Issues in shape optimization for the Navier-Stokes equations

摘要

Sensitivity based methods for shape optimization of fluid flow governed by the Navier-Stokes equations are considered. The crucial components of an algorithm for this task are the proper parametrization of the boundary, the efficient calculation of the sensitivities with respect to the boundary parameters, the selection of a good optimization algorithm, and an efficient scheme for state calculations. Some of these issues are discussed, together with pitfalls and potential solutions.