A numerical approach for shape optimization of fluid flow domains

A numerical method for the shape optimization of fluid flow domains is presented and analyzed. The procedure is based on a flow solver, a mathematical optimization tool, and a technique for shape variation, which are combined into an integrated procedure. The flow solver relies on the discretization of the incompressible Navier-Stokes equations by means of the finite-volume method for block-structured, boundary-fitted grids with multi-grid acceleration. The optimization tool is an implementation of a trust region based derivative-free method. It is designed to minimize smooth functions whose evaluations are considered expensive and whose derivatives are not available or not desirable to approximate. The shape variation is obtained by deforming the computational grid employed by the flow solver. For this purpose, displacement fields scaled by the design variables are added to the initial grid. The displacement vectors are computed once before starting the optimization cycle by using a free-form deformation technique. Applications illustrating the functionality and the properties of the method are presented for some examples of engineering interest, such as the minimization of a pressure drop, the maximization of a lift force, and the optimization of a wall temperature.