International Journal of Aerospace and Lightweight Structures

doi: 10.3850/S2010428612000219

A New Robust Preconditioned GMRES Algorithm for Adjoint Equation in Aerodynamic Optimization Design

Zuo Yingtao^a, Fu Lin^b and Gao Zhenghong^c National Key Laboratory of Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an, 710072 China. ^azuoyingtao@nwpu.edu.cn ^blinf1017@gmail.com ^czgao@nwpu.edu.cn

ABSTRACT

Calculation method of objective function sensitivity in aerodynamic optimization design is researched. To increase the robustness of solving discrete adjoint equation, a new method named GMRES-LU-SGS is proposed. The proposed method solves the adjoint equation implicitly by generalized minimum residual (GMRES) algorithm with a LUSGS based preconditioner. Three cases about complex configuration are tested to validate the proposed method, and the freestream Mach number ranges from subsonic to transonic condition. The results are compared with that of another two adjoint equation solving methods named GMRES-ILU(0) and LU-SGS method. Tests show that the proposed method is more robust than the other two methods, and more effective even though the adjoint equation is poorly diagonal-dominant. A wing-body configuration is optimized using gradient-based method, and the discrete adjoint equation is solved with the proposed method. The fact that objective function reduced successfully indicates the robustness of the proposed method further.

Keywords: Optimization design, Discrete adjoint, Sensitivity, GMRES-LU-SGS, Robust.

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