Holdings: Perspectives in flow control and optimization

Perspectives in flow control and optimization:

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Bibliographic Details
Main Author:	Gunzburger, Max D. (Author)
Format:	Book
Language:	English
Published:	Philadelphia SIAM , Soc. for Industrial and Applied Mathematics 2003
Series:	Advances in design and control
Subjects:	Mathematik Fluid dynamics > Mathematics Mathematical optimization Numerical analysis Numerisches Verfahren Strömungsmesstechnik
Online Access:	Inhaltsverzeichnis
Physical Description:	XIV, 261 S. graph. Darst.
ISBN:	089871527X

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MARC


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adam_text	PERSPECTIVES IN FLOW CONTROL AND OPTIMIZATION MAX D. GUNZBURGER IOWA STATE UNIVERSITY AMES, IOWA 9 AND FLORIDA STATE UNIVERSITY TALLAHASSEE, FLORIDA SIHIN. SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS PHILADELPHIA CONTENTS PREFACE XI 1 INTRODUCTORY COMMENTS 1 1.1 A BRIEF HISTORY OF FLOW CONTROL AND OPTIMIZATION 1 1.1.1 FLOW CONTROL WITHOUT FLUIDS 2 1.1.2 ROW OPTIMIZATION WITHOUT OPTIMIZATION 3 1.1.3 FLOW CONTROL WITHOUT OBJECTIVES 5 1.1.4 FLOW CONTROL AND OPTIMIZATION AND CFD 6 1.2 THE STRUCTURE OF FLOW CONTROL PROBLEMS 7 1.3 SOME PHILOSOPHICAL OBSERVATIONS . . . -. 8 2 THREE APPROACHES TO OPTIMAL CONTROL AND OPTIMIZATION 11 2.1 MODEL CONTROL AND OPTIMIZATION PROBLEMS 11 2.2 ONE-SHOT METHODS 14 2.3 SENSITIVITY- AND ADJOINT-BASED OPTIMIZATION METHODS 21 2.3.1 OPTIMIZATION-BASED METHODS 21 2.3.2 THE GRADIENT OF THE FUNCTIONAL THROUGH SENSITIVITIES 22 2.3.3 THE GRADIENT OF THE FUNCTIONAL THROUGH ADJOINT EQUATIONS .... 26 2.4 OTHER TYPES OF CONTROLS 28 2.4.1 BOUNDARY CONTROLS 29 2.4.2 INFINITE-DIMENSIONAL CONTROLS 32 2.5 OTHER TYPES OF FUNCTIONALS AND PARTIAL CONTROLS 40 2.6 TIME-DEPENDENT PROBLEMS *. 48 2.7 SIDE CONSTRAINTS 52 2.8 ONE-SHOT VS. SENSITIVITY VS. ADJOINT APPROACHES 55 2.9 DIFFERENTIATE-THEN-DISCRETIZE VS. DISCRETIZE-THEN-DIFFERENTIATE 57 3 ILLUSTRATIONS OF THE THREE APPROACHES 63 3.1 ONE-SHOT METHOD FOR A TEMPERATURE MATCHING PROBLEM IN A COUPLED SOLID- FLUID HEAT TRANSFER PROBLEM 63 3.2 SENSITIVITY EQUATION METHOD FOR AN OPTIMIZATION PROBLEM FOR EULER FLOWS . 70 3.3 COMPUTATIONAL EXPERIMENTS FOR THE ADJOINT EQUATION APPROACH TO OPTIMIZA- TION USING FLOW MATCHING FUNCTIONALS 75 3.3.1 DISTRIBUTED CONTROL WITH A PENALIZED FUNCTIONAL 76 VII VIII CONTENTS 3.3.2 DISTRIBUTED CONTROL WITH AN EXPLICIT BOUND ON THE CONTROL . .. . 83 3.3.3 BOUNDARY CONTROL 91 3.4 ADJOINT EQUATION OPTIMIZATION APPROACH TO SUPPRESSING INSTABILITIES IN BOUNDARY LAYERS 94 3.4.1 AN OBSERVATION ABOUT OUTFLOW BOUNDARY CONDITIONS 97 4 QUESTIONS OF ACCURACY AND CONSISTENCY 101 4.1 INSENSITIVE FUNCTIONALS, INCONSISTENT GRADIENTS, SPURIOUS MINIMA, AND REG- ULARIZED FUNCTIONALS IN A VISCOUS FLOW EXAMPLE 101 4.1.1 INSENSITIVE COST FUNCTIONALS 105 4.1.2 INCONSISTENT FUNCTIONAL GRADIENTS 108 4.1.3 SPURIOUS MINIMA 113 4.1.4 REGULARIZATION OF THE FUNCTIONAL 114 4.1.5 IMPLICATIONS FOR PRACTICAL FLOW CONTROL PROBLEMS 118 4.2 SPURIOUS MINIMA AND REGULARIZED FUNCTIONALS FOR FLOWS WITH DISCONTINUITIES 121 4.2.1 SPURIOUS MINIMA 121 4.2.2 REGULARIZATION OF DISCRETIZED FUNCTIONALS 123 4.3 SENSITIVITIES FOR FLOWS WITH DISCONTINUITIES 123 4.3.1 EFFECTS OF INACCURACIES IN THE SENSITIVITIES ON OPTIMIZATION PROBLEMS 137 4.4 INACCURACIES AT THE BOUNDARIES 139 5 REDUCING THE COSTS OF OPTIMIZATION AND CONTROL CALCULATIONS 143 5.1 STORAGE SAVING SCHEMES FOR TIME-DEPENDENT ADJOINT CALCULATIONS 145 5.2 REDUCED-ORDER METHODS 147 5.2.1 PROPER ORTHOGONAL DECOMPOSITION 150 6 A PEEK AT THE ANALYSIS AND NUMERICAL ANALYSIS OF OPTIMAL FLOW CONTROL PROBLEMS 153 6.1 ANALYSIS AND APPROXIMATION OF STATIONARY OPTIMAL CONTROL PROBLEMS .... 153 6.1.1 ANALYSIS OF AN ABSTRACT NONLINEAR STATIONARY CONTROL PROBLEM . . 155 6.1.2 FINITE-DIMENSIONAL APPROXIMATIONS OF AN ABSTRACT NONLINEAR STA- TIONARY CONTROL AND OPTIMIZATION PROBLEM 160 6.1.3 APPLICATION TO A BOUNDARY VELOCITY CONTROL PROBLEM FOR THE STA- TIONARY NAVIER-STOKES EQUATIONS . T 164 6.2 ANALYSIS OF A SHAPE CONTROL PROBLEM FOR THE STATIONARY NAVIER-STOKES EQUATIONS 173 6.2.1 THE MODEL SHAPE CONTROL PROBLEM AND EXISTENCE OF SOLUTIONS . . 179 6.2.2 DIRECT DETERMINATION OF THE OPTIMALITY SYSTEM AND SHAPE GRADIENT 179 6.2.3 THE LAGRANGE MULTIPLIER METHOD 184 6.3 THE VELOCITY TRACKING PROBLEM FOR UNSTEADY NAVIER-STOKES FLOWS WITH BOUNDARY CONTROL 190 6.3.1 FORMULATION AND ANALYSIS OF THE OPTIMAL CONTROL PROBLEM .... 192 6.3.2 SEMIDISCRETE-IN-TIME APPROXIMATIONS 198 6.3.3 FULLY DISCRETE SPACE-TIME APPROXIMATIONS 204 6.3.4 IMPLEMENTATION OF FULLY DISCRETE SPACE-TIME APPROXIMATIONS . .207 CONTENTS IX 7 A BRIEF LOOK AT THE FEEDBACK CONTROL OF FLUIDS FLOWS 209 7.1 LINEAR FEEDBACK CONTROL OF NAVIER*STOKES FLOWS 210 7.2 FEEDBACK CONTROL OF LIFT OSCILLATIONS IN FLOW AROUND A CYLINDER 214 7.3 SUPPRESSION OF 2D TOLLMIEN-SCHLICHTING INSTABILITY THROUGH FEEDBACK . .217 BIBLIOGRAPHY 221 INDEX 253
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spelling	Gunzburger, Max D. Verfasser aut Perspectives in flow control and optimization Max D. Gunzburger Philadelphia SIAM , Soc. for Industrial and Applied Mathematics 2003 XIV, 261 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Advances in design and control Mathematik Fluid dynamics Mathematics Mathematical optimization Numerical analysis Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Strömungsmesstechnik (DE-588)4129610-2 gnd rswk-swf Strömungsmesstechnik (DE-588)4129610-2 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009920554&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Gunzburger, Max D. Perspectives in flow control and optimization Mathematik Fluid dynamics Mathematics Mathematical optimization Numerical analysis Numerisches Verfahren (DE-588)4128130-5 gnd Strömungsmesstechnik (DE-588)4129610-2 gnd
subject_GND	(DE-588)4128130-5 (DE-588)4129610-2
title	Perspectives in flow control and optimization
title_auth	Perspectives in flow control and optimization
title_exact_search	Perspectives in flow control and optimization
title_full	Perspectives in flow control and optimization Max D. Gunzburger
title_fullStr	Perspectives in flow control and optimization Max D. Gunzburger
title_full_unstemmed	Perspectives in flow control and optimization Max D. Gunzburger
title_short	Perspectives in flow control and optimization
title_sort	perspectives in flow control and optimization
topic	Mathematik Fluid dynamics Mathematics Mathematical optimization Numerical analysis Numerisches Verfahren (DE-588)4128130-5 gnd Strömungsmesstechnik (DE-588)4129610-2 gnd
topic_facet	Mathematik Fluid dynamics Mathematics Mathematical optimization Numerical analysis Numerisches Verfahren Strömungsmesstechnik
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