Roger M. Temam's Books

Singular Perturbations and Boundary Layers

By: Gung-Min Gie,Makram Hamouda,Chang-Yeol Jung,Roger M. Temam

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Singular Perturbations and Boundary Layers

By: Gung-Min Gie,Makram Hamouda,Chang-Yeol Jung,Roger M. Temam

Singular perturbations occur when a small coefficient affects the highest order derivatives in a system of partial differential equations. From the physical point of view singular perturbations generate in the system under consideration thin layers located often but not always at the boundary of the domains that are called boundary layers or internal layers if the layer is located inside the domain. Important physical phenomena occur in boundary layers. The most common boundary layers appear in fluid mechanics, e.g., the flow of air around an airfoil or a whole airplane, or the flow of air around a car. Also in many instances in geophysical fluid mechanics, like the interface of air and earth, or air and ocean. This self-contained monograph is devoted to the study of certain classes of singular perturbation problems mostly related to thermic, fluid mechanics and optics and where mostly elliptic or parabolic equations in a bounded domain are considered. This book is a fairly unique resource regarding the rigorous mathematical treatment of boundary layer problems. The explicit methodology developed in this book extends in many different directions the concept of correctors initially introduced by J. L. Lions, and in particular the lower- and higher-order error estimates of asymptotic expansions are obtained in the setting of functional analysis. The review of differential geometry and treatment of boundary layers in a curved domain is an additional strength of this book. In the context of fluid mechanics, the outstanding open problem of the vanishing viscosity limit of the Navier-Stokes equations is investigated in this book and solved for a number of particular, but physically relevant cases. This book will serve as a unique resource for those studying singular perturbations and boundary layer problems at the advanced graduate level in mathematics or applied mathematics and may be useful for practitioners in other related fields in science and engineering such as aerodynamics, fluid mechanics, geophysical fluid mechanics, acoustics and optics.

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Page Count

424

Publisher

Springer

Published Date

ISBN 10

3030006387

ISBN 13

9783030006389

Spectral Methods for Incompressible Viscous Flow

By: Roger Peyret

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Spectral Methods for Incompressible Viscous Flow

By: Roger Peyret

This well-written book explains the theory of spectral methods and their application to the computation of viscous incompressible fluid flow, in clear and elementary terms. With many examples throughout, the work will be useful to those teaching at the graduate level, as well as to researchers working in the area.

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Page Count

438

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1475765576

ISBN 13

9781475765571

Mathematical and Numerical Foundations of Turbulence Models and Applications

By: Tomás Chacón Rebollo,Roger Lewandowski

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Mathematical and Numerical Foundations of Turbulence Models and Applications

By: Tomás Chacón Rebollo,Roger Lewandowski

With applications to climate, technology, and industry, the modeling and numerical simulation of turbulent flows are rich with history and modern relevance. The complexity of the problems that arise in the study of turbulence requires tools from various scientific disciplines, including mathematics, physics, engineering and computer science. Authored by two experts in the area with a long history of collaboration, this monograph provides a current, detailed look at several turbulence models from both the theoretical and numerical perspectives. The k-epsilon, large-eddy simulation and other models are rigorously derived and their performance is analyzed using benchmark simulations for real-world turbulent flows. Mathematical and Numerical Foundations of Turbulence Models and Applications is an ideal reference for students in applied mathematics and engineering, as well as researchers in mathematical and numerical fluid dynamics. It is also a valuable resource for advanced graduate students in fluid dynamics, engineers, physical oceanographers, meteorologists and climatologists.

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Page Count

530

Publisher

Springer

Published Date

ISBN 10

1493904558

ISBN 13

9781493904556

Mathematical Modeling in Continuum Mechanics

By: Roger Temam,Alain Miranville

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Mathematical Modeling in Continuum Mechanics

By: Roger Temam,Alain Miranville

Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.

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Page Count

356

Publisher

Cambridge University Press

Published Date

ISBN 10

1139443216

ISBN 13

9781139443210

Book's by Roger M. Temam

Singular Perturbations and Boundary Layers

Singular Perturbations and Boundary Layers

Spectral Methods for Incompressible Viscous Flow

Spectral Methods for Incompressible Viscous Flow

Mathematical and Numerical Foundations of Turbulence Models and Applications

Mathematical and Numerical Foundations of Turbulence Models and Applications

Mathematical Modeling in Continuum Mechanics

Mathematical Modeling in Continuum Mechanics

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