Comparison of trust-region-based and evolutionary methods for optimization of flow geometries

Optimization has become increasingly important in computer-aided engineering, and applications of engineering optimization to design, control, operations, and planning already exist. Since in the context of numerical flow simulation no information on the gradient information of the objective function is available, or is very difficult to obtain, in such optimization cases it is advantageous to use an optimization technique which does not directly depend on the derivative. The aim of this study is to investigate two optimization techniques, the trust-region-based method and the evolutionary algorithm technique, and compare them quantitatively with respect to efficiency, quality, and working strategy. A tool based on free-form deformation is employed for the variation of flow geometry. This simulation tool is the parallel multigrid flow solver FASTEST, which uses a fully conservative finite-volume method for solving the incompressible Navier–Stokes equations on a non-staggered cell-centred grid arrangement. The optimization tools are investigated by considering the optimization of the connection of two pipes with respect to the minimization of the pressure drop. This problem can be considered as a representative test case for a practical three-dimensional flow configuration.