Instantaneous Control of Backward-Facing Step Flows

Haecheon Choi , Michael Hinzey & Karl Kunisch& Dept. of Mechanical Engng, Seoul National University, Seoul 151-742, Korea y Fachbereich Mathematik, MA 6-3, Technische Universit at Berlin 10623 Berlin, Germany & Institut f ur Mathematik, Universtitat Graz, A-8010 Graz, Austria Abstract In the present paper suboptimal boundary control strategies for the time-dependent, incompressible ow over the backward-facing step are considered. The objective consists in the reduction of the recirculation bubble of the ow behind the step. Several cost functionals are suggested and a frame for the derivation of the optimality systems for a general class of cost functionals is presented. Numerical examples are given. 1 Problem formulation The main objective of the present work is the development of a numerically realizable robust control technique in order to reduce the recirculation bubble behind the step, and thus reducing the re-attachment length of a backward-facing-step ow by controlling the ow at the boundary near the edge of the step. For the following presentation it will be convenient to refer to Fig. 1 which depicts the spatial domain that constitutes the ow region and the subsets of the boundary that we shall refer to. Let (u1; u2; u3) denote the velocity of the ----