Determination of aerodynamic sensitivity coefficients based on the three-dimensional full potential equation

Elbanna, Hesham M.; Carlson, Leland A.

doi:10.2514/6.1992-2670

Cited by 13 publications

(3 citation statements)

References 3 publications

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“…The preconditioned conjugate gradient-like algorithms of Section 3.1.2.2 can be used to solve the linear systems o f aerodynamic sensitivity analysis. In this context, this method may be viewed as a preconditioned version of a second degree iterative scheme C d2z m +ooC5 z m = r |r m+1 (3.14) This class of solution methodology as applied to the aerodynamic sensitivity equation has been examined only recently [53,54,57,67,73]. Its effectiveness in the present design procedure is thoroughly investigated in Chapters 5 and 6.…”

Section: Second Degree Iterative Methodsmentioning

confidence: 99%

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Three-dimensional aerodynamic shape optimization using discrete sensitivity analysis

Burgreen

Baysal

1996

AIAA Journal

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An aerodynamic shape optimization procedure based on discrete sensitivity analysis is extended to treat three-dimensional geometries. The function of sensitivity analysis is to directly couple computational fluid dynamics (CFD) with numerical optimization techniques, which facilitates the construction of efficient direct-design methods. The development of a practical three-dimensional design procedures entails many challenges, such as: 1) the demand for significant efficiency improvements over current design methods; 2) a general and flexible three-dimensional surface representation; and 3) the efficient solution of very large systems of linear algebraic equations. It is demonstrated that each of these challenges is overcome by: .1) employing fully implicit (Newton) methods for the CFD analyses; 2) adopting a Bezier-Bernstein polynomial parameterization of two-and three-dimensional surfaces; and 3) using preconditioned conjugate gradient-like linear system solvers. Whereas each of these extensions independently yields an improvement in computational efficiency, the combined effect of implementing all the extensions simultaneously results in a significant factor of 50 decrease in computational time and a factor of eight reduction in memory over the most efficienVdesign strategies in current use.The new aerodynamic shape optimization procedure is demonstrated in the design of both two-and three-dimensional inviscid aerodynamic problems including a two-dimensional L&

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Section: Second Degree Iterative Methodsmentioning

confidence: 99%

“…The use of the low-memory preconditioned conjugate gradient-like iterative solver is another valid option [57,73,98,100,101] and is evaluated in the following subsection.…”

Section: Direct Inversion Methodsmentioning

confidence: 99%

Three-dimensional aerodynamic shape optimization using discrete sensitivity analysis

Burgreen

Baysal

1996

AIAA Journal

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“…The best method to obtain these subexpressions was to consider the governing equation and the involved intermediate expressions in the original form given in Eqs. (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14). This splitting or nesting of expressions with various intermediate dependencies declared in advance allowed each subexpression to be handled efficiently by the symbolic manipulator, in this case MACSYMA.…”

Section: Symbolic and Numerical Treatmentmentioning

confidence: 99%

Aerodynamic sensitivity coefficients using the three-dimensional full potential equation

Elbanna

Carlson

1994

Journal of Aircraft

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The quasianalytical (QA) approach is applied to the three-dimensional full potential equation to compute wing aerodynamic sensitivity coefficients in the transonic regime. Symbolic manipulation is used and is crucial in reducing the effort associated with obtaining sensitivity equations, and the large sensitivity system is solved using sparse solver routines such as the iterative conjugate gradient method. The results obtained are almost identical to those obtained by the finite difference (FD) approach and indicate that obtaining the sensitivity derivatives using the QA approach is more efficient than computing the derivatives by the FD method, especially as the number of design variables increases. It is concluded that the QA method is an efficient and accurate approach for obtaining transonic aerodynamic sensitivity coefficients in three dimensions.

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Recent Advances in Steady Compressible Aerodynamic Sensitivity Analysis

et al. 1995

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Determination of aerodynamic sensitivity coefficients based on the three-dimensional full potential equation

Cited by 13 publications

References 3 publications

Three-dimensional aerodynamic shape optimization using discrete sensitivity analysis

Three-dimensional aerodynamic shape optimization using discrete sensitivity analysis

Aerodynamic sensitivity coefficients using the three-dimensional full potential equation

Recent Advances in Steady Compressible Aerodynamic Sensitivity Analysis

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