  Bayesian optimization (BO) based on Gaussian process regression (GPR) is
applied to different CFD (computational fluid dynamics) problems which can be
of practical relevance. The problems are i) shape optimization in a lid-driven
cavity to minimize or maximize the energy dissipation, ii) shape optimization
of the wall of a channel flow in order to obtain a desired pressure-gradient
distribution along the edge of the turbulent boundary layer formed on the other
wall, and finally, iii) optimization of the controlling parameters of a
spoiler-ice model to attain the aerodynamic characteristics of the airfoil with
an actual surface ice. The diversity of the optimization problems, independence
of the optimization approach from any adjoint information, the ease of
employing different CFD solvers in the optimization loop, and more importantly,
the relatively small number of the required flow simulations reveal the
flexibility, efficiency, and versatility of the BO-GPR approach in CFD
applications. It is shown that to ensure finding the global optimum of the
design parameters of the size up to 8, less than 90 executions of the CFD
solvers are needed. Furthermore, it is observed that the number of flow
simulations does not significantly increase with the number of design
parameters. The associated computational cost of these simulations can be
affordable for many optimization cases with practical relevance.
