On suboptimal control strategies for the Navier-Stokes equations

We summarize some of the recent developments in the fields of suboptimal control strategies for time dependent incompressible Navier-Stokes Equations. Reduced order modeling (ROM) and instantaneous control strategies are described. Both approaches are applied to compute controls for the laminar backward facing step flow.

[1]  Parviz Moin,et al.  Optimal feedback control of turbulent channel flow , 1993 .

[2]  Kazufumi Ito,et al.  Augmented Lagrangian-SQP-Methods in Hilbert Spaces and Application to Control in the Coefficients Problems , 1996, SIAM J. Optim..

[3]  R. Temam,et al.  On some control problems in fluid mechanics , 1990 .

[4]  Kazufumi Ito,et al.  A Dissipative Feedback Control Synthesis for Systems Arising in Fluid Dynamics , 1994 .

[5]  L. S. Hou,et al.  Optimization Problems for the Navier-Stokes Equations with Regular Boundary Controls , 1993 .

[6]  L. Sirovich Turbulence and the dynamics of coherent structures. II. Symmetries and transformations , 1987 .

[7]  Janet S. Peterson,et al.  The Reduced Basis Method for Incompressible Viscous Flow Calculations , 1989 .

[8]  S. Ravindran,et al.  A Reduced Basis Method for Control Problems Governed by PDEs , 1998 .

[9]  A. Fursikov,et al.  Exact boundary zero controllability of three-dimensional Navier-Stokes equations , 1995 .

[10]  L. Hou,et al.  Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with Dirichlet controls , 1991 .

[11]  R. Temam,et al.  Feedback control for unsteady flow and its application to the stochastic Burgers equation , 1993, Journal of Fluid Mechanics.

[12]  L. Sirovich Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .

[13]  Wr Graham,et al.  Active flow control using a reduced order model and optimum control , 1996 .

[14]  L. Hou,et al.  Boundary Value Problems and Optimal Boundary Control for the Navier--Stokes System: the Two-Dimensional Case , 1998 .