Compressible Viscous Fluids
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| Author | : Eduard Feireisl |
| Publisher | : Birkhäuser |
| Total Pages | : 189 |
| Release | : 2016-11-25 |
| Genre | : Mathematics |
| ISBN | : 3319448358 |
This book offers an essential introduction to the mathematical theory of compressible viscous fluids. The main goal is to present analytical methods from the perspective of their numerical applications. Accordingly, we introduce the principal theoretical tools needed to handle well-posedness of the underlying Navier-Stokes system, study the problems of sequential stability, and, lastly, construct solutions by means of an implicit numerical scheme. Offering a unique contribution – by exploring in detail the “synergy” of analytical and numerical methods – the book offers a valuable resource for graduate students in mathematics and researchers working in mathematical fluid mechanics. Mathematical fluid mechanics concerns problems that are closely connected to real-world applications and is also an important part of the theory of partial differential equations and numerical analysis in general. This book highlights the fact that numerical and mathematical analysis are not two separate fields of mathematics. It will help graduate students and researchers to not only better understand problems in mathematical compressible fluid mechanics but also to learn something from the field of mathematical and numerical analysis and to see the connections between the two worlds. Potential readers should possess a good command of the basic tools of functional analysis and partial differential equations including the function spaces of Sobolev type.
| Author | : Eduard Feireisl |
| Publisher | : Oxford University Press |
| Total Pages | : 228 |
| Release | : 2004 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 9780198528388 |
This text develops the ideas and concepts of the mathematical theory of viscous, compressible and heat conducting fluids. The material is by no means intended to be the last word on the subject but rather to indicate possible directions of future research.
| Author | : Robert William MacCormack |
| Publisher | : AIAA Education |
| Total Pages | : 0 |
| Release | : 2014 |
| Genre | : Technology & Engineering |
| ISBN | : 9781624102646 |
Written for those who want to calculate compressible and viscous flow past aerodynamic bodies, this book allows you to get started in programming for solving initial value problems and to understand numerical accuracy and stability, matrix algebra, finite volume formulations, and the use of flux split algorithms for solving the Euler equations.
| Author | : Eduard Feireisl |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 411 |
| Release | : 2009-03-28 |
| Genre | : Science |
| ISBN | : 3764388439 |
Many interesting problems in mathematical fluid dynamics involve the behavior of solutions of nonlinear systems of partial differential equations as certain parameters vanish or become infinite. Frequently the limiting solution, provided the limit exists, satisfies a qualitatively different system of differential equations. This book is designed as an introduction to the problems involving singular limits based on the concept of weak or variational solutions. The primitive system consists of a complete system of partial differential equations describing the time evolution of the three basic state variables: the density, the velocity, and the absolute temperature associated to a fluid, which is supposed to be compressible, viscous, and heat conducting. It can be represented by the Navier-Stokes-Fourier-system that combines Newton's rheological law for the viscous stress and Fourier's law of heat conduction for the internal energy flux. As a summary, this book studies singular limits of weak solutions to the system governing the flow of thermally conducting compressible viscous fluids.
| Author | : Eduard Feireisl |
| Publisher | : Birkhäuser |
| Total Pages | : 558 |
| Release | : 2017-11-24 |
| Genre | : Mathematics |
| ISBN | : 3319637819 |
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 | : Radyadour Kh. Zeytounian |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 498 |
| Release | : 2013-06-29 |
| Genre | : Science |
| ISBN | : 3662104474 |
This book closes the gap between standard undergraduate texts on fluid mechanics and monographical publications devoted to specific aspects of viscous fluid flows. Each chapter serves as an introduction to a special topic that will facilitate later application by readers in their research work.
| Author | : Tujin Kim |
| Publisher | : Springer Nature |
| Total Pages | : 374 |
| Release | : 2021-09-09 |
| Genre | : Mathematics |
| ISBN | : 3030786595 |
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 | : Akihiro Sasoh |
| Publisher | : Springer Nature |
| Total Pages | : 278 |
| Release | : 2020-01-02 |
| Genre | : Science |
| ISBN | : 9811505047 |
This book offers comprehensive coverage of compressible flow phenomena and their applications, and is intended for undergraduate/graduate students, practicing professionals, and researchers interested in the topic. Thanks to the clear explanations provided of a wide range of basic principles, the equations and formulas presented here can be understood with only a basic grasp of mathematics. The book particularly focuses on shock waves, offering a unique approach to the derivation of shock wave relations from conservation relations in fluids together with a contact surface, slip line or surface; in addition, the thrust of a rocket engine and that of an air-breathing engine are also formulated. Furthermore, the book covers important fundamentals of various aspects of physical fluid dynamics and engineering, including one-dimensional unsteady flows, and two-dimensional flows, in which oblique shock waves and Prandtl-Meyer expansion can be observed.
| Author | : Roger Peyret |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 364 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642859526 |
In developing this book, we decided to emphasize applications and to provide methods for solving problems. As a result, we limited the mathematical devel opments and we tried as far as possible to get insight into the behavior of numerical methods by considering simple mathematical models. The text contains three sections. The first is intended to give the fundamen tals of most types of numerical approaches employed to solve fluid-mechanics problems. The topics of finite differences, finite elements, and spectral meth ods are included, as well as a number of special techniques. The second section is devoted to the solution of incompressible flows by the various numerical approaches. We have included solutions of laminar and turbulent-flow prob lems using finite difference, finite element, and spectral methods. The third section of the book is concerned with compressible flows. We divided this last section into inviscid and viscous flows and attempted to outline the methods for each area and give examples.
| Author | : Aleksandr Nikolaevich Guzʹ |
| Publisher | : Cambridge Scientific Publishers |
| Total Pages | : 440 |
| Release | : 2009 |
| Genre | : Science |
| ISBN | : |
A monograph applied to the theory of small vibrations of rigid and elastic bodies in compressible viscous fluid. The volume also develops the methods of analysis based on the proposed general solutions of linearized Navier-Stokes equations in vector or scalar forms. The volume provides a useful reference text for postgraduates/researchers in this area of applied engineering and mathematics.
