Boundary optimal control of the Navier-Stokes equations - a numerical approach

Abstract

Boundary optimal control problems of the Navier-Stokes equation are studied from a numerical point of view. When the adjoint variable method is used to minimize the objective function, the gradient of the objective function is not obtained accurately due to the insufficient regularity of the adjoint variable at the boundary. The resulting numerical error usually causes the conjugate gradient iteration to terminate prematurely. In the present investigation, a new method is developed that circumvents this difficulty with the adjoint variable method by converting the boundary optimal control problems to the distributed control problems. The present method is applied to two boundary optimal control problems, a driven cavity flow and a channel flow, and is found to solve the problems efficiently with sufficient accuracy. (C) 2002 Elsevier Science Ltd. All rights reserved.