceleration for Fixed-Point Iterations

Walker¹,

Ni²

2011

SIAM J. Numer. Anal.

441

233

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Abstract. This paper concerns an acceleration method for fixed-point iterations that originated in work of D. G. Anderson [J. Assoc. Comput. Mach., 12 (1965), pp. 547-560], which we accordingly call Anderson acceleration here. This method has enjoyed considerable success and wide usage in electronic structure computations, where it is known as Anderson mixing; however, it seems to have been untried or underexploited in many other important applications. Moreover, while other acceleration methods have been extensively studied by the mathematics and numerical analysis communities, this method has received relatively little attention from these communities over the years. A recent paper by H. Fang and Y. Saad [Numer. Linear Algebra Appl., 16 (2009), pp. 197-221] has clarified a remarkable relationship of Anderson acceleration to quasi-Newton (secant updating) methods and extended it to define a broader Anderson family of acceleration methods. In this paper, our goals are to shed additional light on Anderson acceleration and to draw further attention to its usefulness as a general tool. We first show that, on linear problems, Anderson acceleration without truncation is "essentially equivalent" in a certain sense to the generalized minimal residual (GMRES) method. We also show that the Type 1 variant in the Fang-Saad Anderson family is similarly essentially equivalent to the Arnoldi (full orthogonalization) method. We then discuss practical considerations for implementing Anderson acceleration and illustrate its performance through numerical experiments involving a variety of applications.

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“…An alternative approach that maintains the quadratic convergence of Newton's method, but allows for greater flexibility in the choice of solver for each system component is nonlinear elimination. Nonlinear elimination has been used in circuit simulation [16,23] (also called the "Two-level Newton" technique in the circuit community), aerostructures [29], and chemically reacting flows [28]. A theoretical analysis with convergence proofs can be found in [13,27].…”

Section: Nonlinear Eliminationmentioning

confidence: 99%

A theory manual for multi-physics code coupling in LIME.

Belcourt¹,

Bartlett²,

Pawlowski³

et al. 2011

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The Lightweight Integrating Multi-physics Environment (LIME) is a software package for creating multi-physics simulation codes. Its primary application space is when computer codes are currently available to solve different parts of a multi-physics problem and now need to be coupled with other such codes. In this report we define a common domain language for discussing multi-physics coupling and describe the basic theory associated with multiphysics coupling algorithms that are to be supported in LIME. We provide an assessment of coupling techniques for both steady-state and time dependent coupled systems. Example couplings are also demonstrated.iii

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Nonlinear Elimination in Aerodynamic Analysis and Design Optimization

Cited by 20 publications

References 17 publications

Curvature constraints for airfoil shape optimization in turbulent flow

Curvature constraints for airfoil shape optimization in turbulent flow

Anderson Acceleration for Fixed-Point Iterations

A theory manual for multi-physics code coupling in LIME.

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