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Geometric Theory Of Incompressible Flows With Applications To Fluid Dynamics
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Book Synopsis Geometric Theory of Incompressible Flows with Applications to Fluid Dynamics by : Tian Ma
Download or read book Geometric Theory of Incompressible Flows with Applications to Fluid Dynamics written by Tian Ma and published by American Mathematical Soc.. This book was released on 2005 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph 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 its applications to fluid dynamics and geophysical fluid dynamics. The development of the theory and its applications goes well beyond its original motivation of the study of oceanic dynamics. The authors present a substantial advance in the use of geometric and topological methods to analyze and classify incompressible fluid flows. The approach introduces genuinely innovative ideas to the study of the partial differential equations of fluid dynamics. One particularly useful development is a rigorous theory for boundary layer separation of incompressible fluids. The study of incompressible flows has two major interconnected parts. 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. The material is suitable for researchers and advanced graduate students interested in nonlinear PDEs and fluid dynamics.
Book Synopsis An Introduction to the Geometry and Topology of Fluid Flows by : Renzo L. Ricca
Download or read book An Introduction to the Geometry and Topology of Fluid Flows written by Renzo L. Ricca and published by Springer. This book was released on 2001-11-30 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leading experts present a unique, invaluable introduction to the study of the geometry and typology of fluid flows. From basic motions on curves and surfaces to the recent developments in knots and links, the reader is gradually led to explore the fascinating world of geometric and topological fluid mechanics. Geodesics and chaotic orbits, magnetic knots and vortex links, continual flows and singularities become alive with more than 160 figures and examples. In the opening article, H. K. Moffatt sets the pace, proposing eight outstanding problems for the 21st century. The book goes on to provide concepts and techniques for tackling these and many other interesting open problems.
Author :Radyadour K. Zeytounian Publisher :Springer Science & Business Media ISBN 13 :3642562159 Total Pages :302 pages Book Rating :4.6/5 (425 download)
Book Synopsis Theory and Applications of Nonviscous Fluid Flows by : Radyadour K. Zeytounian
Download or read book Theory and Applications of Nonviscous Fluid Flows written by Radyadour K. Zeytounian and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "Researchers in fluid dynamics and applied mathematics will enjoy this book for its breadth of coverage, hands-on treatment of important ideas, many references, and historical and philosophical remarks." Mathematical Reviews
Book Synopsis Fluid Flow Phenomena by : Paolo Orlandi
Download or read book Fluid Flow Phenomena written by Paolo Orlandi and published by Springer Science & Business Media. This book was released on 2000 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dealing with the simulation of the incompressible Navier-Stokes equations for laminar and turbulent flows, this work permits the reader to play with the Navier-Stokes equations and to understand the complex physics related to fluid mechanics. Numerical simulations are useful tools for understanding the complexity of the flows, which often is difficult to derive from laboratory experiments. This book, then, can be very useful to scholars doing laboratory experiments, since they often do not have extra time to study the large variety of numerical methods; furthermore they cannot spend more time in transferring one of the methods into a computer language. By means of numerical simulations, for example, insights into the vorticity field can be obtained which are difficult to obtain by measurements. This book can be used by graduate as well as undergraduate students while reading books on theoretical fluid mechanics; it teaches how to simulate the dynamics of flow fields on personal computers. This will provide a better way of understanding the theory.
Book Synopsis Modern Fluid Dynamics: Incompressible flow by : N. Curle
Download or read book Modern Fluid Dynamics: Incompressible flow written by N. Curle and published by . This book was released on 1968 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis High-Order Methods for Incompressible Fluid Flow by : M. O. Deville
Download or read book High-Order Methods for Incompressible Fluid Flow written by M. O. Deville and published by Cambridge University Press. This book was released on 2002-08-15 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description
Book Synopsis Vorticity and Incompressible Flow by : Andrew J. Majda
Download or read book Vorticity and Incompressible Flow written by Andrew J. Majda and published by Cambridge University Press. This book was released on 2002 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive introduction to the mathematical theory of vorticity and incompressible flow ranging from elementary introductory material to current research topics. While the contents center on mathematical theory, many parts of the book showcase the interaction between rigorous mathematical theory, numerical, asymptotic, and qualitative simplified modeling, and physical phenomena. The first half forms an introductory graduate course on vorticity and incompressible flow. The second half comprise a modern applied mathematics graduate course on the weak solution theory for incompressible flow.
Book Synopsis Geometrical Theory of Dynamical Systems and Fluid Flows by : Tsutomu Kambe
Download or read book Geometrical Theory of Dynamical Systems and Fluid Flows written by Tsutomu Kambe and published by World Scientific. This book was released on 2004 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory textbook on the geometrical theory of dynamical systems, fluid flows, and certain integrable systems. The subjects are interdisciplinary and extend from mathematics, mechanics and physics to mechanical engineering, and the approach is very fundamental. The underlying concepts are based on differential geometry and theory of Lie groups in the mathematical aspect, and on transformation symmetries and gauge theory in the physical aspect. A great deal of effort has been directed toward making the description elementary, clear and concise, so that beginners will have an access to the topics.
Book Synopsis Computational Fluid Dynamics by : Takeo Kajishima
Download or read book Computational Fluid Dynamics written by Takeo Kajishima and published by Springer. This book was released on 2016-10-17 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This computational fluid dynamics (CFD) textbook presents numerical solution techniques for incompressible turbulent flows that occur in a variety of scientific and engineering settings including aerodynamics of ground-based vehicles and low-speed aircraft, fluid flows in energy systems, atmospheric flows, and biological flows. This book encompasses fluid mechanics, partial differential equations, numerical methods, and turbulence models, and emphasizes the foundation on how the governing partial differential equations for incompressible fluid flow can be solved numerically in an accurate and efficient manner. Extensive discussions on incompressible flow solvers and turbulence modeling are also offered. As CFD is widely used for a range of problems in theoretical research to industrial applications, and its use is expected to continue growing into the foreseeable future, this text is an ideal instructional resource and reference for students, professional engineers, and research scientists interested in analyzing fluid flows using numerical simulations.
Book Synopsis New Trends and Results in Mathematical Description of Fluid Flows by : Miroslav Bulíček
Download or read book New Trends and Results in Mathematical Description of Fluid Flows written by Miroslav Bulíček and published by Springer. This book was released on 2018-09-26 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents recent results and new trends in the theory of fluid mechanics. Each of the four chapters focuses on a different problem in fluid flow accompanied by an overview of available older results. The chapters are extended lecture notes from the ESSAM school "Mathematical Aspects of Fluid Flows" held in Kácov (Czech Republic) in May/June 2017. The lectures were presented by Dominic Breit (Heriot-Watt University Edinburgh), Yann Brenier (École Polytechnique, Palaiseau), Pierre-Emmanuel Jabin (University of Maryland) and Christian Rohde (Universität Stuttgart), and cover various aspects of mathematical fluid mechanics – from Euler equations, compressible Navier-Stokes equations and stochastic equations in fluid mechanics to equations describing two-phase flow; from the modeling and mathematical analysis of equations to numerical methods. Although the chapters feature relatively recent results, they are presented in a form accessible to PhD students in the field of mathematical fluid mechanics.
Book Synopsis Incompressible Flow by : Ronald L. Panton
Download or read book Incompressible Flow written by Ronald L. Panton and published by John Wiley & Sons. This book was released on 2013-08-05 with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most teachable book on incompressible flow— now fully revised, updated, and expanded Incompressible Flow, Fourth Edition is the updated and revised edition of Ronald Panton's classic text. It continues a respected tradition of providing the most comprehensive coverage of the subject in an exceptionally clear, unified, and carefully paced introduction to advanced concepts in fluid mechanics. Beginning with basic principles, this Fourth Edition patiently develops the math and physics leading to major theories. Throughout, the book provides a unified presentation of physics, mathematics, and engineering applications, liberally supplemented with helpful exercises and example problems. Revised to reflect students' ready access to mathematical computer programs that have advanced features and are easy to use, Incompressible Flow, Fourth Edition includes: Several more exact solutions of the Navier-Stokes equations Classic-style Fortran programs for the Hiemenz flow, the Psi-Omega method for entrance flow, and the laminar boundary layer program, all revised into MATLAB A new discussion of the global vorticity boundary restriction A revised vorticity dynamics chapter with new examples, including the ring line vortex and the Fraenkel-Norbury vortex solutions A discussion of the different behaviors that occur in subsonic and supersonic steady flows Additional emphasis on composite asymptotic expansions Incompressible Flow, Fourth Edition is the ideal coursebook for classes in fluid dynamics offered in mechanical, aerospace, and chemical engineering programs.
Book Synopsis Incompressible Bipolar and Non-Newtonian Viscous Fluid Flow by : Hamid Bellout
Download or read book Incompressible Bipolar and Non-Newtonian Viscous Fluid Flow written by Hamid Bellout and published by Springer Science & Business Media. This book was released on 2013-11-19 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of incompressible multipolar viscous fluids is a non-Newtonian model of fluid flow, which incorporates nonlinear viscosity, as well as higher order velocity gradients, and is based on scientific first principles. The Navier-Stokes model of fluid flow is based on the Stokes hypothesis, which a priori simplifies and restricts the relationship between the stress tensor and the velocity. By relaxing the constraints of the Stokes hypothesis, the mathematical theory of multipolar viscous fluids generalizes the standard Navier-Stokes model. The rigorous theory of multipolar viscous fluids is compatible with all known thermodynamical processes and the principle of material frame indifference; this is in contrast with the formulation of most non-Newtonian fluid flow models which result from ad hoc assumptions about the relation between the stress tensor and the velocity. The higher-order boundary conditions, which must be formulated for multipolar viscous flow problems, are a rigorous consequence of the principle of virtual work; this is in stark contrast to the approach employed by authors who have studied the regularizing effects of adding artificial viscosity, in the form of higher order spatial derivatives, to the Navier-Stokes model. A number of research groups, primarily in the United States, Germany, Eastern Europe, and China, have explored the consequences of multipolar viscous fluid models; these efforts, and those of the authors, which are described in this book, have focused on the solution of problems in the context of specific geometries, on the existence of weak and classical solutions, and on dynamical systems aspects of the theory. This volume will be a valuable resource for mathematicians interested in solutions to systems of nonlinear partial differential equations, as well as to applied mathematicians, fluid dynamicists, and mechanical engineers with an interest in the problems of fluid mechanics.
Book Synopsis The Mathematical Theory of Viscous Incompressible Flow by : O. A. Ladyzhenskaia
Download or read book The Mathematical Theory of Viscous Incompressible Flow written by O. A. Ladyzhenskaia and published by . This book was released on 2014-07-18 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: 2014 Reprint of 1963 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. Olga Aleksandrovna Ladyzhenskaya was a Soviet and Russian mathematician. She was known for her work on partial differential equations (especially Hilbert's 19th problem) and fluid dynamics. She provided the first rigorous proofs of the convergence of a finite difference method for the Navier-Stokes equations. This is a revised and updated edition of a book of fundamental importance in the rigorous theory of solutions of the Navier-Stokes equations. The author considers the questions of their existence and uniqueness when satisfying appropriate boundary conditions. For this purpose she extends the class of permissible functions from the infinitely differentiable class (classical solutions) to a class of generalized functions defined in the distributional sense. Thus existence of solution in the new class is a necessary but not sufficient condition for existence in the classical sense. Linear and non-linear, steady and unsteady forms of the equations and both finite and infinite domains are all considered: in each type of problem important theorems are established in the course of which many new ideas and methods are developed. The book is strongly recommended to mathematicians interested in modern analysis and the rigorous theory of fluid mechanics.
Book Synopsis Computational Fluid Dynamics for Incompressible Flows by : D.G. Roychowdhury
Download or read book Computational Fluid Dynamics for Incompressible Flows written by D.G. Roychowdhury and published by CRC Press. This book was released on 2020-08-20 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook covers fundamental and advanced concepts of computational fluid dynamics, a powerful and essential tool for fluid flow analysis. It discusses various governing equations used in the field, their derivations, and the physical and mathematical significance of partial differential equations and the boundary conditions. It covers fundamental concepts of finite difference and finite volume methods for diffusion, convection-diffusion problems both for cartesian and non-orthogonal grids. The solution of algebraic equations arising due to finite difference and finite volume discretization are highlighted using direct and iterative methods. Pedagogical features including solved problems and unsolved exercises are interspersed throughout the text for better understanding. The textbook is primarily written for senior undergraduate and graduate students in the field of mechanical engineering and aerospace engineering, for a course on computational fluid dynamics and heat transfer. The textbook will be accompanied by teaching resources including a solution manual for the instructors. Written clearly and with sufficient foundational background to strengthen fundamental knowledge of the topic. Offers a detailed discussion of both finite difference and finite volume methods. Discusses various higher-order bounded convective schemes, TVD discretisation schemes based on the flux limiter essential for a general purpose CFD computation. Discusses algorithms connected with pressure-linked equations for incompressible flow. Covers turbulence modelling like k-ε, k-ω, SST k-ω, Reynolds Stress Transport models. A separate chapter on best practice guidelines is included to help CFD practitioners.
Book Synopsis Mathematical Theory of Compressible Fluid Flow by : Richard Von Mises
Download or read book Mathematical Theory of Compressible Fluid Flow written by Richard Von Mises and published by Elsevier. This book was released on 2012-12-02 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Theory of Compressible Fluid Flow covers the conceptual and mathematical aspects of theory of compressible fluid flow. This five-chapter book specifically tackles the role of thermodynamics in the mechanics of compressible fluids. This text begins with a discussion on the general theory of characteristics of compressible fluid with its application. This topic is followed by a presentation of equations delineating the role of thermodynamics in compressible fluid mechanics. The discussion then shifts to the theory of shocks as asymptotic phenomena, which is set within the context of rational mechanics. The remaining two chapters is a thorough description of the hodograph method. These chapters provide a comparison of the modern integration theories. The features, characteristics, and application of transonic flow are also explored. This book is an ideal advanced textbook for both graduate students and research workers.
Book Synopsis Geometric Methods in Computational Fluid Dynamics by : Peter R. Eiseman
Download or read book Geometric Methods in Computational Fluid Dynamics written by Peter R. Eiseman and published by . This book was released on 1980 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fundamentals of Incompressible Flow by : V. Babu
Download or read book Fundamentals of Incompressible Flow written by V. Babu and published by CRC Press. This book was released on 2018-04 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes a novel approach to incompressible flow by first elucidating concepts such as viscosity and Reynolds number. The author derives incompressible Navier-Stokes equations and discusses the mathematical nature of their solutions. In this context, he introduces the notion of outer and inner singular perturbation solutions and then deals with the inviscid (outer) solutions, also deriving boundary layer (inner) solutions. The book also explores separation of the boundary layer, its consequences, and drag. It also covers parallel and creeping analytical solutions and discusses the nature and importance of turbulent flows in the context of internal and external flows, respectively.
