Scientific Computation

By: Jean Cousteix, Jacques Mauss

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Hardcover | 16 March 2007

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456 Pages

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23.5 x 15.88 x 2.54

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This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows.

Industry Reviews

From the reviews: "Asymptotic Analysis and Boundary Layers is an extended English edition of Analyse asymptotique et couche limite published in the Springer series Mathematique et Applications. The book presents a new method of asymptotic analysis of boundary layer problems, the successive Complementary Expansion Method (SCEM). ... With its chapter summaries, detailed derivations of results, discussed examples and fully worked out problems and solutions, the book is selfcontained. It is accessible to graduate and postgraduate students of engineering and physics with a good knowledge in fluid mechanics." (Francisco Perez Acosta, Zentralblatt MATH, Vol. 1115 (17), 2007) "The book falls into two quite distinct parts, reflecting the expertises of the two authors. The first part gives a detailed and formal description of asymptotic methods, whilst the second part considers a number of fluid mechanics problems. ... There are numerous problems presented at the end of each chapter, which are accompanied by extremely comprehensive solutions ... . this book should prove a useful text for final year undergraduate students and for postgraduate (both taught and research) students wishing to master modern asymptotic methods." (P. W. Duck, Mathematical Reviews, Issue 2008 a)

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Paperback

Published: 30th November 2010

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Preface	p. V
Acknowledgements	p. VIII
Abbreviations	p. XVII
Introduction	p. 1
Introduction to Singular Perturbation Problems	p. 7
Regular and Singular Problems	p. 8
Linear Oscillator	p. 8
Secular Problem	p. 11
Singular Problem	p. 14
Approximation Methods for Singular Perturbation Problems	p. 15
Method of Matched Asymptotic Expansions	p. 16
Successive Complementary Expansion Method	p. 19
Multiple Scale Method	p. 20
Poincaré-Lighthill's Method	p. 22
Renormalization Group Method	p. 24
Conclusion	p. 25
Problems	p. 25
Boundary Layer Structure	p. 31
Study of a Second Order Differential Equation	p. 31
Analysis of each Case	p. 35
Conclusion	p. 40
Problems	p. 41
Asymptotic Expansions	p. 43
Order Functions. Order of a Function	p. 43
Definition of an Order Function	p. 43
Comparison of Order Functions	p. 43
Total Ordering	p. 44
Order of a Function	p. 45
Asymptotic Sequence	p. 46
Definition of an Asymptotic Sequence	p. 46
Class of Equivalence	p. 46
Gauge Functions	p. 47
Asymptotic Expansion	p. 47
Asymptotic Approximation	p. 47
Regular Functions	p. 49
Regular and Generalized Asymptotic Expansions	p. 50
Convergence and Accuracy	p. 51
Operations on Asymptotic Expansions	p. 54
Conclusion	p. 55
Problems	p. 55
Successive Complementary Expansion Method	p. 59
Method of Matched Asymptotic Expansions	p. 59
Expansion Operator	p. 59
Outer Expansion - Inner Expansion	p. 60
Asymptotic Matching	p. 61
Boundary Layer	p. 65
Expansion Operator to a Given Order	p. 65
Significant Approximations	p. 66
Intermediate Matching	p. 67
Kaplun's Extension Theorem	p. 67
Study of Examples	p. 67
Rule of Intermediate Matching	p. 69
Asymptotic Matching Principle	p. 71
Van Dyke's Principle	p. 71
Modified Van Dyke's Principle	p. 72
Examples and Counter-Examples	p. 72
Example 1	p. 72
Example 2	p. 73
Example 3	p. 74
Example 4	p. 75
Discussion of the Matching Principle	p. 76
Corrective Boundary Layer	p. 77
The MVDP from the Overlap Hypothesis	p. 79
Successive Complementary Expansion Method	p. 81
Principle	p. 81
Equivalence of MVDP and of Regular SCEM	p. 84
Applications of SCEM	p. 86
Example 1	p. 86
Example 2	p. 88
Example 3	p. 89
Conclusion	p. 90
Problems	p. 91
Ordinary Differential Equations	p. 99
Example 1	p. 99
Application of MMAE	p. 100
Application of SCEM	p. 102
Example 2	p. 107
Application of MMAE	p. 107
Application of SCEM	p. 109
Identification with MMAE Results	p. 111
Numerical Results	p. 112
Example 3	p. 112
Application of MMAE	p. 112
Application of SCEM	p. 116
Identification with MMAE Results	p. 118
Stokes-Oseen's Flow Model	p. 118
Application of SCEM	p. 118
Numerical Results	p. 120
Terrible Problem	p. 121
Application of SCEM	p. 122
Numerical Results	p. 125
Conclusion	p. 125
Problems	p. 127
High Reynolds Number Flows	p. 133
Boundary Layer Theories	p. 135
Prandtl's Boundary Layer	p. 135
Triple Deck	p. 140
Analysis of an Integral Method	p. 148
Integral Method	p. 148
Direct Mode	p. 151
Inverse Mode	p. 152
Simultaneous Mode	p. 153
Viscous-Inviscid Interaction	p. 155
Conclusion	p. 157
Problems	p. 158
Interactive Boundary Layer	p. 169
Application of SCEM	p. 170
Outer Approximation	p. 170
Determination of a Uniformly Valid Approximation	p. 171
Gauge for the Pressure	p. 173
First Order Interactive Boundary Layer	p. 173
Generalized Boundary Layer Equations	p. 173
Boundary Conditions	p. 174
Estimate of the Remainders of Equations	p. 175
Second Order Interactive Boundary Layer	p. 175
Generalized Boundary Layer Equations	p. 175
Boundary Conditions	p. 176
Estimate of the Remainders of Equations	p. 176
Displacement Effect	p. 177
Reduced Model for an Irrotational External Flow	p. 178
Conclusion	p. 180
Problems	p. 181
Applications of Interactive Boundary Layer Models	p. 185
Calculation of a Flow with Separation	p. 186
Definition of the Flow	p. 186
Numerical Method	p. 186
Results	p. 188
Application to Aerodynamic Flows	p. 190
Flat Plate of Finite Length	p. 190
Airfoils at High Reynolds Numbers	p. 192
Influence of a Rotational External Flow	p. 195
Inviscid Flow	p. 195
Method of Resolution	p. 197
Flows Studied	p. 200
Results	p. 200
Conclusion	p. 211
Problems	p. 211
Regular Forms of Interactive Boundary Layer	p. 215
Second Order Boundary Layer Model	p. 215
Second Order Interactive Boundary Layer Model	p. 217
Van Dyke's Second Order Model	p. 217
Triple Deck Model	p. 221
Flow on a Flat Plate with a Small Hump	p. 221
Regular Expansions	p. 223
Summary of Approximations of Navier-Stokes Equations	p. 226
Conclusion	p. 226
Problems	p. 227
Turbulent Boundary Layer	p. 237
Results of the Standard Asymptotic Analysis	p. 237
Averaged Navier-Stokes Equations	p. 237
Scales	p. 238
Structure of the Flow	p. 239
Application of SCEM	p. 243
First Approximation	p. 243
Contribution of the Outer Region of the Boundary Layer	p. 243
Contribution of the Inner Region of the Boundary Layer	p. 246
Interactive Boundary Layer	p. 249
First Order Model	p. 249
Second Order Model	p. 250
Global Model	p. 250
Reduced Model for an Irrotational External Flow	p. 251
Approximation of the Boundary Layer: Velocity Profile	p. 254
Formulation of the Problem	p. 254
Turbulence Model	p. 256
Outer Region	p. 256
Equation to Solve	p. 257
Examples of Results	p. 258
Conclusion	p. 260
Problems	p. 260
Channel Flow	p. 267
Formulation of the problem	p. 267
Uniformly Valid Approximation	p. 270
IBL Model for the Lower Wall	p. 272
Global IBL Model	p. 274
Numerical Solution	p. 275
General Method	p. 275
Simplified Method for the Pressure	p. 277
Application of the Global IBL model	p. 279
Discussion of the Numerical Procedure	p. 279
Comparisons with Smith's theory	p. 283
Comparison with Navier-Stokes Solutions	p. 290
Conclusion	p. 295
Problems	p. 295
Conclusion	p. 301
Appendices
Navier-Stokes Equations	p. 303
Elements of Two-Dimensional Linearized Aerodynamics	p. 305
Thickness Problem (Non Lifting Case)	p. 306
Zero-Thickness Problem (Lifting Case)	p. 307
Solutions of the Upper Deck of the Triple Deck Theory	p. 309
Two Dimensional Flow	p. 309
Three-Dimensional Flow	p. 312
Zero Perturbations at Infinity	p. 313
Non Zero Cross-Flow Perturbations at Downstream Infinity	p. 314
Second Order Triple Deck Theory	p. 319
Main Results	p. 319
Global Model for the Main Deck and the Lower Deck	p. 325
Behaviour of an Asymptotic Expansion	p. 327
Formulation of the Problem	p. 327
Study of the Gauge Functions	p. 328
Study of the Outer Expansion	p. 330
Solutions of Problems	p. 332
References	p. 419
Author index	p. 427
Subject index	p. 428
Table of Contents provided by Publisher. All Rights Reserved.

Scientific Computation

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Hardcover

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