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2016 | Buch

Introduction Kapitel lesen Erstes Kapitel lesen

Waves and Compressible Flow

verfasst von: Hilary Ockendon, John R. Ockendon

Verlag: Springer New York

Buchreihe : Texts in Applied Mathematics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

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Über dieses Buch

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)

Inhaltsverzeichnis

Frontmatter
Chapter 1. Introduction
Abstract
This book owes its origins to a lecture course that was first conceived five decades ago and then modified in the 1970s to form the basis for “Inviscid Fluid Flows” [42]. That monograph was retitled and rewritten to reflect developments in the 1990s as the first edition of “Waves and Compressible Flow” which was published in 2002. This edition has been further expanded to show how the methodologies expounded in the earlier books can shed light on even more phenomena outside the area of fluid mechanics.
Hilary Ockendon, John R. Ockendon
Chapter 2. The Equations of Inviscid Compressible Flow
Abstract
In this chapter, we will derive the equations of inviscid compressible flow of a perfect gas. We will do this mostly by making the traditional assumption that we are working on length scales for which it is reasonable to model the gas as a continuum, that is, to say it can be described by variables that are “smoothly” defined almost everywhere. This means that the gas is infinitely divisible into smaller and smaller fluid elements or fluid particles, and we will see that it will help our understanding to relate these particles to the “particles” of classical mechanics.
Hilary Ockendon, John R. Ockendon
Chapter 3. Models for Linear Wave Propagation
Abstract
This chapter will discuss models for several quite different classes of waves with the common characteristic that the models can be linearised for waves of sufficiently small amplitude. We will focus on waves in fluids, but even here we will find that the models are far from trivial and can look very different from each other. Their unifying features will become more apparent when we embark on their mathematical analysis in Chapter 4 We begin with sound waves which are one of the most familiar of all waves.
Hilary Ockendon, John R. Ockendon
Chapter 4. Theories for Linear Waves
Abstract
Looking back at the models derived in the last chapter, we see that many of them comprise linear partial differential equations in time and at least one space variable, together with linear boundary conditions. Moreover, in most of the equations, many of the terms have constant coefficients. We therefore start this chapter by reviewing the mathematical methodologies that are available for the analysis of such models.
Hilary Ockendon, John R. Ockendon
Chapter 5. Nonlinear Waves in Fluids
Abstract
We have already encountered several deficiencies in the theories presented in Chapter 4 that indicate the limitations of the linear approximation. In this chapter we will consider three specific nonlinear models, namely, unsteady one-dimensional gas dynamics, two-dimensional steady gas dynamics and shallow water theory.
Hilary Ockendon, John R. Ockendon
Chapter 6. Shock Waves
Abstract
The time has come to face up to the task of making a mathematical model that can deal with flows containing shock waves or shocks, across which the various dependent physical variables themselves have discontinuities. Such discontinuities are often called jump discontinuities in contrast to situations in which only the derivatives of the physical variables have discontinuities.
Hilary Ockendon, John R. Ockendon
Chapter 7. Epilogue
Abstract
As explained in Chapter 1, the authors have changed the emphasis from that of its progenitor “Inviscid Fluid Flows” by reorganising the material so that the applicability of the analysis can be demonstrated as widely as possible. This has revealed how many mathematical methods that seem to be intimately connected with compressible flow or shallow water theory turn out to be equally useful in areas such as electromagnetism, plasma physics and plasticity.
Hilary Ockendon, John R. Ockendon
Backmatter
Metadaten
Titel
Waves and Compressible Flow
verfasst von
Hilary Ockendon
John R. Ockendon
Copyright-Jahr
2016
Verlag
Springer New York
Electronic ISBN
978-1-4939-3381-5
Print ISBN
978-1-4939-3379-2
DOI
https://doi.org/10.1007/978-1-4939-3381-5

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