Author: Story

Publisher: iUniverse

ISBN: 0595339212

Category: Mathematics

Page: 168

View: 8710

Introduction to Differential Geometry with applications to Navier-Stokes Dynamics is an invaluable manuscript for anyone who wants to understand and use exterior calculus and differential geometry, the modern approach to calculus and geometry. Author Troy Story makes use of over thirty years of research experience to provide a smooth transition from conventional calculus to exterior calculus and differential geometry, assuming only a knowledge of conventional calculus. Introduction to Differential Geometry with applications to Navier-Stokes Dynamics includes the topics: Geometry, Exterior calculus, Homology and co-homology, Applications of differential geometry and exterior calculus to: Hamiltonian mechanics, geometric optics, irreversible thermodynamics, black hole dynamics, electromagnetism, classical string fields, and Navier-Stokes dynamics.
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Author: Tian Ma,Shouhong Wang

Publisher: American Mathematical Soc.

ISBN: 0821836935

Category: Mathematics

Page: 234

View: 1949

This book presents a geometric theory for incompressible flow and its applications to fluid dynamics. The main objective is to study the stability and transitions of the structure of incompressible flows, and applications to fluid dynamics and geophysical fluid dynamics. The development of the theory and its applications has gone well beyond the original motivation, which was the study of oceanic dynamics. One such development is a rigorous theory for boundary layer separation of incompressible fluid flows. This study of incompressible flows has two major parts, which are interconnected. The first is the development of a global geometric theory of divergence-free fields on general two-dimensional compact manifolds. The second is the study of the structure of velocity fields for two-dimensional incompressible fluid flows governed by the Navier-Stokes equations or the Euler equations. Motivated by the study of problems in geophysical fluid dynamics, the program of research in this book seeks to develop a new mathematical theory, maintaining close links to physics along the way. In return, the theory is applied to physical problems, with more problems yet to be explored.
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A Modern Introduction

Author: Vladimir G. Ivancevic,Tijana T. Ivancevic

Publisher: World Scientific

ISBN: 9812706143

Category: Mathematics

Page: 1311

View: 7980

This graduate-level monographic textbook treats applied differential geometry from a modern scientific perspective. Co-authored by the originator of the world's leading human motion simulator ? ?Human Biodynamics Engine?, a complex, 264-DOF bio-mechanical system, modeled by differential-geometric tools ? this is the first book that combines modern differential geometry with a wide spectrum of applications, from modern mechanics and physics, via nonlinear control, to biology and human sciences. The book is designed for a two-semester course, which gives mathematicians a variety of applications for their theory and physicists, as well as other scientists and engineers, a strong theory underlying their models.
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An Introduction with Applications

Author: Grzegorz Łukaszewicz,Piotr Kalita

Publisher: Springer

ISBN: 331927760X

Category: Mathematics

Page: 390

View: 2601

This volume is devoted to the study of the Navier–Stokes equations, providing a comprehensive reference for a range of applications: from advanced undergraduate students to engineers and professional mathematicians involved in research on fluid mechanics, dynamical systems, and mathematical modeling. Equipped with only a basic knowledge of calculus, functional analysis, and partial differential equations, the reader is introduced to the concept and applications of the Navier–Stokes equations through a series of fully self-contained chapters. Including lively illustrations that complement and elucidate the text, and a collection of exercises at the end of each chapter, this book is an indispensable, accessible, classroom-tested tool for teaching and understanding the Navier–Stokes equations. Incompressible Navier–Stokes equations describe the dynamic motion (flow) of incompressible fluid, the unknowns being the velocity and pressure as functions of location (space) and time variables. A solution to these equations predicts the behavior of the fluid, assuming knowledge of its initial and boundary states. These equations are one of the most important models of mathematical physics: although they have been a subject of vivid research for more than 150 years, there are still many open problems due to the nature of nonlinearity present in the equations. The nonlinear convective term present in the equations leads to phenomena such as eddy flows and turbulence. In particular, the question of solution regularity for three-dimensional problem was appointed by Clay Institute as one of the Millennium Problems, the key problems in modern mathematics. The problem remains challenging and fascinating for mathematicians, and the applications of the Navier–Stokes equations range from aerodynamics (drag and lift forces), to the design of watercraft and hydroelectric power plants, to medical applications such as modeling the flow of blood in the circulatory system.
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A Classification of Flows and Exact Solutions

Author: P. G. Drazin,N. Riley

Publisher: Cambridge University Press

ISBN: 9780521681629

Category: Mathematics

Page: 196

View: 7978

This 2006 book details exact solutions to the Navier-Stokes equations for senior undergraduates and graduates or research reference.
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Będlewo, Poland, October 2013

Author: Jacek Banasiak,Adam Bobrowski,Mirosław Lachowicz

Publisher: Springer

ISBN: 3319121456

Category: Mathematics

Page: 337

View: 7198

Many results, both from semi group theory itself and from the applied sciences, are phrased in discipline-specific languages and hence are hardly known to a broader community. This volume contains a selection of lectures presented at a conference that was organised as a forum for all mathematicians using semi group theory to learn what is happening outside their own field of research. The collection will help to establish a number of new links between various sub-disciplines of semigroup theory, stochastic processes, differential equations and the applied fields. The theory of semigroups of operators is a well-developed branch of functional analysis. Its foundations were laid at the beginning of the 20th century, while the fundamental generation theorem of Hille and Yosida dates back to the forties. The theory was, from the very beginning, designed as a universal language for partial differential equations and stochastic processes, but at the same time it started to live as an independent branch of operator theory. Nowadays, it still has the same distinctive flavour: it develops rapidly by posing new ‘internal’ questions and in answering them, discovering new methods that can be used in applications. On the other hand, it is influenced by questions from PDEs and stochastic processes as well as from applied sciences such as mathematical biology and optimal control, and thus it continually gathers a new momentum. Researchers and postgraduate students working in operator theory, partial differential equations, probability and stochastic processes, analytical methods in biology and other natural sciences, optimization and optimal control will find this volume useful.
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Author: Vladimir D. Liseikin

Publisher: Springer Science & Business Media

ISBN: 3540342362

Category: Science

Page: 294

View: 1906

The process of breaking up a physical domain into smaller sub-domains, known as meshing, facilitates the numerical solution of partial differential equations used to simulate physical systems. In an updated and expanded Second Edition, this monograph gives a detailed treatment based on the numerical solution of inverted Beltramian and diffusion equations with respect to monitor metrics for generating both structured and unstructured grids in domains and on surfaces.
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Author: James C. Robinson,José L. Rodrigo,Witold Sadowski,Alejandro Vidal-López

Publisher: Cambridge University Press

ISBN: 131658934X

Category: Mathematics

Page: N.A

View: 3945

The rigorous mathematical theory of the Navier–Stokes and Euler equations has been a focus of intense activity in recent years. This volume, the product of a workshop in Venice in 2013, consolidates, surveys and further advances the study of these canonical equations. It consists of a number of reviews and a selection of more traditional research articles on topics that include classical solutions to the 2D Euler equation, modal dependency for the 3D Navier–Stokes equation, zero viscosity Boussinesq equations, global regularity and finite-time singularities, well-posedness for the diffusive Burgers equations, and probabilistic aspects of the Navier–Stokes equation. The result is an accessible summary of a wide range of active research topics written by leaders in their field, together with some exciting new results. The book serves both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.
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Author: Heinz-Otto Kreiss,Jens Lorenz

Publisher: SIAM

ISBN: 0898715652

Category: Science

Page: 420

View: 8648

Initial-Boundary Value Problems and the Navier-Stokes Equations gives an introduction to the vast subject of initial and initial-boundary value problems for PDEs. Applications to parabolic and hyperbolic systems are emphasized in this text. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. The subjects addressed in the book, such as the well-posedness of initial-boundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The book explains the principles of these subjects. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. Audience: when the book was written, the main intent was to write a text on initial-boundary value problems that was accessible to a rather wide audience. Functional analytical prerequisites were kept to a minimum or were developed in the book. Boundary conditions are analyzed without first proving trace theorems, and similar simplifications have been used throughout. This book continues to be useful to researchers and graduate students in applied mathematics and engineering.
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Classical Theory

Author: James C. Robinson,José L. Rodrigo,Witold Sadowski

Publisher: Cambridge University Press

ISBN: 1107019664

Category: Mathematics

Page: 446

View: 1330

An accessible treatment of the main results in the mathematical theory of the Navier-Stokes equations, primarily aimed at graduate students.
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Author: Bengt Andersson,Ronnie Andersson,Love Håkansson,Mikael Mortensen,Rahman Sudiyo,Berend van Wachem

Publisher: Cambridge University Press

ISBN: 1139505564

Category: Technology & Engineering

Page: N.A

View: 9153

Computational fluid dynamics, CFD, has become an indispensable tool for many engineers. This book gives an introduction to CFD simulations of turbulence, mixing, reaction, combustion and multiphase flows. The emphasis on understanding the physics of these flows helps the engineer to select appropriate models to obtain reliable simulations. Besides presenting the equations involved, the basics and limitations of the models are explained and discussed. The book combined with tutorials, project and power-point lecture notes (all available for download) forms a complete course. The reader is given hands-on experience of drawing, meshing and simulation. The tutorials cover flow and reactions inside a porous catalyst, combustion in turbulent non-premixed flow, and multiphase simulation of evaporation spray respectively. The project deals with design of an industrial-scale selective catalytic reduction process and allows the reader to explore various design improvements and apply best practice guidelines in the CFD simulations.
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Author: University of California, Santa Cruz

Publisher: N.A

ISBN: N.A

Category:

Page: N.A

View: 9776

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Second Edition

Author: Roger Temam

Publisher: SIAM

ISBN: 0898713404

Category: Technology & Engineering

Page: 141

View: 9064

This second edition attempts to arrive as simply as possible at some central problems in the Navier-Stokes equations.
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Author: H. Lomax,Thomas H. Pulliam,David W. Zingg

Publisher: Springer Science & Business Media

ISBN: 3662046547

Category: Science

Page: 250

View: 6263

The chosen semi-discrete approach of a reduction procedure of partial differential equations to ordinary differential equations and finally to difference equations gives the book its distinctiveness and provides a sound basis for a deep understanding of the fundamental concepts in computational fluid dynamics.
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Principles of Analysis and Design

Author: Stanley Middleman

Publisher: John Wiley & Sons Incorporated

ISBN: 9780471182092

Category: Technology & Engineering

Page: 513

View: 2947

This comprehensive text links abstract mathematics to engineering applications in order to provide a clear and thorough exploration of fluid dynamics. Focus is on the development of mathematical models of physical phenomena and the wide range of technologies available to students. Filled with examples and problems inspired by real engineering applications, this resource will not only teach, but motivate students to further emerge themselves in the field.
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An Introduction

Author: Eugene L. Allgower,Kurt Georg

Publisher: Springer Science & Business Media

ISBN: 3642612571

Category: Mathematics

Page: 388

View: 8493

Over the past fifteen years two new techniques have yielded extremely important contributions toward the numerical solution of nonlinear systems of equations. This book provides an introduction to and an up-to-date survey of numerical continuation methods (tracing of implicitly defined curves) of both predictor-corrector and piecewise-linear types. It presents and analyzes implementations aimed at applications to the computation of zero points, fixed points, nonlinear eigenvalue problems, bifurcation and turning points, and economic equilibria. Many algorithms are presented in a pseudo code format. An appendix supplies five sample FORTRAN programs with numerical examples, which readers can adapt to fit their purposes, and a description of the program package SCOUT for analyzing nonlinear problems via piecewise-linear methods. An extensive up-to-date bibliography spanning 46 pages is included. The material in this book has been presented to students of mathematics, engineering and sciences with great success, and will also serve as a valuable tool for researchers in the field.
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Author: Franck Boyer,Pierre Fabrie

Publisher: Springer Science & Business Media

ISBN: 1461459753

Category: Mathematics

Page: 526

View: 8537

The objective of this self-contained book is two-fold. First, the reader is introduced to the modelling and mathematical analysis used in fluid mechanics, especially concerning the Navier-Stokes equations which is the basic model for the flow of incompressible viscous fluids. Authors introduce mathematical tools so that the reader is able to use them for studying many other kinds of partial differential equations, in particular nonlinear evolution problems. The background needed are basic results in calculus, integration, and functional analysis. Some sections certainly contain more advanced topics than others. Nevertheless, the authors’ aim is that graduate or PhD students, as well as researchers who are not specialized in nonlinear analysis or in mathematical fluid mechanics, can find a detailed introduction to this subject. .
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Author: Yasuki Nakayama

Publisher: Butterworth-Heinemann

ISBN: 008102438X

Category: Technology & Engineering

Page: 400

View: 2552

Introduction to Fluid Mechanics, Second Edition, uses clear images and animations of flow patterns to help readers grasp the fundamental rules of fluid behavior. Everyday examples are provided for practical context, before tackling the more involved mathematic techniques that form the basis for computational fluid mechanics. This fully updated and expanded edition builds on the author’s flair for flow visualization with new content. With basic introductions to all essential fluids theory, and exercises to test your progress, this is the ideal introduction to fluids for anyone involved in mechanical, civil, chemical, or biomedical engineering. Provides illustrations and animations to demonstrate fluid behavior Includes examples and exercises drawn from a range of engineering fields Explains a range of computerized and traditional methods for flow visualization, and how to choose the correct one Features a fully reworked section on computational fluid dynamics based on discretization methods
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Author: Joel H. Ferziger,Milovan Peric

Publisher: Springer Science & Business Media

ISBN: 3642976514

Category: Technology & Engineering

Page: 364

View: 9075

A detailed description of the methods most often used in practice. The authors are experts in their fields and cover such advanced techniques as direct and large-eddy simulation of turbulence, multigrid methods, parallel computing, moving grids, structured, block-structured and unstructured boundary-fitted grids, and free surface flows. The book shows common roots and basic principles for many apparently different methods, while also containing a great deal of practical advice for code developers and users. All the computer codes can be accessed from the Springer server on the internet. Designed to be equally useful for beginners and experts.
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Author: Walter Craig

Publisher: Springer Science & Business Media

ISBN: 1402069642

Category: Mathematics

Page: 441

View: 8177

This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems. Applications are also presented to several important areas of research, including problems in classical mechanics, continuum mechanics, and partial differential equations.
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