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The Navier-Stokes equations were firmly established in the 19th Century as the system of nonlinear partial differential equations which describe the motion of most commonly occurring fluids in air and water, and since that time exact solutions have been sought by scientists. Collectively these solutions allow a clear insight into the behavior of fluids, providing a vehicle for novel mathematical methods and a useful check for computations in fluid dynamics, a field in which theoretical research is now dominated by computational methods. This 2006 book draws together exact solutions from widely differing sources and presents them in a coherent manner, in part by classifying solutions via their temporal and geometric constraints. It will prove to be a valuable resource to all who have an interest in the subject of fluid mechanics, and in particular to those who are learning or teaching the subject at the senior undergraduate and graduate levels.
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This book presents the new discovery of the origin of turbulence from Navier-Stokes equations. The fully developed turbulence is found to be composed of singularities of flow field. The mechanisms of flow stability and turbulent transition are described using the energy gradient theory, which states all the flow instability and breakdown resulted from the gradient of the total mechanical energy normal to the flow direction. This approach is universal for flow instability in Newtonian flow and non-Newtonian flow. The theory has been used to solve several problems, such as plane and pipe Poiseuille flows, plane Couette flow, Taylor-Couette flow, flows in straight coaxial annulus, flows in curved pipes and ducts, thermal convection flow, viscoelastic flow, and magnet fluid flow, etc. The theory is in agreement with results from numerical simulations and experiments. The analytical method used in this book is novel and is different from the traditional approaches. This book includes the fundamental basics of flow stability and turbulent transition, the essentials of the energy gradient theory, and the applications of the theory to several practical problems. This book is suitable for researchers and graduate students.
Fluid mechanics --- ingenieurswetenschappen --- vloeistoffen --- Navier-Stokes equations.
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This volume deals with the classical Navier-Stokes system of equations governing the planar flow of incompressible, viscid fluid. It is a first-of-its-kind book, devoted to all aspects of the study of such flows, ranging from theoretical to numerical, including detailed accounts of classical test problems such as "driven cavity" and "double-driven cavity".A comprehensive treatment of the mathematical theory developed in the last 15 years is elaborated, heretofore never presented in other books. It gives a detailed account of the modern compact schemes based on a "pure streamfunction" approach.
Navier-Stokes equations. --- Equations, Navier-Stokes --- Differential equations, Partial --- Fluid dynamics --- Viscous flow
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Navier-Stokes equations. --- Equations, Navier-Stokes --- Differential equations, Partial --- Fluid dynamics --- Viscous flow
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This book aims to bridge the gap between practising mathematicians and the practitioners of turbulence theory. It presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. The book is the result of many years of research by the authors to analyse turbulence using Sobolev spaces and functional analysis. In this way the authors have recovered parts of the conventional theory of turbulence, deriving rigorously from the Navier-Stokes equations what had been arrived at earlier by phenomenological arguments. The mathematical technicalities are kept to a minimum within the book, enabling the language to be at a level understood by a broad audience. Each chapter is accompanied by appendices giving full details of the mathematical proofs and subtleties. This unique presentation should ensure a volume of interest to mathematicians, engineers and physicists.
Turbulence. --- Navier-Stokes equations. --- Equations, Navier-Stokes --- Differential equations, Partial --- Fluid dynamics --- Viscous flow --- Flow, Turbulent --- Turbulent flow --- Turbulence --- Navier-Stokes equations
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Finite volume method. --- Navier-Stokes equations. --- Equations, Navier-Stokes --- Differential equations, Partial --- Fluid dynamics --- Viscous flow --- Numerical analysis --- Equacions de Navier-Stokes --- Navier-Stokes (Equacions) --- Dinàmica de fluids --- Equacions en derivades parcials
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Problems, ideas and notions from the theory of finite-dimensional dynamical systems have penetrated deeply into the theory of infinite-dimensional systems and partial differential equations. From the standpoint of the theory of the dynamical systems, many scientists have investigated the evolutionary equations of mathematical physics. Such equations include the Navier-Stokes system, magneto-hydrodynamics equations, reaction-diffusion equations, and damped semilinear wave equations. Due to the recent efforts of many mathematicians, it has been established that the attractor of the Navier-Stokes
Navier-Stokes equations --- Attractors (Mathematics) --- Numerical solutions. --- Numerical solutions
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Gas dynamics. --- Navier-Stokes equations. --- Equations, Navier-Stokes --- Differential equations, Partial --- Fluid dynamics --- Viscous flow --- Gasdynamics --- Thermodynamics
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The lecture notes in this book are based on the TCC (Taught Course Centre for graduates) course given by the author in Trinity Terms of 2009-2011 at the Mathematical Institute of Oxford University. It contains more or less an elementary introduction to the mathematical theory of the Navier-Stokes equations as well as the modern regularity theory for them. The latter is developed by means of the classical PDE's theory in the style that is quite typical for St Petersburg's mathematical school of the Navier-Stokes equations. The global unique solvability (well-posedness) of initial boundary value
Navier-Stokes equations. --- Fluid dynamics. --- Dynamics --- Fluid mechanics --- Equations, Navier-Stokes --- Differential equations, Partial --- Fluid dynamics --- Viscous flow
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Three-Dimensional Navier-Stokes Equations for Turbulence provides a rigorous but still accessible account of research into local and global energy dissipation, with particular emphasis on turbulence modeling. The mathematical detail is combined with coverage of physical terms such as energy balance and turbulence to make sure the reader is always in touch with the physical context. All important recent advancements in the analysis of the equations, such as rigorous bounds on structure functions and energy transfer rates in weak solutions, are addressed, and connections are made to numerical methods with many practical application The book is written to make this subject accessible to a range of readers, carefully tackling interdisciplinary topics where the combination of theory, numerics, and modeling can be a challenge. --
Navier-Stokes equations. --- Turbulence --- Mathematics. --- Flow, Turbulent --- Turbulent flow --- Fluid dynamics --- Equations, Navier-Stokes --- Differential equations, Partial --- Viscous flow
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