Equations Of Motion For Incompressible Viscous Fluids

Author : Tujin Kim,Daomin Cao
Publisher : Springer Nature
Page : 374 pages
File Size : 40,9 Mb
Release : 2021-09-09
Category : Mathematics
ISBN : 9783030786595

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Equations of Motion for Incompressible Viscous Fluids by Tujin Kim,Daomin Cao Pdf

This monograph explores the motion of incompressible fluids by presenting and incorporating various boundary conditions possible for real phenomena. The authors’ approach carefully walks readers through the development of fluid equations at the cutting edge of research, and the applications of a variety of boundary conditions to real-world problems. Special attention is paid to the equivalence between partial differential equations with a mixture of various boundary conditions and their corresponding variational problems, especially variational inequalities with one unknown. A self-contained approach is maintained throughout by first covering introductory topics, and then moving on to mixtures of boundary conditions, a thorough outline of the Navier-Stokes equations, an analysis of both the steady and non-steady Boussinesq system, and more. Equations of Motion for Incompressible Viscous Fluids is ideal for postgraduate students and researchers in the fields of fluid equations, numerical analysis, and mathematical modelling.

Author : Tujin Kim,Daomin Cao
Publisher : Unknown
Page : 0 pages
File Size : 55,8 Mb
Release : 2021
Category : Electronic
ISBN : 3030786609

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Equations of Motion for Incompressible Viscous Fluids by Tujin Kim,Daomin Cao Pdf

This monograph explores the motion of incompressible fluids by presenting and incorporating various boundary conditions possible for real phenomena. The authors' approach carefully walks readers through the development of fluid equations at the cutting edge of research, and the applications of a variety of boundary conditions to real-world problems. Special attention is paid to the equivalence between partial differential equations with a mixture of various boundary conditions and their corresponding variational problems, especially variational inequalities with one unknown. A self-contained approach is maintained throughout by first covering introductory topics, and then moving on to mixtures of boundary conditions, a thorough outline of the Navier-Stokes equations, an analysis of both the steady and non-steady Boussinesq system, and more. Equations of Motion for Incompressible Viscous Fluids is ideal for postgraduate students and researchers in the fields of fluid equations, numerical analysis, and mathematical modelling.

Author : Malcolm S. Longair
Publisher : Cambridge University Press
Page : 592 pages
File Size : 40,5 Mb
Release : 2003-12-04
Category : Science
ISBN : 052152878X

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Theoretical Concepts in Physics by Malcolm S. Longair Pdf

A highly original, and truly novel, approach to theoretical reasoning in physics. This book illuminates the subject from the perspective of real physics as practised by research scientists. It is intended to be a supplement to the final years of an undergraduate course in physics and assumes that the reader has some grasp of university physics. By means of a series of seven case studies, the author conveys the excitement of research and discovery, highlighting the intellectual struggles to attain understanding of some of the most difficult concepts in physics. Case studies include the origins of Newton's law of gravitation, Maxwell's equations, mechanics and dynamics, linear and non-linear, thermodynamics and statistical physics, the origins of the concepts of quanta, special relativity, general relativity and cosmology. The approach is the same as that in the highly acclaimed first edition, but the text has been completely revised and many new topics introduced.

Author : P. E. Doudna
Publisher : Unknown
Page : 160 pages
File Size : 44,6 Mb
Release : 1897
Category : Electronic
ISBN : WISC:89085974095

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Equations of Motion of a Viscous Liquid by P. E. Doudna Pdf

Author : Roland Glowinski,Tsorng-Whay Pan
Publisher : Walter de Gruyter GmbH & Co KG
Page : 236 pages
File Size : 44,5 Mb
Release : 2022-09-20
Category : Mathematics
ISBN : 9783110785050

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Numerical Simulation of Incompressible Viscous Flow by Roland Glowinski,Tsorng-Whay Pan Pdf

This book on finite element-based computational methods for solving incompressible viscous fluid flow problems shows readers how to apply operator splitting techniques to decouple complicated computational fluid dynamics problems into a sequence of relatively simpler sub-problems at each time step, such as hemispherical cavity flow, cavity flow of an Oldroyd-B viscoelastic flow, and particle interaction in an Oldroyd-B type viscoelastic fluid. Efficient and robust numerical methods for solving those resulting simpler sub-problems are introduced and discussed. Interesting computational results are presented to show the capability of methodologies addressed in the book.

Author : William Layton
Publisher : SIAM
Page : 220 pages
File Size : 54,7 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9780898718904

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Introduction to the Numerical Analysis of Incompressible Viscous Flows by William Layton Pdf

Introduction to the Numerical Analysis of Incompressible Viscous Flows treats the numerical analysis of finite element computational fluid dynamics. Assuming minimal background, the text covers finite element methods; the derivation, behavior, analysis, and numerical analysis of Navier-Stokes equations; and turbulence and turbulence models used in simulations. Each chapter on theory is followed by a numerical analysis chapter that expands on the theory. This book provides the foundation for understanding the interconnection of the physics, mathematics, and numerics of the incompressible case, which is essential for progressing to the more complex flows not addressed in this book (e.g., viscoelasticity, plasmas, compressible flows, coating flows, flows of mixtures of fluids, and bubbly flows). With mathematical rigor and physical clarity, the book progresses from the mathematical preliminaries of energy and stress to finite element computational fluid dynamics in a format manageable in one semester. Audience: this unified treatment of fluid mechanics, analysis, and numerical analysis is intended for graduate students in mathematics, engineering, physics, and the sciences who are interested in understanding the foundations of methods commonly used for flow simulations.

Author : Michael Edward O'Neill,Frank Chorlton
Publisher : Unknown
Page : 408 pages
File Size : 43,5 Mb
Release : 1989
Category : Fluid dynamics
ISBN : UCAL:B5043364

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Viscous and Compressible Fluid Dynamics by Michael Edward O'Neill,Frank Chorlton Pdf

Textbooks for students of applied mathematics, engineers, and useful for meteorologists. Introduction to the theory of fluid mechanics, companion to same authors' Ideal and incompressible fluid dynamics. Some prior knowledge of ideal compressiblity is desirable. Much of the basic mathematical techniques is included. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Hamid Bellout,Frederick Bloom
Publisher : Springer Science & Business Media
Page : 583 pages
File Size : 53,7 Mb
Release : 2013-11-19
Category : Science
ISBN : 9783319008912

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Incompressible Bipolar and Non-Newtonian Viscous Fluid Flow by Hamid Bellout,Frederick Bloom Pdf

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.

Author : Eduard Feireisl,Antonín Novotný
Publisher : Birkhäuser
Page : 524 pages
File Size : 40,5 Mb
Release : 2017-11-24
Category : Mathematics
ISBN : 9783319637815

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Singular Limits in Thermodynamics of Viscous Fluids by Eduard Feireisl,Antonín Novotný Pdf

This book is about singular limits of systems of partial differential equations governing the motion of thermally conducting compressible viscous fluids. "The main aim is to provide mathematically rigorous arguments how to get from the compressible Navier-Stokes-Fourier system several less complex systems of partial differential equations used e.g. in meteorology or astrophysics. However, the book contains also a detailed introduction to the modelling in mechanics and thermodynamics of fluids from the viewpoint of continuum physics. The book is very interesting and important. It can be recommended not only to specialists in the field, but it can also be used for doctoral students and young researches who want to start to work in the mathematical theory of compressible fluids and their asymptotic limits." Milan Pokorný (zbMATH) "This book is of the highest quality from every point of view. It presents, in a unified way, recent research material of fundament al importance. It is self-contained, thanks to Chapter 3 (existence theory) and to the appendices. It is extremely well organized, and very well written. It is a landmark for researchers in mathematical fluid dynamics, especially those interested in the physical meaning of the equations and statements." Denis Serre (MathSciNet)

Author : Wolfgang Arendt,Haim Brezis,Michel Pierre
Publisher : Birkhäuser
Page : 803 pages
File Size : 44,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034879248

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Nonlinear Evolution Equations and Related Topics by Wolfgang Arendt,Haim Brezis,Michel Pierre Pdf

Philippe Bénilan was a most original and charismatic mathematician who had a deep and decisive impact on the theory of Nonlinear Evolution Equations. Dedicated to him, Nonlinear Evolution Equations and Related Topics contains research papers written by highly distinguished mathematicians. They are all related to Philippe Benilan's work and reflect the present state of this most active field. The contributions cover a wide range of nonlinear and linear equations.

Author : Hilary Ockendon,J. R. Ockendon
Publisher : Cambridge University Press
Page : 130 pages
File Size : 41,5 Mb
Release : 1995-01-27
Category : Mathematics
ISBN : 0521458811

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Viscous Flow by Hilary Ockendon,J. R. Ockendon Pdf

Many of the topics in inviscid fluid dynamics are not only vitally important mechanisms in everyday life but they are also readily observable without any need for instrumentation. It is therefore stimulating when the mathematics that emerges when these phenomena are modelled is novel and suggestive of alternative methodologies. This book provides senior undergraduates who are already familiar with inviscid fluid dynamics with some of the basic facts about the modelling and analysis of viscous flows. It clearly presents the salient physical ideas and the mathematical ramifications with exercises designed to be an integral part of the text. By showing the basic theoretical framework which has developed as a result of the study of viscous flows, the book should be ideal reading for students of applied mathematics who should then be able to delve further into the subject and be well placed to exploit mathematical ideas throughout the whole of applied science.

Author : Guido Buresti
Publisher : World Scientific Publishing Company
Page : 604 pages
File Size : 52,6 Mb
Release : 2012-06-26
Category : Technology & Engineering
ISBN : 9781908977045

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Elements of Fluid Dynamics by Guido Buresti Pdf

Elements of Fluid Dynamics is intended to be a basic textbook, useful for undergraduate and graduate students in different fields of engineering, as well as in physics and applied mathematics. The main objective of the book is to provide an introduction to fluid dynamics in a simultaneously rigorous and accessible way, and its approach follows the idea that both the generation mechanisms and the main features of the fluid dynamic loads can be satisfactorily understood only after the equations of fluid motion and all their physical and mathematical implications have been thoroughly assimilated. Therefore, the complete equations of motion of a compressible viscous fluid are first derived and their physical and mathematical aspects are thoroughly discussed. Subsequently, the necessity of simplified treatments is highlighted, and a detailed analysis is made of the assumptions and range of applicability of the incompressible flow model, which is then adopted for most of the rest of the book. Furthermore, the role of the generation and dynamics of vorticity on the development of different flows is emphasized, as well as its influence on the characteristics, magnitude and predictability of the fluid dynamic loads acting on moving bodies. The book is divided into two parts which differ in target and method of utilization. The first part contains the fundamentals of fluid dynamics that are essential for any student new to the subject. This part of the book is organized in a strictly sequential way, i.e. each chapter is assumed to be carefully read and studied before the next one is tackled, and its aim is to lead the reader in understanding the origin of the fluid dynamic forces on different types of bodies. The second part of the book is devoted to selected topics that may be of more specific interest to different students. In particular, some theoretical aspects of incompressible flows are first analysed and classical applications of fluid dynamics such as the aerodynamics of airfoils, wings and bluff bodies are then described. The one-dimensional treatment of compressible flows is finally considered, together with its application to the study of the motion in ducts. Sample Chapter(s) Chapter 1: Introduction (133 KB) Request Inspection Copy

Author : P McCormack
Publisher : Elsevier
Page : 512 pages
File Size : 47,9 Mb
Release : 2012-12-02
Category : Technology & Engineering
ISBN : 9780323147521

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Physical Fluid Dynamics by P McCormack Pdf

Physical Fluid Dynamics is a textbook for students of physics that reflects the origins and the future development of fluid dynamics. This book forms a concise and logically developed course in contemporary Newtonian fluid dynamics, suitable for physics and engineering science students. The text is composed of chapters devoted to the discussion of the physical properties of fluids, vortex dynamics, slow viscous flow, and particulate fluid dynamics. An adequate course in the dynamics of real (viscous) fluids, kinematics, equations of motion, boundary-layer theory, and compressible flow is also given. The textbook is intended for junior or senior undergraduate level students of physics and engineering.

Author : Stephen Childress
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 50,9 Mb
Release : 2009-10-09
Category : Science
ISBN : 9780821848883

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An Introduction to Theoretical Fluid Mechanics by Stephen Childress Pdf

This book gives an overview of classical topics in fluid dynamics, focusing on the kinematics and dynamics of incompressible inviscid and Newtonian viscous fluids, but also including some material on compressible flow. The topics are chosen to illustrate the mathematical methods of classical fluid dynamics. The book is intended to prepare the reader for more advanced topics of current research interest.

Author : M.D.Raisinghania
Publisher : S. Chand Publishing
Page : 872 pages
File Size : 41,9 Mb
Release : 2003-12-01
Category : Mathematics
ISBN : 9788121908696

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Fluid Dynamics by M.D.Raisinghania Pdf

For Honours, Post Graduate and M.Phil Students of All Indian Universities, Engineering Students and Various Competitive Examinations