A reduced-order method for simulation and control of fluid flows

This article presents a reduced-order modeling approach for simulation and control of viscous incompressible flows. The reduced-order models suitable for control and which capture the essential physics are developed using the reduced-basis method. The so-called Lagrange approach is used to define reduced bases and the basis functions in this approach are obtained from the numerical solutions. The feasibility of this method for flow control is demonstrated on boundary control problems in closed cavity and in wall-bounded channel flows. Control action is effected through boundary surface movement on a part of the solid wall. Our formulation of the reduced-order method applied to flow control problems leads to a constrained minimization problem and is solved by applying Newton-like methods to the necessary conditions of optimality. Through our computational experiments we demonstrate the feasibility and applicability of the reduced-order method for simulation and control of fluid flows. (C) 1998 Academic Press.