抄録
To obtain the optimal shape of a 3D object minimizing the fluid traction, an adjoint variable method based on the variational principle is formulated and applied to the finite element method. The optimality condition of the present method consists of the state equations, the adjoint equations, and the sensitivity equations. In high Reynold's number cases, shape optimization methods are demanded that the initial shape be sufficiently close to the optimal shape and that Korman vortices not be present in the computational domain. Therefore, these methods were geneally applied to the steady state of the flows. In the present paper, the 3D adjoint variable method used to decrease the traction force of an object in unsteady flow is formulated by using FEM. The particularity of this method resides in the fact that both the start of the test time and the end of the test time in the optimization are determined by the stationary condition of the Lagrange function. The state variable is calculated from the start of the test time to the end of the test time in forward time and this data is saved, while the adjoint variable is calculated in backward time by using the saved data. The algorithm of the method is implemented using HEC-MW. By using the prepared algorithm, robust convergence of the cost function can be attained. This robustness makes possible the shape optimization even under unsteady flow containing Karman vortices.
