Aerodynamic Shape Optimization Using Symbolic Sensitivity Analysis

Ali Elham, Michel van Tooren

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

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Abstract

The least-squares finite element method is used to solve the compressible Euler equations around airfoils in transonic regime. The symbolic analysis method is used to generate the element stiffness and force matrices. The equations of the element matrices are derived symbolically based on the flow primitive variables and the position of the element nodes. The symbolic analysis is also used to compute the exact derivatives of the residuals with respect to both design variables (e.g. the airfoil geometry) and the state variables (e.g. the flow velocity). The symbolic analysis allows to compute the exact Jacobian of the governing equations in a computationally efficient way, which is used for Newton iteration. Besides, using the symbolic analysis the sensitivities of the outputs, such as the airfoil drag, with respect to the design variables, such as the airfoil geometry, are computed using the discrete adjoint method without the need for automatic differentiation. This makes the analysis and optimization computationally more efficient.
Original languageEnglish
Title of host publication58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
Subtitle of host publicationGrapevine, Texas, USA
PublisherAmerican Institute of Aeronautics and Astronautics Inc. (AIAA)
Number of pages16
ISBN (Electronic)978-1-62410-453-4
DOIs
Publication statusPublished - 2017
Event58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference - Grapevine, United States
Duration: 9 Jan 201713 Jan 2017
Conference number: 58
http://arc.aiaa.org/doi/book/10.2514/MSDM17

Conference

Conference58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
CountryUnited States
CityGrapevine
Period9/01/1713/01/17
Internet address

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