Cousteix / Mauss Asymptotic Analysis and Boundary Layers

1. Auflage 2007
ISBN: 978-3-540-46489-1
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 434 Seiten

Reihe: Scientific Computation

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.

Autoren/Hrsg.

Cousteix, Jean

Mauss, Jacques

Inhaltsverzeichnis

1;Preface;5
2;Acknowledgements;8
3;Contents;9
4;Abbreviations;15
5;1 Introduction;16
6;2 Introduction to Singular Perturbation Problems;22
6.1;2.1 Regular and Singular Problems;23
6.2;2.2 Approximation Methods for Singular Perturbation Problems;30
6.3;2.3 Conclusion;40
6.4;Problems;40
7;3 Boundary Layer Structure;45
7.1;3.1 Study of a Second Order Differential Equation;45
7.2;3.2 Analysis of each Case;49
7.3;3.3 Conclusion;54
7.4;Problems;55
8;4 Asymptotic Expansions;57
8.1;4.1 Order Functions. Order of a Function;57
8.2;4.2 Asymptotic Sequence;60
8.3;4.3 Asymptotic Expansion;61
8.4;4.4 Conclusion;69
8.5;Problems;69
9;5 Successive Complementary Expansion Method;72
9.1;5.1 Method of Matched Asymptotic Expansions;72
9.2;5.2 Boundary Layer;78
9.3;5.3 Intermediate Matching;80
9.4;5.4 Asymptotic Matching Principle;84
9.5;5.5 Examples and Counter-Examples;85
9.6;5.6 Discussion of the Matching Principle;89
9.7;5.7 Successive Complementary Expansion Method;94
9.8;5.8 Applications of SCEM;99
9.9;5.9 Conclusion;103
9.10;Problems;104
10;6 Ordinary Differential Equations;112
10.1;6.1 Example 1;112
10.2;6.2 Example 2;120
10.3;6.3 Example 3;125
10.4;6.4 Stokes-Oseen’s Flow Model;131
10.5;6.5 Terrible Problem;134
10.6;6.6 Conclusion;138
10.7;Problems;140
11;7 High Reynolds Number Flows;145
11.1;7.1 Boundary Layer Theories;147
11.2;7.2 Analysis of an Integral Method;160
11.3;7.3 Viscous-Inviscid Interaction;167
11.4;7.4 Conclusion;169
11.5;Problems;170
12;8 Interactive Boundary Layer;180
12.1;8.1 Application of SCEM;181
12.2;8.2 First Order Interactive Boundary Layer;184
12.3;8.3 Second Order Interactive Boundary Layer;186
12.4;8.4 Displacement Effect;188
12.5;8.5 Reduced Model for an Irrotational External Flow;189
12.6;8.6 Conclusion;191
12.7;Problems;192
13;9 Applications of Interactive Boundary Layer Models;195
13.1;9.1 Calculation of a Flow with Separation;196
13.2;9.2 Application to Aerodynamic Flows;200
13.3;9.3 Influence of a Rotational External Flow;205
13.4;9.4 Conclusion;221
13.5;Problems;221
14;10 Regular Forms of Interactive Boundary Layer;224
14.1;10.1 Second Order Boundary Layer Model;224
14.2;10.2 Triple Deck Model;230
14.3;10.3 Summary of Approximations of Navier- Stokes Equations;235
14.4;10.4 Conclusion;235
14.5;Problems;236
15;11 Turbulent Boundary Layer;245
15.1;11.1 Results of the Standard Asymptotic Analysis;245
15.2;11.2 Application of SCEM;251
15.3;11.3 Interactive Boundary Layer;257
15.4;11.4 Approximation of the Boundary Layer: Velocity Profile;262
15.5;11.5 Conclusion;268
15.6;Problems;268
16;12 Channel Flow;274
16.1;12.1 Formulation of the problem;274
16.2;12.2 Uniformly Valid Approximation;277
16.3;12.3 IBL Model for the Lower Wall;279
16.4;12.4 Global IBL Model;281
16.5;12.5 Numerical Solution;282
16.6;12.6 Application of the Global IBL model;286
16.7;12.7 Conclusion;302
16.8;Problems;302
17;13 Conclusion;307
18;I Navier-Stokes Equations;309
19;II Elements of Two-Dimensional Linearized Aerodynamics;311
19.1;II.1 Thickness Problem (Non Lifting Case);312
19.2;II.2 Zero-Thickness Problem (Lifting Case);313
20;III Solutions of the Upper Deck of the Triple Deck Theory;315
20.1;III.1 Two-Dimensional Flow;315
20.2;III.2 Three-Dimensional Flow;318
21;IV Second Order Triple Deck Theory;324
21.1;IV.1 Main Results;324
21.2;IV.2 Global Model for the Main Deck and the Lower Deck;330
22;V Behaviour of an Asymptotic Expansion;332
22.1;V.1 Formulation of the Problem;332
22.2;V.2 Study of the Gauge Functions;333
22.3;V.3 Study of the Outer Expansion;335
23;Solutions of Problems;337
24;References;423
25;Author index;430
26;Subject index;431