Airfoil design optimization based on lattice Boltzmann method and adjoint approach  

作　　者：Xiaowei LI Liang FANG Yan PENG 

机构地区：[1]Research Institute of Unmanned Surface Vehicles Engineering,Shanghai University [2]Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2018年第6期891-904,共14页应用数学和力学（英文版）

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

摘　　要：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 dis- tribution 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 par- ticularly 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.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 dis- tribution 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 par- ticularly 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.

关 键 词：lattice Boltzmann method （LBM） adjoint approach boundary treatment aerodynamic design optimization 

分 类 号：O35[理学—流体力学]