Mathematical Theory Of Compressible Fluid Flow

Author : Richard von Mises
Publisher : Courier Corporation
Page : 530 pages
File Size : 54,7 Mb
Release : 2013-02-21
Category : Mathematics
ISBN : 9780486174211

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Mathematical Theory of Compressible Fluid Flow by Richard von Mises Pdf

A pioneer in the fields of statistics and probability theory, Richard von Mises (1883–1953) made notable advances in boundary-layer-flow theory and airfoil design. This text on compressible flow, unfinished upon his sudden death, was subsequently completed in accordance with his plans, and von Mises' first three chapters were augmented with a survey of the theory of steady plane flow. Suitable as a text for advanced undergraduate and graduate students — as well as a reference for professionals — Mathematical Theory of Compressible Fluid Flow examines the fundamentals of high-speed flows, with detailed considerations of general theorems, conservation equations, waves, shocks, and nonisentropic flows. In this, the final work of his distinguished career, von Mises summarizes his extensive knowledge of a central branch of fluid mechanics. Characteristically, he pays particular attention to the basics, both conceptual and mathematical. The novel concept of a specifying equation clarifies the role of thermodynamics in the mechanics of compressible fluids. The general theory of characteristics receives a remarkably complete and simple treatment, with detailed applications, and the theory of shocks as asymptotic phenomena appears within the context of rational mechanics.

Author : Antonín Novotny,Ivan Straskraba
Publisher : Oxford University Press on Demand
Page : 527 pages
File Size : 48,8 Mb
Release : 2004-06-17
Category : Mathematics
ISBN : 9780198530848

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Introduction to the Mathematical Theory of Compressible Flow by Antonín Novotny,Ivan Straskraba Pdf

These parts are presented in a textbook style with auxiliary material in supporting sections and appendices. The book includes an index and bibliography, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of compressible flow."--Jacket.

Author : Eduard Feireisl,Trygve G. Karper,Milan Pokorný
Publisher : Birkhäuser
Page : 186 pages
File Size : 50,9 Mb
Release : 2016-11-25
Category : Mathematics
ISBN : 9783319448350

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Mathematical Theory of Compressible Viscous Fluids by Eduard Feireisl,Trygve G. Karper,Milan Pokorný Pdf

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 : Richard Von Mises
Publisher : Unknown
Page : 390 pages
File Size : 45,9 Mb
Release : 1949
Category : Compressibility
ISBN : UOM:39015000995202

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Notes on Mathematical Theory of Compressible Fluid Flow by Richard Von Mises Pdf

Author : Barbara Kaltenbacher,Igor Kukavica,Irena Lasiecka,Roberto Triggiani,Amjad Tuffaha,Justin T. Webster
Publisher : Springer
Page : 309 pages
File Size : 53,7 Mb
Release : 2018-06-21
Category : Mathematics
ISBN : 9783319927831

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Mathematical Theory of Evolutionary Fluid-Flow Structure Interactions by Barbara Kaltenbacher,Igor Kukavica,Irena Lasiecka,Roberto Triggiani,Amjad Tuffaha,Justin T. Webster Pdf

This book is devoted to the study of coupled partial differential equation models, which describe complex dynamical systems occurring in modern scientific applications such as fluid/flow-structure interactions. The first chapter provides a general description of a fluid-structure interaction, which is formulated within a realistic framework, where the structure subject to a frictional damping moves within the fluid. The second chapter then offers a multifaceted description, with often surprising results, of the case of the static interface; a case that is argued in the literature to be a good model for small, rapid oscillations of the structure. The third chapter describes flow-structure interaction where the compressible Navier-Stokes equations are replaced by the linearized Euler equation, while the solid is taken as a nonlinear plate, which oscillates in the surrounding gas flow. The final chapter focuses on a the equations of nonlinear acoustics coupled with linear acoustics or elasticity, as they arise in the context of high intensity ultrasound applications.

Author : Radyadour Kh. Zeytounian
Publisher : Springer Science & Business Media
Page : 498 pages
File Size : 52,8 Mb
Release : 2013-06-29
Category : Science
ISBN : 9783662104477

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Theory and Applications of Viscous Fluid Flows by Radyadour Kh. Zeytounian Pdf

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 : Miloslav Feistauer,Jiří Felcman,Ivan Straškraba
Publisher : Oxford University Press, USA
Page : 560 pages
File Size : 45,6 Mb
Release : 2003
Category : Computers
ISBN : 0198505884

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Mathematical and Computational Methods for Compressible Flow by Miloslav Feistauer,Jiří Felcman,Ivan Straškraba Pdf

This book is concerned with mathematical and numerical methods for compressible flow. It aims to provide the reader with a sufficiently detailed and extensive, mathematically precise, but comprehensible guide, through a wide spectrum of mathematical and computational methods used in Computational Fluid Dynamics (CFD) for the numerical simulation of compressible flow. Up-to-date techniques applied in the numerical solution of inviscid as well as viscous compressible flow on unstructured meshes are explained, thus allowing the simulation of complex three-dimensional technically relevant problems. Among some of the methods addressed are finite volume methods using approximate Riemann solvers, finite element techniques, such as the streamline diffusion and the discontinuous Galerkin methods, and combined finite volume - finite element schemes. The book gives a complex insight into the numerics of compressible flow, covering the development of numerical schemes and their theoretical mathematical analysis, their verification on test problems and use in solving practical engineering problems. The book will be helpful to specialists coming into contact with CFD - pure and applied mathematicians, aerodynamists, engineers, physicists and natural scientists. It will also be suitable for advanced undergraduate, graduate and postgraduate students of mathematics and technical sciences.

Author : Stephen Childress
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 47,5 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.Z.v. Krzywoblocki
Publisher : Springer-Verlag
Page : 198 pages
File Size : 45,7 Mb
Release : 2013-07-02
Category : Technology & Engineering
ISBN : 9783709139943

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Bergman’s Linear Integral Operator Method in the Theory of Compressible Fluid Flow by M.Z.v. Krzywoblocki Pdf

Author : Josef Malek,Jindrich Necas,Mirko Rokyta
Publisher : Springer Science & Business Media
Page : 232 pages
File Size : 40,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642573088

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Advances in Mathematical Fluid Mechanics by Josef Malek,Jindrich Necas,Mirko Rokyta Pdf

This book consists of six survey contributions that are focused on several open problems of theoretical fluid mechanics both for incompressible and compressible fluids. The first article "Viscous flows in Besov spaces" by M area Cannone ad dresses the problem of global existence of a uniquely defined solution to the three-dimensional Navier-Stokes equations for incompressible fluids. Among others the following topics are intensively treated in this contribution: (i) the systematic description of the spaces of initial conditions for which there exists a unique local (in time) solution or a unique global solution for small data, (ii) the existence of forward self-similar solutions, (iii) the relation of these results to Leray's weak solutions and backward self-similar solutions, (iv) the extension of the results to further nonlinear evolutionary problems. Particular attention is paid to the critical spaces that are invariant under the self-similar transform. For sufficiently small Reynolds numbers, the conditional stability in the sense of Lyapunov is also studied. The article is endowed by interesting personal and historical comments and an exhaustive bibliography that gives the reader a complete picture about available literature. The papers "The dynamical system approach to the Navier-Stokes equa tions for compressible fluids" by Eduard Feireisl, and "Asymptotic problems and compressible-incompressible limits" by Nader Masmoudi are devoted to the global (in time) properties of solutions to the Navier-Stokes equa and three tions for compressible fluids. The global (in time) analysis of two dimensional motions of compressible fluids were left open for many years.

Author : Richard Von Mises
Publisher : Elsevier
Page : 529 pages
File Size : 49,9 Mb
Release : 2012-12-02
Category : Science
ISBN : 9780323146999

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Mathematical Theory of Compressible Fluid Flow by Richard Von Mises Pdf

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.

Author : Eduard Feireisl,Antonín Novotný
Publisher : Birkhäuser
Page : 524 pages
File Size : 47,9 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 : Miroslav Bulíček,Eduard Feireisl,Milan Pokorný
Publisher : Springer
Page : 190 pages
File Size : 48,5 Mb
Release : 2018-09-26
Category : Mathematics
ISBN : 9783319943435

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New Trends and Results in Mathematical Description of Fluid Flows by Miroslav Bulíček,Eduard Feireisl,Milan Pokorný Pdf

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.

Author : Eduard Feireisl,Mária Lukáčová-Medviďová,Hana Mizerová,Bangwei She
Publisher : Springer Nature
Page : 530 pages
File Size : 44,7 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9783030737887

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Numerical Analysis of Compressible Fluid Flows by Eduard Feireisl,Mária Lukáčová-Medviďová,Hana Mizerová,Bangwei She Pdf

This book is devoted to the numerical analysis of compressible fluids in the spirit of the celebrated Lax equivalence theorem. The text is aimed at graduate students in mathematics and fluid dynamics, researchers in applied mathematics, numerical analysis and scientific computing, and engineers and physicists. The book contains original theoretical material based on a new approach to generalized solutions (dissipative or measure-valued solutions). The concept of a weak-strong uniqueness principle in the class of generalized solutions is used to prove the convergence of various numerical methods. The problem of oscillatory solutions is solved by an original adaptation of the method of K-convergence. An effective method of computing the Young measures is presented. Theoretical results are illustrated by a series of numerical experiments. Applications of these concepts are to be expected in other problems of fluid mechanics and related fields.

Author : Hilary Ockendon,John R. Ockendon
Publisher : Springer
Page : 243 pages
File Size : 48,5 Mb
Release : 2016-01-21
Category : Mathematics
ISBN : 9781493933815

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Waves and Compressible Flow by Hilary Ockendon,John R. Ockendon Pdf

Now in its second edition, this book continues to give readers a broad mathematical basis for modelling and understanding the wide range of wave phenomena encountered in modern applications. New and expanded material includes topics such as elastoplastic waves and waves in plasmas, as well as new exercises. Comprehensive collections of models are used to illustrate the underpinning mathematical methodologies, which include the basic ideas of the relevant partial differential equations, characteristics, ray theory, asymptotic analysis, dispersion, shock waves, and weak solutions. Although the main focus is on compressible fluid flow, the authors show how intimately gasdynamic waves are related to wave phenomena in many other areas of physical science. Special emphasis is placed on the development of physical intuition to supplement and reinforce analytical thinking. Each chapter includes a complete set of carefully prepared exercises, making this a suitable textbook for students in applied mathematics, engineering, and other physical sciences. Reviews of the first edition: "This book ... is an introduction to the theory of linear and nonlinear waves in fluids, including the theory of shock waves. ... is extraordinarily accurate and free of misprints ... . I enjoyed reading this book. ... most attractive and enticing appearance, and I’m certain that many readers who browse through it will wish to buy a copy. The exercises ... are excellent. ... A beginner who worked through these exercises would not only enjoy himself or herself, but would rapidly acquire mastery of techniques used...in JFM and many other journals..." (C. J. Chapman, Journal of Fluid Mechanics, Vol. 521, 2004) "The book targets a readership of final year undergraduates and first year graduates in applied mathematics. In the reviewer’s opinion, it is very well designed to catch the student’s interest ... while every chapter displays essential features in some important area of fluid dynamics. Additionally, students may practice by solving 91 exercises. This volume is mainly devoted to inviscid flows. ... The book is very well written." (Denis Serre, Mathematical Reviews, 2004)