The purpose of this paper is to investigate the characteristics of an adjoint-based aerodynamic shape optimization on non-hody-fitted meshes. The shape sensitivities are computed on non-body-fitted hierarchical Cartesian meshes with the immerscd-boundary method (IBM). In our approach, all of the computational domain consists of similar square cells and the shape sensitivities on the mesh arc kept zero. Thus, the mesh sensitivity calculation, the differentiation of the linear reconstruction method, and the spatial gradient calculation with respect to the mesh are eliminated. The effect due to the variation of the shape appears only through the wall boundary condition defined by the IBM. The shape sensitivity calculation algorithm becomes simple compared with that on the body-fitted meshes. An adjoint solver based on the Cartesian-based mesh generator and flow solver (UTCart) is developed to demonstrate this aspect. To verify the possibility of non-body-fitted meshes for shape optimization, a benchmark problem (Case 1) from the AIAA Aerodynamic Design Optimization Discussion Group (ADODG) is solved to show the ability of the current approach. The problem is solved automatically, generating meshes at each design iteration. The optimization results show good agreement with the past researches.
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