Shape optimization of 3D viscous flow fields

This article presents a numerical solution technique for shape optimization problems of steady-state, 3D viscous flow fields. In a previous study, the authors formulated shape optimization problems by considering the minimization of total dissipation energy in the domain of a viscous flow field, proposing a solution technique in which the traction method is applied by making use of a shape gradient. This approach was found to be effective for 2D problems for low Reynolds number flows. In the present study, the validity of the proposed solution technique is confirmed by extending its application to 3D problems.