Mathematical Analysis Of Shock Wave Reflection

Author : Shuxing Chen
Publisher : Unknown
Page : 260 pages
File Size : 52,7 Mb
Release : 2020
Category : Differential equations, Partial
ISBN : 9811577536

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Mathematical Analysis of Shock Wave Reflection by Shuxing Chen Pdf

This book is aimed to make careful analysis to various mathematical problems derived from shock reflection by using the theory of partial differential equations. The occurrence, propagation and reflection of shock waves are important phenomena in fluid dynamics. Comparing the plenty of studies of physical experiments and numerical simulations on this subject, this book makes main efforts to develop the related theory of mathematical analysis, which is rather incomplete so far. The book first introduces some basic knowledge on the system of compressible flow and shock waves, then presents the concept of shock polar and its properties, particularly the properties of the shock polar for potential flow equation, which are first systematically presented and proved in this book. Mathematical analysis of regular reflection and Mach reflection in steady and unsteady flow are the most essential parts of this book. To give challenges in future research, some long-standing open problems are listed in the end. This book is attractive to researchers in the fields of partial differential equations, system of conservation laws, fluid dynamics, and shock theory.

Author : Gui-Qiang G Chen,Mikhail Feldman
Publisher : Princeton University Press
Page : 829 pages
File Size : 46,9 Mb
Release : 2018-02-27
Category : Mathematics
ISBN : 9780691160559

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The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures by Gui-Qiang G Chen,Mikhail Feldman Pdf

This book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differential equations (PDEs), as well as a set of fundamental open problems for further development. Shock waves are fundamental in nature. They are governed by the Euler equations or their variants, generally in the form of nonlinear conservation laws—PDEs of divergence form. When a shock hits an obstacle, shock reflection-diffraction configurations take shape. To understand the fundamental issues involved, such as the structure and transition criteria of different configuration patterns, it is essential to establish the global existence, regularity, and structural stability of shock reflection-diffraction solutions. This involves dealing with several core difficulties in the analysis of nonlinear PDEs—mixed type, free boundaries, and corner singularities—that also arise in fundamental problems in diverse areas such as continuum mechanics, differential geometry, mathematical physics, and materials science. Presenting recently developed approaches and techniques, which will be useful for solving problems with similar difficulties, this book opens up new research opportunities.

Author : Shuxing Chen
Publisher : Springer Nature
Page : 260 pages
File Size : 50,8 Mb
Release : 2020-09-04
Category : Mathematics
ISBN : 9789811577529

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Mathematical Analysis of Shock Wave Reflection by Shuxing Chen Pdf

This book is aimed to make careful analysis to various mathematical problems derived from shock reflection by using the theory of partial differential equations. The occurrence, propagation and reflection of shock waves are important phenomena in fluid dynamics. Comparing the plenty of studies of physical experiments and numerical simulations on this subject, this book makes main efforts to develop the related theory of mathematical analysis, which is rather incomplete so far. The book first introduces some basic knowledge on the system of compressible flow and shock waves, then presents the concept of shock polar and its properties, particularly the properties of the shock polar for potential flow equation, which are first systematically presented and proved in this book. Mathematical analysis of regular reflection and Mach reflection in steady and unsteady flow are the most essential parts of this book. To give challenges in future research, some long-standing open problems are listed in the end. This book is attractive to researchers in the fields of partial differential equations, system of conservation laws, fluid dynamics, and shock theory.

Author : Richard Courant,K.O. Friedrichs
Publisher : Springer Science & Business Media
Page : 488 pages
File Size : 41,5 Mb
Release : 1999-02-11
Category : Mathematics
ISBN : 0387902325

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Supersonic Flow and Shock Waves by Richard Courant,K.O. Friedrichs Pdf

Courant and Friedrich's classical treatise was first published in 1948 and tThe basic research for it took place during World War II. However, many aspects make the book just as interesting as a text and a reference today. It treats the dynamics of compressible fluids in mathematical form, and attempts to present a systematic theory of nonlinear wave propagation, particularly in relation to gas dynamics. Written in the form of an advanced textbook, it should appeal to engineers, physicists and mathematicians alike.

Author : Fedor Vasil?evich Shugaev,L. S. Shtemenko
Publisher : World Scientific
Page : 264 pages
File Size : 48,8 Mb
Release : 1998
Category : Science
ISBN : 9810230109

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Propagation and Reflection of Shock Waves by Fedor Vasil?evich Shugaev,L. S. Shtemenko Pdf

This volume deals with the propagation of three-dimensional shock waves and their reflection from curved walls. It is divided into two parts. The first part presents a ray method. This is based on the expansion of fluid properties in power series at an arbitrary point on the shock front. Continuous fractions are used. Results for shock propagation in non-uniform fluids are given.The second part discusses the shock reflection from a concave body. The important shock-focusing problem is included. The work is supported by both numerical and experimental results. Many interesting features, such as formation of a jet, vortices and the appearance of disturbances on the shock front, are discussed.Besides shock waves in gases, the distinctive features of shock propagation through a weakly ionized plasma are considered.

Author : Heinrich Freistühler,Anders Szepessy
Publisher : Springer Science & Business Media
Page : 527 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201939

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Advances in the Theory of Shock Waves by Heinrich Freistühler,Anders Szepessy Pdf

In the field known as "the mathematical theory of shock waves," very exciting and unexpected developments have occurred in the last few years. Joel Smoller and Blake Temple have established classes of shock wave solutions to the Einstein Euler equations of general relativity; indeed, the mathematical and physical con sequences of these examples constitute a whole new area of research. The stability theory of "viscous" shock waves has received a new, geometric perspective due to the work of Kevin Zumbrun and collaborators, which offers a spectral approach to systems. Due to the intersection of point and essential spectrum, such an ap proach had for a long time seemed out of reach. The stability problem for "in viscid" shock waves has been given a novel, clear and concise treatment by Guy Metivier and coworkers through the use of paradifferential calculus. The L 1 semi group theory for systems of conservation laws, itself still a recent development, has been considerably condensed by the introduction of new distance functionals through Tai-Ping Liu and collaborators; these functionals compare solutions to different data by direct reference to their wave structure. The fundamental prop erties of systems with relaxation have found a systematic description through the papers of Wen-An Yong; for shock waves, this means a first general theorem on the existence of corresponding profiles. The five articles of this book reflect the above developments.

Author : Gabi Ben-Dor
Publisher : Unknown
Page : 336 pages
File Size : 43,8 Mb
Release : 1992
Category : Science
ISBN : STANFORD:36105030690080

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Shock Wave Reflection Phenomena by Gabi Ben-Dor Pdf

Author : Joel Smoller
Publisher : Springer Science & Business Media
Page : 596 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781468401523

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Shock Waves and Reaction—Diffusion Equations by Joel Smoller Pdf

. . . the progress of physics will to a large extent depend on the progress of nonlinear mathe matics, of methods to solve nonlinear equations . . . and therefore we can learn by comparing different nonlinear problems. WERNER HEISENBERG I undertook to write this book for two reasons. First, I wanted to make easily available the basics of both the theory of hyperbolic conservation laws and the theory of systems of reaction-diffusion equations, including the generalized Morse theory as developed by C. Conley. These important subjects seem difficult to learn since the results are scattered throughout the research journals. 1 Second, I feel that there is a need to present the modern methods and ideas in these fields to a wider audience than just mathe maticians. Thus, the book has some rather sophisticated aspects to it, as well as certain textbook aspects. The latter serve to explain, somewhat, the reason that a book with the title Shock Waves and Reaction-Diffusion Equations has the first nine chapters devoted to linear partial differential equations. More precisely, I have found from my classroom experience that it is far easier to grasp the subtleties of nonlinear partial differential equations after one has an understanding of the basic notions in the linear theory. This book is divided into four main parts: linear theory, reaction diffusion equations, shock wave theory, and the Conley index, in that order. Thus, the text begins with a discussion of ill-posed problems.

Author : Anonim
Publisher : Unknown
Page : 912 pages
File Size : 41,9 Mb
Release : 2024-05-23
Category : Science
ISBN : CORNELL:31924057185294

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Technical Abstract Bulletin by Anonim Pdf

Author : Raymond Brun,Lucien Z. Dumitrescu
Publisher : Springer Science & Business Media
Page : 508 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642795329

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Shock Waves @ Marseille IV by Raymond Brun,Lucien Z. Dumitrescu Pdf

Recently, there have been significant advances in the fields of high-enthalpy hypersonic flows, high-temperature gas physics, and chemistry shock propagation in various media, industrial and medical applications of shock waves, and shock-tube technology. This series contains all the papers and lectures of the 19th International Symposium on Shock Waves held in Marseille in 1993. They are published in four topical volumes, each containing papers on related topics, and preceded by an overview written by a leading international expert. The volumes may be purchased independently.

Author : Anonim
Publisher : Unknown
Page : 600 pages
File Size : 51,9 Mb
Release : 1962
Category : Research
ISBN : UOM:39015086565986

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U.S. Government Research Reports by Anonim Pdf

Author : Gabi Ben-Dor
Publisher : Springer Science & Business Media
Page : 321 pages
File Size : 49,8 Mb
Release : 2013-06-29
Category : Science
ISBN : 9781475742794

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Shock Wave Reflection Phenomena by Gabi Ben-Dor Pdf

The phenomenon of shock wave reflection was first reported by the distinguished philosopher Ernst Mach in 1878. Its study was then abandoned for a period of about 60 years until its investigation was initiated in the early 1940s by Professor John von Neumann and Professor Bleakney. Under their supervision, 15 years of intensive research related to various aspects of the reflection of shock waves in pseudo-steady flows were carried out. It was during this period that the four basic shock wave reflection configurations were discovered. Then, for a period of about 10 years from the mid 1950s until the mid 1960s, investigation of the reflection phenomenon of shock waves was kept on a low flame all over the world (e. g. Australia, Japan, Canada, U. S. A. , U. S. S. R. , etc. ) until Professor Bazhenova from the U. S. S. R. , Professor Irvine Glass from Canada, and Professor Roy Henderson from Australia re initiated the study of this and related phenomena. Under their scientific supervision and leadership, numerous findings related to this phenomenon were reported. Probably the most productive research group in the mid 1970s was that led by Professor Irvine Glass in the Institute of Aerospace Studies of the University of Toronto. In 1978, exactly 100 years after Ernst Mach first reported his discovery of the reflection phenomenon, I published my Ph. D. thesis in which, for the first time, analytical transition criteria between the various shock wave reflection configurations were established.

Author : R. Courant
Publisher : Trieste Publishing
Page : 306 pages
File Size : 41,6 Mb
Release : 2017-10-04
Category : History
ISBN : 064971637X

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Supersonic Flow and Shock Waves by R. Courant Pdf

Trieste Publishing has a massive catalogue of classic book titles. Our aim is to provide readers with the highest quality reproductions of fiction and non-fiction literature that has stood the test of time. The many thousands of books in our collection have been sourced from libraries and private collections around the world.The titles that Trieste Publishing has chosen to be part of the collection have been scanned to simulate the original. Our readers see the books the same way that their first readers did decades or a hundred or more years ago. Books from that period are often spoiled by imperfections that did not exist in the original. Imperfections could be in the form of blurred text, photographs, or missing pages. It is highly unlikely that this would occur with one of our books. Our extensive quality control ensures that the readers of Trieste Publishing's books will be delighted with their purchase. Our staff has thoroughly reviewed every page of all the books in the collection, repairing, or if necessary, rejecting titles that are not of the highest quality. This process ensures that the reader of one of Trieste Publishing's titles receives a volume that faithfully reproduces the original, and to the maximum degree possible, gives them the experience of owning the original work.We pride ourselves on not only creating a pathway to an extensive reservoir of books of the finest quality, but also providing value to every one of our readers. Generally, Trieste books are purchased singly - on demand, however they may also be purchased in bulk. Readers interested in bulk purchases are invited to contact us directly to enquire about our tailored bulk rates.

Author : Tai-Ping Liu
Publisher : American Mathematical Soc.
Page : 437 pages
File Size : 44,6 Mb
Release : 2021-10-12
Category : Education
ISBN : 9781470466251

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Shock Waves by Tai-Ping Liu Pdf

This book presents the fundamentals of the shock wave theory. The first part of the book, Chapters 1 through 5, covers the basic elements of the shock wave theory by analyzing the scalar conservation laws. The main focus of the analysis is on the explicit solution behavior. This first part of the book requires only a course in multi-variable calculus, and can be used as a text for an undergraduate topics course. In the second part of the book, Chapters 6 through 9, this general theory is used to study systems of hyperbolic conservation laws. This is a most significant well-posedness theory for weak solutions of quasilinear evolutionary partial differential equations. The final part of the book, Chapters 10 through 14, returns to the original subject of the shock wave theory by focusing on specific physical models. Potentially interesting questions and research directions are also raised in these chapters. The book can serve as an introductory text for advanced undergraduate students and for graduate students in mathematics, engineering, and physical sciences. Each chapter ends with suggestions for further reading and exercises for students.

Author : Anonim
Publisher : Unknown
Page : 1040 pages
File Size : 40,8 Mb
Release : 1973
Category : Aeronautics
ISBN : UIUC:30112106854216

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Scientific and Technical Aerospace Reports by Anonim Pdf

Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.