Shape Optimization of a Body Located in Viscous Flows Using Acoustic Velocity Method

Abstract

The purpose of this study is to find an optimal shape of a body located in viscous flows using the acoustic velocity method. The optimal shape is defined such as to minimize fluid forces acting on the body. 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 adjoint equation method. As the minimization technique, the gradient based method is applied. For the discretization of both state and adjoint equations, the finite element method based on the bubble function is used. The optimal shape in the flow at Reynolds number Re = 50000 can be obtained.