Book contents
- Frontmatter
- Contents
- Preface
- Contributing Authors
- 1 A Few Tools For Turbulence Models In Navier-Stokes Equations
- 2 On Some Finite Element Methods for the Numerical Simulation of Incompressible Viscous Flow
- 3 CFD - An Industrial Perspective
- 4 Stabilized Finite Element Methods
- 5 Optimal Control and Optimization of Viscous, Incompressible Flows
- 6 A Fully-Coupled Finite Element Algorithm, Using Direct and Iterative Solvers, for the Incompressible Navier-Stokes Equations
- 7 Numerical Solution of the Incompressible Navier-Stokes Equations in Primitive Variables on Unstaggered Grids
- 8 Spectral Element and Lattice Gas Methods for Incompressible Fluid Dynamics
- 9 Design of Incompressible Flow Solvers: Practical Aspects
- 10 The Covolume Approach to Computing Incompressible Flows
- 11 Vortex Methods: An Introduction and Survey of Selected Research Topics
- 12 New Emerging Methods in Numerical Analysis: Applications to Fluid Mechanics
- 13 The Finite Element Method for Three Dimensional Incompressible Flow
- 14 A Posteriori Error Estimators and Adaptive Mesh-Refinement Techniques for the Navier-Stokes Equations
- Index
5 - Optimal Control and Optimization of Viscous, Incompressible Flows
Published online by Cambridge University Press: 12 January 2010
- Frontmatter
- Contents
- Preface
- Contributing Authors
- 1 A Few Tools For Turbulence Models In Navier-Stokes Equations
- 2 On Some Finite Element Methods for the Numerical Simulation of Incompressible Viscous Flow
- 3 CFD - An Industrial Perspective
- 4 Stabilized Finite Element Methods
- 5 Optimal Control and Optimization of Viscous, Incompressible Flows
- 6 A Fully-Coupled Finite Element Algorithm, Using Direct and Iterative Solvers, for the Incompressible Navier-Stokes Equations
- 7 Numerical Solution of the Incompressible Navier-Stokes Equations in Primitive Variables on Unstaggered Grids
- 8 Spectral Element and Lattice Gas Methods for Incompressible Fluid Dynamics
- 9 Design of Incompressible Flow Solvers: Practical Aspects
- 10 The Covolume Approach to Computing Incompressible Flows
- 11 Vortex Methods: An Introduction and Survey of Selected Research Topics
- 12 New Emerging Methods in Numerical Analysis: Applications to Fluid Mechanics
- 13 The Finite Element Method for Three Dimensional Incompressible Flow
- 14 A Posteriori Error Estimators and Adaptive Mesh-Refinement Techniques for the Navier-Stokes Equations
- Index
Summary
Introduction
The control of fluid motions for the purpose of achieving some desired objective is crucial to many technological applications. In the past, these control problems have been addressed either through expensive experimental processes or through the introduction of significant simplifications into the analyses used in the development of control mechanisms. Only recently have flow control problems been addressed, by scientists and mathematicians, in a systematic, rigorous manner. This interest is quickly expanding so that, at this time, flow control is becoming a very active and successful area of inquiry. For example, recent publications, e.g., [1] [28], provide analyses of various aspects of flow control problems, and include one or more of the following components:
the construction of mathematical models, invoking minimal assumptions about the physical phenomena;
the analysis of the mathematical models to answer questions about the existence and regularity of solutions and to derive necessary conditions that optimal controls and states must satisfy;
the construction and analysis of discretization methods for determining approximate solutions of the optimal control problems, and the rigorous derivation of error estimates; and
the development of computer codes implementing discretization algorithms, both for the purpose of showing the efficacy of these methods, and also to solve problems of practical interest.
An optimal control or optimization problem is composed of two ingredients: a desired objective and control mechanisms that are used to (hopefully) achieve the desired objective. In a mathematical description of such problems, the desired objective is usually expressed in terms of the extremization of a functional depending on the state of the system, and possibly also on the control mechanisms.
- Type
- Chapter
- Information
- Incompressible Computational Fluid DynamicsTrends and Advances, pp. 109 - 150Publisher: Cambridge University PressPrint publication year: 1993
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