Computations of optimal controls for incompressible flows

This paper is concerned with numerical solutions of optimal control problems for unsteady, viscous, incompressible flows. In general, controls can be of the distributed type (external body force) or Dirichlet type (e.g., boundary velocity). Here, we only consider the former case, although most of what we present is also applicable to the latter. Two different optimization objectives and associated solution methodologies are described. One involves a global-in-time functional, the other a local-in-time functional. Which method is preferred depends on the specific application. Some test computational results are presented.