A Shape Optimization Method of A Body Located in Viscous Flow using Acoustic Velocity

The purpose of this study is to find an optimal shape of a body located in the viscous flow using the acoustic velocity. The optimal shape is defined so as to minimize fluid forces acting on the body. In this paper, the formulation is based on an optimal control theory, in which a performance function is expressed by the fluid force. The performance function should be minimized satisfying state equations. Therefore, the optimal control problem results in the minimization problem with constraint conditions. The problem can be transformed into the minimization problem without constraint condition by the Lagrange multiplier method. As the minimization technique, the gradient based method is applied. For the discretization, the finite element method is used to the state and adjoint equations. The shape determination of the minimum drag and lift forces is carried out