Optimal and instantaneous control of the instationary Navier-Stokes equations

Abstract

Contents Danksagung 1 Chapter 1. Introduction 5 1. Aims and scope of flow control 5 2. A brief review in active flow control 8 Chapter 2. Notation and preliminary results 15 1. Quasi-Stokes problems 15 2. Instationary Navier-Stokes equations in 2d 16 3. Navier-Stokes numerics 19 Chapter 3. Optimal control of the instationary Navier-Stokes equations 23 1. The optimal control problem 23 2. Derivatives 25 3. First order necessary optimality condition 29 4. Second order conditions 31 Chapter 4. Convergence for second order methods 35 1. Newton's algorithm 36 2. The BFGS method 38 3. Basic SQP--method 39 4. Schur--complement SQP--method 42 5. Reduced SQP--method 44 6. Reduced SQP-BFGS method 47 7. Newton's method for driven-cavity control 49 Chapter 5. Instantaneous control for finite dimensional systems 59 1. Scope of the method 59 2. The model problem 60 3. The instantaneous control strategy 61 4. Discrete and continuous output control laws 63 5. Convergence of the control laws 6