Suboptimal Control Strategies for Backward Facing Step Ows

In this note suboptimal distributed and boundary control strategies for uid ows governed by the Navier-Stokes equation (NSE) together with aspects of the numerical and practical implementation of the underlying algorithms are presented. The objective of our numerical investigations is the development of practically relevant feedback control laws for ows over the backward facing step. For what follows let IR 2 (IR 3) denote the ow region with boundary ? = ? c ? d , where in the case of boundary control ? c denotes the part of the boundary where control is applied and ? d is the remaining part of the boundary part where xed Dirichlet data are prescribed. Furthermore let obs denote the observation volume. For the case of boundary control and volume observation the control problem is given by