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Airfoil design optimization based on lattice Boltzmann method and adjoint approach

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Abstract

We present a new aerodynamic design method based on the lattice Boltzmann method (LBM) and the adjoint approach. The flow field and the adjoint equation are numerically simulated by the GILBM (generalized form of interpolation supplemented LBM) on non-uniform meshes. The first-order approximation for the equilibrium distribution function on the boundary is proposed to diminish the singularity of boundary conditions. Further, a new treatment of the solid boundary in the LBM is described particularly for the airfoil optimization design problem. For a given objective function, the adjoint equation and its boundary conditions are derived analytically. The feasibility and accuracy of the new approach have been perfectly validated by the design optimization of NACA0012 airfoil.

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Authors and Affiliations

  1. Research Institute of Unmanned Surface Vehicles Engineering, Shanghai University, Shanghai, 200072, China

    Xiaowei Li & Yan Peng

  2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072, China

    Liang Fang

Authors
  1. Xiaowei Li
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  2. Liang Fang
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  3. Yan Peng
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Correspondence to Xiaowei Li.

Additional information

Project supported by the National Basic Research Program of China (No. 2014CB744100), the National Natural Science Foundation of China (Nos. 61403245 and 91648119), and the Shanghai Municipal Science and Technology Commision (No. 14500500400)

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Li, X., Fang, L. & Peng, Y. Airfoil design optimization based on lattice Boltzmann method and adjoint approach. Appl. Math. Mech.-Engl. Ed. 39, 891–904 (2018). https://doi.org/10.1007/s10483-018-2333-9

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  • DOI: https://doi.org/10.1007/s10483-018-2333-9

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

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