Accuracy and efficiency improvements in finite difference sensitivity calculations

Özhamam, Murat
Accuracy of the finite difference sensitivity calculations are improved by calculating the optimum finite difference interval sizes. In an aerodynamic inverse design algorithm, a compressor cascade geometry is perturbed by shape functions and finite differences sensitivity derivatives of the flow variables are calculated with respect to the base geometry flow variables. Sensitivity derivatives are used in an optimization code and a new airfoil is designed verifying given design characteristics. Accurate sensitivities are needed for optimization process. In order to find the optimum finite difference interval size, a method is investigated. Convergence error estimation techniques in iterative solutions and second derivative estimations are investigated to facilitate this method. For validation of the method, analytical sensitivity calculations of Euler equations are used and several applications are performed. Efficiency of the finite difference sensitivity calculations is improved by parallel computing. Finite difference sensitivity calculations are independent tasks in an inverse aerodynamic design algorithm and can be computed separately. Sensitivity calculations are performed on parallel processors and computing time is decreased.


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Oygür, Özgür Sinan; Kayran, Altan; Department of Aerospace Engineering (2008)
In this study, anisotropic shells of revolution subject to symmetric and unsymmetrical static loads are analysed. In derivation of governing equations to be used in the solution, first order transverse shear effects are included in the formulation. The governing equations can be listed as kinematic equations, constitutive equations, and equations of motion. The equations of motion are derived from Hamilton’s principle, the constitutive equations are developed under the assumptions of the classical laminatio...
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Akgun, MA; Haftka, RT; Wu, KC; Walsh, JL; Garcelon, JH (American Institute of Aeronautics and Astronautics (AIAA), 2001-03-01)
Adjoint sensitivity calculation of stress, buckling, and displacement constraints may be much less expensive than direct sensitivity calculation when the number of load cases is large. In general, it is more difficult to implement the adjoint method than the direct method, but it is shown that the use of the continuum adjoint method, along with homogeneity conditions, can alleviate the problem. Expressions for von Mises stress and local buckling sensitivities For isotropic plate elements are derived. Comput...
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Özyörük, Yusuf (American Institute of Aeronautics and Astronautics (AIAA), 2000-05-01)
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Seber, Guclu; Bendiksen, Oddvar O. (American Institute of Aeronautics and Astronautics (AIAA), 2008-06-01)
A fully nonlinear aeroelastic formulation of the direct Eulerian-Lagrangian computational scheme is presented in which both structural and aerodynamic nonlinearities are treated without approximations. The method is direct in the sense that the calculations are done at the finite element level, both in the fluid and structural domains, and the fluid-structure system is time-marched as a single dynamic system using a multistage Runge-Kutta scheme. The exact nonlinear boundary condition at the fluid-structure...
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Citation Formats
M. Özhamam, “Accuracy and efficiency improvements in finite difference sensitivity calculations,” M.S. - Master of Science, Middle East Technical University, 2007.