Preface |
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xi | |
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1 | (10) |
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A brief history of flow control and optimization |
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1 | (6) |
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Flow control without fluids |
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2 | (1) |
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Flow optimization without optimization |
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3 | (2) |
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Flow control without objectives |
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5 | (1) |
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Flow control and optimization and CFD |
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6 | (1) |
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The structure of flow control problems |
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7 | (1) |
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Some philosophical observations |
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8 | (3) |
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Three Approaches to Optimal Control and Optimization |
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11 | (52) |
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Model control and optimization problems |
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11 | (3) |
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14 | (7) |
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Sensitivity- and adjoint-based optimization methods |
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21 | (7) |
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Optimization-based methods |
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21 | (1) |
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The gradient of the functional through sensitivities |
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22 | (4) |
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The gradient of the functional through adjoint equations |
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26 | (2) |
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28 | (12) |
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29 | (3) |
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Infinite-dimensional controls |
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32 | (8) |
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Other types of functionals and partial controls |
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40 | (8) |
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48 | (4) |
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52 | (3) |
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One-shot vs. sensitivity vs. adjoint approaches |
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55 | (2) |
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Differentiate-then-discretize vs. discretize-then-differentiate |
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57 | (6) |
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Illustrations of the Three Approaches |
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63 | (38) |
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One-shot method for a temperature matching problem in a coupled solid-fluid heat transfer problem |
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63 | (7) |
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Sensitivity equation method for an optimization problem for Euler flows |
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70 | (5) |
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Computational experiments for the adjoint equation approach to optimization using flow matching functionals |
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75 | (19) |
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Distributed control with a penalized functional |
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76 | (7) |
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Distributed control with an explicit bound on the control |
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83 | (8) |
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91 | (3) |
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Adjoint equation optimization approach to suppressing instabilities in boundary layers |
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94 | (7) |
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An observation about outflow boundary conditions |
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97 | (4) |
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Questions of Accuracy and Consistency |
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101 | (42) |
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Insensitive functionals, inconsistent gradients, spurious minima, and regularized functionals in a viscous flow example |
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101 | (20) |
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Insensitive cost functionals |
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105 | (3) |
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Inconsistent functional gradients |
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108 | (5) |
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113 | (1) |
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Regularization of the functional |
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114 | (4) |
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Implications for practical flow control problems |
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118 | (3) |
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Spurious minima and regularized functionals for flows with discontinuities |
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121 | (2) |
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121 | (2) |
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Regularization of discretized functionals |
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123 | (1) |
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Sensitivities for flows with discontinuities |
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123 | (16) |
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Effects of inaccuracies in the sensitivities on optimization problems |
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137 | (2) |
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Inaccuracies at the boundaries |
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139 | (4) |
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Reducing the Costs of Optimization and Control Calculations |
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143 | (10) |
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Storage saving schemes for time-dependent adjoint calculations |
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145 | (2) |
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147 | (6) |
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Proper orthogonal decomposition |
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150 | (3) |
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A Peek at the Analysis and Numerical Analysis of Optimal Flow Control Problems |
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153 | (56) |
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Analysis and approximation of stationary optimal control problems |
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153 | (20) |
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Analysis of an abstract nonlinear stationary control problem |
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155 | (5) |
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Finite-dimensional approximations of an abstract nonlinear stationary control and optimization problem |
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160 | (4) |
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Application to a boundary velocity control problem for the stationary Navier--Stokes equations |
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164 | (9) |
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Analysis of a shape control problem for the stationary Navier--Stokes equations |
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173 | (17) |
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The model shape control problem and existence of solutions |
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179 | (1) |
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Direct determination of the optimality system and shape gradient |
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179 | (5) |
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The Lagrange multiplier method |
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184 | (6) |
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The velocity tracking problem for unsteady Navier--Stokes flows with boundary control |
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190 | (19) |
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Formulation and analysis of the optimal control problem |
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192 | (6) |
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Semidiscrete-in-time approximations |
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198 | (6) |
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Fully discrete space-time approximations |
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204 | (3) |
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Implementation of fully discrete space-time approximations |
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207 | (2) |
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A Brief Look at the Feedback Control of Fluids Flows |
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209 | (12) |
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Linear feedback control of Navier--Stokes Flows |
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210 | (4) |
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Feedback control of lift oscillations in flow around a cylinder |
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214 | (3) |
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Suppression of 2D Tollmien--Schlichting instability through feedback |
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217 | (4) |
Bibliography |
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221 | (32) |
Index |
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253 | |