Stability and Transition: Theory and Application: Efficient Numerical Methods with Computer Programs

Book Description

Cebeci addresses transition from laminar to turbulent flows and considers solutions, mainly with the help of the linear stability theory and the ways in which it can be implemented accurately by numerical procedures. The main concern is transition of wall boundary layers, although one chapter is devoted to an approach based on the Navier-Stokes equations. The first three chapters summarize physical knowledge of the transition process, consider the stability equations and methods for predicting transition by linear stability theory, and describe efficient and accurate numerical methods for the solution of stability equations. Chapters 4 to 7 describe computer programs based on stability-theory approach to identify the location of transition in two- and three-dimensional incompressible and compressible flows, respectively, and Chapter 7 describes a computer program within the framework of parabolized stability equations. These programs are provided on an accompanying CD-ROM.

Thermodynamics of Flowing Systems: with Internal Microstructure (Oxford Engineering Science Series)

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Thermodynamics of Flowing Systems: with Internal Microstructure (Oxford Engineering Science Series)
Antony N. Beris , and Brian J. Edwards
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

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ASIN: 019507694X

Book Description

This much-needed monograph presents a systematic, step-by-step approach to the continuum modeling of flow phenomena exhibited within materials endowed with a complex internal microstructure, such as polymers and liquid crystals. By combining the principles of Hamiltonian mechanics with those of irreversible thermodynamics, Antony N. Beris and Brian J. Edwards, renowned authorities on the subject, expertly describe the complex interplay between conservative and dissipative processes. Throughout the book, the authors emphasize the evaluation of the free energy--largely based on ideas from statistical mechanics--and how to fit the values of the phenomenological parameters against those of microscopic models. With Thermodynamics of Flowing Systems in hand, mathematicians, engineers, and physicists involved with the theoretical study of flow behavior in structurally complex media now have a superb, self-contained theoretical framework on which to base their modeling efforts.

Differential Equations and Dynamical Systems

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Very good graduate ODEs text, with some flaws
A Book on Advanced Dynamical Systems

Differential Equations and Dynamical Systems
Lawrence Perko
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0387951164

Book Description

This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem, the use of the Poincare map in the theory of limit cycles, the theory of rotated vector fields and its use in the study of limit cycles and homoclinic loops, and a description of the behavior and termination of one-parameter families of limit cycles. In addition to minor corrections and updates throughout, this new edition includes materials on higher order Melnikov theory and the bifurcation of limit cycles for planar systems of differential equations, including new sections on Francoise's algorithm for higher order Melnikov functions and on the finite codimension bifurcations that occur in the class of bounded quadratic systems.

Customer Reviews:

Very good graduate ODEs text, with some flaws.......2003-12-12

Perko's book is one of the best books that gives an advanced introduction to dynamical systems from the point of differential equations. Many other good books tread the same ground, without emphasizing the connection to ODEs. Perko's text is particularly strong in several respects. First, the dynamical systems it considers are almost always expressed in terms of underlying differential equations. Second, it gives proofs or outlines of proofs of most major theorems used in this field. Third, it covers the most important topics, including: local theory of hyperbolic equilibria, invariant manifolds, Hamiltonian systems, flows on R^2, stability theory, and elementary bifurcations. Also reviewed are the results from linear systems theory, in a particularly well-written and easy to follow introductory chapter. Another great feature of this book is its solid coverage of center manifold theory, which is an important and somewhat difficult topic.

There are a couple of problems with this book. The proofs to some of the major theorems are occasionally abstruse or poorly derived. Perko seems to bend over backwards to give analytical proofs, when algebraic or topological proofs might be easier. Many of the problems reuse the same elementary example equations. This is OK insofar as it allows the reader to see how different techniques can be used to analyze the same systems, but it limits the reader's exposure to the full variety of interesting dynamical systems that can arise in practice. The author also tends to emphasize polynomial vector fields, which is a potential limitation. Occasionally the problems are significantly more difficult than the examples worked in the text.

Overall, Perko's text is a very solid introduction to advanced ODEs and continuous dynamics. It is especially well-suited for scientists and engineers who want a readable introduction to the qualitative theory of ODEs.

A Book on Advanced Dynamical Systems.......2000-04-08

This book is a useful textbook for advanced courses on differential equations and dynamical systems for senior undergraduate students or first year graduate students.

The book presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems.

The book has a sketch of the proof of the Hartman-Grobman Theorem which was useful for my second undergraduate course on dynamical systems and nonlinear differential equations.

Book Description

Although the current dynamical system approach offers several important insights into the turbulence problem, issues still remain that present challenges to conventional methodologies and concepts. These challenges call for the advancement and application of new physical concepts, mathematical modeling, and analysis techniques. Bringing together experts from physics, applied mathematics, and engineering, Mathematical and Physical Theory of Turbulence discusses recent progress and some of the major unresolved issues in two- and three-dimensional turbulence as well as scalar compressible turbulence. Containing introductory overviews as well as more specialized sections, this book examines a variety of turbulence-related topics. The authors concentrate on theory, experiments, computational, and mathematical aspects of Navier-Stokes turbulence; geophysical flows; modeling; laboratory experiments; and compressible/magnetohydrodynamic effects. The topics discussed in these areas include finite-time singularities and inviscid dissipation energy; validity of the idealized model incorporating local isotropy, homogeneity, and universality of small scales of high Reynolds numbers, Lagrangian statistics, and measurements; and subrigid-scale modeling and hybrid methods involving a mix of Reynolds-averaged Navier-Stokes (RANS), large-eddy simulations (LES), and direct numerical simulations (DNS). By sharing their expertise and recent research results, the authoritative contributors in Mathematical and Physical Theory of Turbulence promote further advances in the field, benefiting applied mathematicians, physicists, and engineers involved in understanding the complex issues of the turbulence problem.

Perspectives in Flow Control and Optimization (Advances in Design and Control)

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Perspectives in Flow Control and Optimization (Advances in Design and Control)
Max D. Gunzburger
Manufacturer: Society for Industrial Mathematics
ProductGroup: Book
Binding: Hardcover

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ASIN: 089871527X

Book Description

Flow control and optimization has been an important part of experimental flow science throughout the last century. As research in computational fluid dynamics (CFD) matured, CFD codes were routinely used for the simulation of fluid flows. Subsequently, mathematicians and engineers began examining the use of CFD algorithms and codes for optimization and control problems for fluid flows. The marriage of mature CFD methodologies with state-of-the-art optimization methods has become the center of activity in computational flow control and optimization. Perspectives in Flow Control and Optimization presents flow control and optimization as a subdiscipline of computational mathematics and computational engineering. It introduces the development and analysis of several approaches for solving flow control and optimization problems through the use of modern CFD and optimization methods.

Nonlinearities in Action: Oscillations, Chaos, Order, Fractals

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Nonlinearities in Action: Oscillations, Chaos, Order, Fractals
Andrei V. Gaponov-Grekhov , and Mikhail I. Rabinovich
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Book Description

This concise and comprehensive overview of nonlinear processes addresses all those interested in natural sciences and mathematics. It also contains a beautifully illustrated color insert easily accessible to the interested layperson. Thus it is suitable for leisure reading and also for an introductory (under)graduate course in nonlinear physics. Both well-established and more recent new results are discussed, outlining the relation between classical aspects of nonlinear physics and important current problems like the birth of chaos in simple deterministic systems and the emergence of order out of disorder and turbulence. Keywords: Chaos, fractals, strange attractors, turbulence.

Statistical Theory and Modeling for Turbulent Flows

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many print errors
Student's perspective

Statistical Theory and Modeling for Turbulent Flows
P. A. Durbin , and B. A. Pettersson Reif
Manufacturer: Wiley
ProductGroup: Book
Binding: Paperback

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Turbulent Flows

ASIN: 0471497444

Book Description

Most natural and industrial flows are turbulent. The atmosphere and oceans, automobile and aircraft engines, all provide examples of this ubiquitous phenomenon. In recent years, turbulence has become a very lively area of scientific research and application, and this work offers a grounding in the subject of turbulence, developing both the physical insight and the mathematical framework needed to express the theory. Providing a solid foundation in the key topics in turbulence, this valuable reference resource enables the reader to become a knowledgeable developer of predictive tools.
This central and broad ranging topic would be of interest to graduate students in a broad range of subjects, including aeronautical and mechanical engineering, applied mathematics and the physical sciences. The accompanying solutions manual to the text also makes this a valuable teaching tool for lecturers and for practising engineers and scientists in computational and experimental and experimental fluid dynamics.

Customer Reviews:

many print errors.......2007-09-24

There are a lot of print errors in this book. Nearly all the equations are not right. I asked some other persons who also bought this book. This problem is very common. May you find a solution about this problem?
3x.

Student's perspective.......2007-09-05

I bought this book as required reading for a class. It's pretty clear and easy to understand, although I have the advantage that my professor is one of the authors. Concepts are explained well, with examples.

The major problem with this book is that for some reason, all the horizontal lines are missing from the equations. So there are no fraction bars, and it's really hard to tell where an average is meant, as opposed to a random variable. I wouldn't recommend this book to someone without a background in basic statistics, because the math would be nearly impossible to follow.

Control of Fluid Flow (Lecture Notes in Control and Information Sciences)

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Control of Fluid Flow (Lecture Notes in Control and Information Sciences)

Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 3540251405

Book Description

This carefully edited monograph presents the state of the art of theory and applications in fluid flow control. It collects contributions by leading experts in the field of fluid flow control interesting for engineers, physicists, or mathematicians in control and fluid dynamics. "Control of Fluid Flow" covers a wide range of recent topics including vortex based control algorithms, incompressible turbulent boundary layers, aerodynamic flow control, control of mixing and reactive flow processes or nonlinear modeling and control of combustion dynamics.

Flow and Transport in Porous Media and Fractured Rock: From Classical Methods to Modern Approaches

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Flow and Transport in Porous Media and Fractured Rock: From Classical Methods to Modern Approaches
Muhammad Sahimi
Manufacturer: Wiley-VCH Verlag GmbH
ProductGroup: Book
Binding: Hardcover

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Book Description

Theoretical and experimental approaches to flow, hydrodynamic dispersion, and miscible displacements in porous media and fractured rock are considered. Two different approaches are discussed and contrasted with each other. The first approach is based on the classical equations of flow and transport, called 'continuum models'. The second approach is based on modern methods of statistical physics of disordered media; that is, on 'discrete models', which have become increasingly popular over the past 15 years. The book is unique in its scope, since (1) there is currently no book that compares the two approaches, and covers all important aspects of porous media problems; and (2) includes discussion of fractured rocks, which so far has been treated as a separate subject.

Portions of the book would be suitable for an advanced undergraduate course. The book would be ideal for graduate courses on the subject, and can be used by chemical, petroleum, civil, environmental engineers, and geologists, as well as physicists, applied physicist and allied scientists that deal with various porous media problems.

Fundamentals of Two-Fluid Dynamics, Part I: Mathematical Theory and Applications (Interdisciplinary Applied Mathematics)

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Fundamentals of Two-Fluid Dynamics, Part I: Mathematical Theory and Applications (Interdisciplinary Applied Mathematics)
Daniel D. Joseph , and Yuriko Y. Renardy
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0387979131

Book Description

Two-fluid dynamics is a challenging subject rich in interdisciplinary science. Reporting from the forefront of research in this area, these volumes combine scientific, engineering, and technological results in a sound mathematical framework. The analytical techniques used throughout the books are rigorously derived in Part I, Mathematic Theory and Applications, making the books appropriate for graduate study. Rotating flows of two liquids, the two-layer Bérnard problem, and plane channel flows are also thoroughly covered. In Part II, Lubricated Transport, Drops and Miscible Liquids, an extensive discussion of lubricated pipelining is given with the serious intention of advancing the technology. Core-annular flow, vortex rings in free fall, two-fluids with phase change, and miscible liquids are some of the topics presented in detail. Photographs, figures, graphs, and tables augment continuous comparison of theory and observations. These volumes are bound to become a standard source in a field which is attracting much scientific and industrial interest.

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