Analysis, approximation, and computations of unsteady optimal flow control problems

L. Steven Hou
Iowa State University

Abstract: This talk 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 to be preferred depends on the specific application. Theretical results are given on the dynamics of the optimal solutions and of the approximate optimal solutions. Some test numerical results are presented.