Stynes / O'Riordan / Kopteva BAIL 2008 - Boundary and Interior Layers

Proceedings of the International Conference on Boundary and Interior Layers - Computational and Asymptotic Methods, Limerick, July 2008
1. Auflage 2009
ISBN: 978-3-642-00605-0
Verlag: Springer
Format: PDF
Kopierschutz: Wasserzeichen (»Systemvoraussetzungen)

E-Book, Englisch, 312 Seiten

These Proceedings contain a selection of the lectures given at the conference BAIL 2008: Boundary and Interior Layers - Computational and Asymptotic Methods, which was held from 28th July to 1st August 2008 at the University of Limerick, Ireland. The ?rst three BAIL conferences (1980, 1982, 1984) were organised by Professor John Miller in Trinity College Dublin, Ireland. The next seven were held in Novosibirsk (1986), Shanghai (1988), Colorado (1992), Beijing (1994), Perth (2002),Toulouse(2004),and Got ¨ tingen(2006).With BAIL 2008the series returned to Ireland. BAIL 2010 is planned for Zaragoza. The BAIL conferences strive to bring together mathematicians and engineers whose research involves layer phenomena,as these two groups often pursue largely independent paths. BAIL 2008, at which both communities were well represented, succeeded in this regard. The lectures given were evenly divided between app- cations and theory, exposing all conference participants to a broad spectrum of research into problems exhibiting solutions with layers. The Proceedings give a good overview of current research into the theory, app- cation and solution (by both numerical and asymptotic methods) of problems that involve boundaryand interior layers. In addition to invited and contributed lectures, the conference included four mini-symposia devoted to stabilized ?nite element methods, asymptotic scaling of wall-bounded ?ows, systems of singularly p- turbed differential equations, and problems with industrial applications (supported by MACSI, the Mathematics Applications Consortium for Science and Industry). These titles exemplify the mix of interests among the participants.

Autoren/Hrsg.

Stynes, Martin

O'Riordan, Eugene

Kopteva, Natalia

Hegarty., Alan

Hegarty, Alan

Inhaltsverzeichnis

1;Preface;4
2;Contents;5
3;List of Contributors;8
4;Part I Invited Papers;13
4.1;High-Reynolds-Number Asymptotics of Turbulent Boundary Layers: From Fully Attached to Marginally Separated Flows;14
4.1.1;1 Introduction;14
4.1.2;2 Classical Theory of Turbulent Small-Defect Turbulent Boundary Layers;15
4.1.2.1;2.1 Preliminaries;15
4.1.2.2;2.2 Leading-Order Approximation;17
4.1.2.3;2.3 Second-Order Outer Problem;18
4.1.2.4;2.4 Can Classical Small-Defect Theory Describe Boundary Layer Separation?;19
4.1.3;3 Moderately Large Velocity Defect;21
4.1.3.1;3.1 Intermediate Layer;21
4.1.3.2;3.2 Outer Defect Region;22
4.1.4;4 Large Velocity Deficit;25
4.1.4.1;4.1 Outer Wake Region;25
4.1.4.2;4.2 Inner Wake Region;26
4.1.4.3;4.3 Numerical Solution of the Leading-Order Outer-Wake Problem;27
4.1.4.4;4.4 Marginal Separation;29
4.1.5;5 Conclusions and Outlook;31
4.1.6;References;32
4.2;A Deterministic Multiscale Approach for Simulating Dilute Polymeric Fluids;34
4.2.1;1 Introduction;34
4.2.2;2 The Fokker–Planck Equation in Configuration Space;38
4.2.2.1;2.1 Weak Formulation and Backward Euler Semidiscretisation;38
4.2.2.2;2.2 Fully-Discrete Spectral Method;39
4.2.3;3 An Alternating-Direction Scheme for the Full Fokker–Planck Equation;41
4.2.3.1;3.1 The Alternating-Direction Methods;42
4.2.4;4 The Micro–Macro Model;45
4.2.5;5 Conclusions;48
4.2.6;References;48
4.3;Temperature Factor Effect on Separated Flow Features in Supersonic Gas Flow;50
4.3.1;Nomenclature;50
4.3.2;1 Introduction;51
4.3.3;2 Analytical Investigation;52
4.3.4;3 Numerical Investigation;57
4.3.5;4 Results;58
4.3.6;5 Conclusion;63
4.3.7;References;64
4.4;Recent Results on Local Projection Stabilization for Convection-Diffusion and Flow Problems;66
4.4.1;1 Introduction;66
4.4.2;2 Convection-Diffusion Problem;67
4.4.2.1;2.1 Standard Galerkin and SUPG;67
4.4.2.2;2.2 Local Projection Stabilization (LPS);68
4.4.2.3;2.3 Basics in the Error Analysis of LPS;69
4.4.2.4;2.4 Relationship to Other StabilizationMethods;72
4.4.2.5;2.5 Choice of the Stabilization Parameter;73
4.4.2.6;2.6 LPS on Layer Adapted Meshes;73
4.4.3;3 Stokes Problem;75
4.4.3.1;3.1 Standard Galerkin and PSPG;75
4.4.3.2;3.2 Local Projection Stabilization;76
4.4.3.3;3.3 Error Estimates;77
4.4.3.4;3.4 Examples;78
4.4.3.5;3.5 Elimination of Enrichments;80
4.4.4;4 Oseen Problem;81
4.4.4.1;4.1 Standard Galerkin and LPS;81
4.4.4.2;4.2 LPS for Inf–Sup Stable Elements;82
4.4.4.3;4.3 LPS as an hp-Method;83
4.4.4.4;4.4 LPS on Anisotropic Meshes;84
4.4.5;References;84
5;Part II Contributed Papers;87
5.1;Numerical Simulation of the Towing Tank Problem Using High Order Schemes;88
5.1.1;1 Introduction;88
5.1.2;2 Mathematical Model;89
5.1.3;3 Numerical Schemes;90
5.1.4;4 Obstacle Modelling;92
5.1.5;5 Numerical Results;93
5.1.6;6 Conclusion;100
5.1.7;References;102
5.2;Nonlinear Singular Kelvin Modes in a Columnar Vortex;103
5.2.1;1 Introduction;103
5.2.2;2 Outer Flow;104
5.2.3;3 Critical Layer Analysis;106
5.2.4;4 The Small-Vorticity Limit;107
5.2.5;5 The Long-Wave Nonlinear Critical Layer;110
5.2.6;6 Concluding Remarks;111
5.2.7;References;113
5.3;High Order Schemes for Reaction–Diffusion Singularly Perturbed Systems;114
5.3.1;1 Introduction;114
5.3.2;2 The Numerical Method;115
5.3.3;3 The Case of Equal Diffusion Parameters;118
5.3.4;4 The General Case: e1