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A reduced-order model for gradient-based aerodynamic shape optimisation

Yao, Weigang, Marques, Simao, Robinson, Trevor, Armstrong, Cecil and Sun, Liang (2020) A reduced-order model for gradient-based aerodynamic shape optimisation Aerospace Science and Technology, 106, 106120.

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This work presents a reduced order model for gradient based aerodynamic shape optimization. The solution of the fluid Euler equations is converted to reduced Newton iterations by using the Least Squares Petrov-Galerkin projection. The reduced order basis is extracted by Proper Orthogonal Decomposition from snapshots based on the fluid state. The formulation distinguishes itself by obtaining the snapshots for all design parameters by solving a linear system of equations. Similarly, the reduced gradient formulation is derived by projecting the full-order model state onto the subspace spanned by the reduced basis. Auto-differentiation is used to evaluate the reduced Jacobian without forming the full fluid Jacobian explicitly during the reduced Newton iterations. Throughout the optimisation trajectory, the residual of the reduced Newton iterations is used as an indicator to update the snapshots and enrich the reduced order basis. The resulting multi-fidelity optimisation problem is managed by a trust-region algorithm. The ROM is demonstrated for a subsonic inverse design problem and for an aerofoil drag minimization problem in the transonic regime. The results suggest that the proposed algorithm is capable of aerodynamic shape optimization while reducing the number of full-order model queries and time to solution with respect to an adjoint gradient based optimisation framework.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mechanical Engineering Sciences
Authors :
Yao, Weigang
Robinson, Trevor
Armstrong, Cecil
Sun, Liang
Date : November 2020
Funders : Engineering and Physical Sciences Research Council (EPSRC)
DOI : 10.1016/j.ast.2020.106120
Uncontrolled Keywords : ROM; CFD; Aerodynamics; Shape optimisation; Gradient-based optimisation; Trust-region
Depositing User : Clive Harris
Date Deposited : 16 Sep 2020 23:00
Last Modified : 16 Sep 2020 23:00

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