Abstract
These Lecture Notes review the formulation and application of optimization techniques based on control theory for aerodynamic shape design in both inviscid and viscous compressible flow. The theory is applied to a system defined by the partial differential equations of the flow, with the boundary shape acting as the control. The Frechet derivative of the cost function is determined via the solution of an adjoint partial differential equation, and the boundary shape is then modified in a direction of descent. This process is repeated until an optimum solution is approached. Each design cycle requires the numerical solution of both the flow and the adjoint equations, leading to a computational cost roughly equal to the cost of two flow solutions. Representative results are presented for viscous optimization of transonic wing-body combinations and inviscid optimization of complex configurations.
Keywords
- AIAA Paper
- Lift Coefficient
- Adjoint Equation
- Design Cycle
- Aerodynamic Design
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Jameson, A., Martinelli, L. (2000). Aerodynamic shape optimization techniques based on control theory. In: Burkard, R.E., et al. Computational Mathematics Driven by Industrial Problems. Lecture Notes in Mathematics, vol 1739. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0103920
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DOI: https://doi.org/10.1007/BFb0103920
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