Aerodynamic shape optimization of supersonic aircraft configurations via an adjoint formulation on distributed memory parallel computers

Reuther, James; Alonso, Juan J.; Rimlinger, Mark J.; Jameson, Antony

doi:10.1016/s0045-7930(98)00050-4

Cited by 81 publications

(50 citation statements)

References 34 publications

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“…Many of the methods that have been developed for a deforming mesh are either algebraic [1,15], iterative [3], or analytical [2]. The algebraic and analytical methods while relatively inexpensive to run, are limited to small amplitude motions.…”

Section: Grid Deformation Methodsmentioning

confidence: 99%

“…Let F , G, H be the parameterized values of a grid point in the I, J, and K indices. The 1-D TFI in the K-direction is simply (2) where ∆E refers to the deformation of an edge, which in this example varies in the k-index, while P 1,1,1 and ∆P 1,1,kmax are the deformations of the two corner points of the edge. The 2-D TFI is defined as (for a surface in the I=1 plane):…”

Section: Single Block Approachmentioning

confidence: 99%

“…Reliable deforming grid algorithms are also useful for aerodynamic shape optimization studies. Jones and SamarehAbolhassani [1] and Reuter, et al [2] developed structured grid generation systems for multi-disciplinary design optimization use. Robinson, Batina and Yang [3] proposed a deforming method which is applicable for structured and unstructured grids for flutter calculations.…”

Section: Introductionmentioning

confidence: 99%

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Unsteady flow calculations with a multi-block moving mesh algorithm

Wong¹,

Tsai²,

Cai³

et al. 2000

38th Aerospace Sciences Meeting and Exhibit

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An effective dynamic moving mesh algorithm suitable for multiblock parallel unsteady flow calculations using body fitted grids is presented in this paper. The moving grid algorithm within each block uses a method of arc-length based transfinite interpolation which is performed independently on local processors where the blocks reside. A spring network approach is used to determine the motion of the corner points of the blocks which may be connected in an unstructured fashion in a general multi-block method. A smoothing operator is applied to the points of the block face boundaries and edges in order to maintain grid smoothness and grid angles. A multi-block parallel Euler/Navier-Stokes solver using multigrid and dual-time stepping is developed along with the moving mesh method. Computational results are presented for the unsteady flow calculations of airfoils and wings with deforming shapes as found in flutter simulations.

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Section: Grid Deformation Methodsmentioning

confidence: 99%

Section: Single Block Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Unsteady flow calculations with a multi-block moving mesh algorithm

Wong¹,

Tsai²,

Cai³

et al. 2000

38th Aerospace Sciences Meeting and Exhibit

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“…A strain energy function U is defined in terms of traction and displacement as Expressed in discretized form for numerical implementation, equation (9) takes the form where u e and t e denote, respectively, the displacements and tractions at the nodal points of a boundary element, and, N c is the interpolation (shape) function and J the Jacobian of transformation between global and local coordinates. Rewriting (10) For a given set of displacement vectors [u i ] at internal points, the strain energy function U is to be minimized so as to avoid undue deformation of the structure. This is a constrained quadratic minimization problem that can be solved using the Lagrange multiplier technique.…”

Section: Constructing the Spline Matrixmentioning

confidence: 99%

Application of Spline Matrix for Mesh Deformation with Dynamic Multi-Block Grids

Lai

Tsai

Liu

2003

21st AIAA Applied Aerodynamics Conference

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“…14,17 This work is largely based on algorithms developed for Aerodynamic Shape Optimization (ASO) for a steady flow environment. 6,8,15,18,19 Nadarajah derived and applied the time accurate adjoint equations (both the continuous and discrete) to the redesign of an oscillating airfoil in an inviscid transonic flow. The redesigned shape achieved a reduction in the time-averaged drag while maintaining the time-averaged lift.…”

Section: Introductionmentioning

confidence: 99%

Optimum Shape Design for Unsteady Three-Dimensional Viscous Flows Using a Nonlinear Frequency-Domain Method

Nadarajah

Jameson

2007

Journal of Aircraft

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This paper presents an adjoint method for the optimum shape design of unsteady three-dimensional viscous flows. The goal is to develop a set of discrete unsteady adjoint equations and the corresponding boundary condition for the non-linear frequency domain method. First, this paper presents the complete formulation of the time dependent optimal design problem. Second, we present the non-linear frequency domain adjoint equations for three-dimensional viscous transonic flows. Third, we present results that demonstrate the application of the theory to a three-dimensional wing.

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Aerodynamic shape optimization of supersonic aircraft configurations via an adjoint formulation on distributed memory parallel computers

Cited by 81 publications

References 34 publications

Unsteady flow calculations with a multi-block moving mesh algorithm

Unsteady flow calculations with a multi-block moving mesh algorithm

Application of Spline Matrix for Mesh Deformation with Dynamic Multi-Block Grids

Optimum Shape Design for Unsteady Three-Dimensional Viscous Flows Using a Nonlinear Frequency-Domain Method

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