Adjoint equation-based methods for control problems in incompressible, viscous flows. (English) Zbl 0996.76024

Gunzburger, Max

Flow Turbul. Combust. 65, No. 3-4, 249-272 (2000).

Summary: A review of adjoint equation-based methodologies for viscous, incompressible flow control and optimization problems is given and illustrated by a drag minimization example. We discuss a number of approaches to ameliorating the high storage and CPU costs associated with straighforward implementations of adjoint equation based methodologies. Other issues, including the relative merits of the differentiate-then-discretize and discretize-then-differentiate approaches to deriving discrete adjoint equations, the incorporation of side constraints into adjoint equation-based methodologies, and inaccuracies that occur due to differentiations at the boundary, are also discussed.

MSC:

76D55	Flow control and optimization for incompressible viscous fluids
76D05	Navier-Stokes equations for incompressible viscous fluids

Keywords:

adjoint equation-based methods; control problems; Navier-Stokes equations; viscous incompressible flow; drag minimization

Software:

ADIFOR; Odyssee