Ebook: Asymptotic Modelling of Fluid Flow Phenomena

for the fluctuations around the means but rather fluctuations, and appearing in the following incompressible system of equations: on any wall; at initial time, and are assumed known. This contribution arose from discussion with J. P. Guiraud on attempts to push forward our last co-signed paper (1986) and the main idea is to put a stochastic structure on fluctuations and to identify the large eddies with a part of the probability space. The Reynolds stresses are derived from a kind of Monte-Carlo process on equations for fluctuations. Those are themselves modelled against a technique, using the Guiraud and Zeytounian (1986). The scheme consists in a set of like equations, considered as random, because they mimic the large eddy fluctuations. The Reynolds stresses are got from stochastic averaging over a family of their solutions. Asymptotics underlies the scheme, but in a rather loose hidden way. We explain this in relation with homogenizati- localization processes (described within the §3. 4 ofChapter 3). Ofcourse the mathematical well posedness of the scheme is not known and the numerics would be formidable! Whether this attempt will inspire researchers in the field of highly complex turbulent flows is not foreseeable and we have hope that the idea will prove useful.

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This is the first book devoted entirely to asymptotic modelling of fluid flow phenomena and deals with the art of the asymptotic modelling of Newtonian laminar fluid flows. This asymptotic modelling consists of deriving fluid flow model problems in such a way that they become amenable to mathematical analysis and to numerical simulations. The main goal of the text is modelling and not the presentation of solutions.

One may assume that for some time to come the further expansion of the capabilities of numerical simulations will depend on, or will at least be related to, the development of asymptotic modelling. The book includes the basic aspects, recent developments, and the current issues important to the asymptotic modelling of fluid flow phenomena.

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This is the first book devoted entirely to asymptotic modelling of fluid flow phenomena and deals with the art of the asymptotic modelling of Newtonian laminar fluid flows. This asymptotic modelling consists of deriving fluid flow model problems in such a way that they become amenable to mathematical analysis and to numerical simulations. The main goal of the text is modelling and not the presentation of solutions.

One may assume that for some time to come the further expansion of the capabilities of numerical simulations will depend on, or will at least be related to, the development of asymptotic modelling. The book includes the basic aspects, recent developments, and the current issues important to the asymptotic modelling of fluid flow phenomena.

Content:
Front Matter....Pages i-xviii
Introductory Comments and Summary....Pages 1-18
Front Matter....Pages 19-19
Newtonian Fluid Flow: Equations and Conditions....Pages 21-40
Some Basic Aspects of Asymptotic Analysis and Modelling....Pages 41-60
Useful Limiting Forms of the NS-F Equations....Pages 61-84
Front Matter....Pages 85-85
The Navier-Fourier Viscous Incompressible Model....Pages 87-112
The Inviscid/Nonviscous Euler Model and Some Hydro-Aerodynamics Problems....Pages 113-214
Boundary-Layer Models for High-Reynolds Numbers....Pages 215-292
Some Models of Nonlinear Acoustics....Pages 293-325
Low-Reynolds Numbers Asymptotics....Pages 327-367
Front Matter....Pages 369-369
Asymptotic Modelling of Thermal Convection and Interfacial Phenomena....Pages 371-422
Meteo-Fluid-Dynamics Models....Pages 423-469
Singular Coupling and the Triple-Deck Model....Pages 471-525
Back Matter....Pages 527-549

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This is the first book devoted entirely to asymptotic modelling of fluid flow phenomena and deals with the art of the asymptotic modelling of Newtonian laminar fluid flows. This asymptotic modelling consists of deriving fluid flow model problems in such a way that they become amenable to mathematical analysis and to numerical simulations. The main goal of the text is modelling and not the presentation of solutions.

One may assume that for some time to come the further expansion of the capabilities of numerical simulations will depend on, or will at least be related to, the development of asymptotic modelling. The book includes the basic aspects, recent developments, and the current issues important to the asymptotic modelling of fluid flow phenomena.

Content:
Front Matter....Pages i-xviii
Introductory Comments and Summary....Pages 1-18
Front Matter....Pages 19-19
Newtonian Fluid Flow: Equations and Conditions....Pages 21-40
Some Basic Aspects of Asymptotic Analysis and Modelling....Pages 41-60
Useful Limiting Forms of the NS-F Equations....Pages 61-84
Front Matter....Pages 85-85
The Navier-Fourier Viscous Incompressible Model....Pages 87-112
The Inviscid/Nonviscous Euler Model and Some Hydro-Aerodynamics Problems....Pages 113-214
Boundary-Layer Models for High-Reynolds Numbers....Pages 215-292
Some Models of Nonlinear Acoustics....Pages 293-325
Low-Reynolds Numbers Asymptotics....Pages 327-367
Front Matter....Pages 369-369
Asymptotic Modelling of Thermal Convection and Interfacial Phenomena....Pages 371-422
Meteo-Fluid-Dynamics Models....Pages 423-469
Singular Coupling and the Triple-Deck Model....Pages 471-525
Back Matter....Pages 527-549
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