A Graphical Solution of Shock Equations PDF Download

Author: Charles E. Treanor
Publisher:
ISBN:
Category : Shock waves
Languages : en
Pages : 88

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Author: Charles E. Treanor
Publisher:
ISBN:
Category : Shock waves
Languages : en
Pages : 64

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Author: Mark L. Wilkins
Publisher:
ISBN:
Category : Fluid mechanics
Languages : en
Pages : 34

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Book Description
The Hugoniot relations, which express conservation of mass, momentum, and energy across a discontinuity, are derived. The relations are applied to a perfect gas for illustration, and graphical methods of solving shock problems are presented.

Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 24

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A theory of the propagation of shock waves from explosive sources was presented in NDRC Report A-318 (OSRD - 4814). In that report, a pair of ordinary differential equations for peak pressure and shock-wave energy as functions of the distance from the source were formulated from the equations of hydrodynamics by imposing a similarity restraint on the shape of the energy-time curve of the shock wave. Two-parameter families of peak pressure-distance curves are obtained by the solution of these propagation equations. The parameters are conveniently chosen as the initial values of the pressure and shock-wave energy. In the present report, tables and graphs of the two-parameter families of curves for shock waves from explosive sources in sea water are presented. A method is outlined for the determination of the parameters from experimental values of the peak pressure and impulse over a limited range of distances from the source.

Author: Heinrich Freistühler
Publisher: Springer Science & Business Media
ISBN: 1461201934
Category : Mathematics
Languages : en
Pages : 527

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Book Description
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: Michael Shearer
Publisher: SIAM
ISBN: 9780898712834
Category : Science
Languages : en
Pages : 272

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Book Description
One strongly represented theme is the power of ideas from dynamical systems that are being adapted and developed in the context of shock waves.

Author: Joel Smoller
Publisher: Springer Science & Business Media
ISBN: 1468401521
Category : Science
Languages : en
Pages : 596

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Book Description
. . . 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: Tai-Ping Liu
Publisher: American Mathematical Soc.
ISBN: 1470466252
Category : Education
Languages : en
Pages : 437

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Book Description
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: United States. Air Force. Office of Scientific Research
Publisher:
ISBN:
Category : Research
Languages : en
Pages : 718

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Author: Seán Prunty
Publisher: Springer Nature
ISBN: 3030636062
Category : Science
Languages : en
Pages : 356

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Book Description
This book provides an elementary introduction to one-dimensional fluid flow problems involving shock waves in air. The differential equations of fluid flow are approximated by finite difference equations and these in turn are numerically integrated in a stepwise manner, with artificial viscosity introduced into the numerical calculations in order to deal with shocks. This treatment of the subject is focused on the finite-difference approach to solve the coupled differential equations of fluid flow and presents the results arising from the numerical solution using Mathcad programming. Both plane and spherical shock waves are discussed with particular emphasis on very strong explosive shocks in air. This expanded second edition features substantial new material on sound wave parameters, Riemann's method for numerical integration of the equations of motion, approximate analytical expressions for weak shock waves, short duration piston motion, numerical results for shock wave interactions, and new appendices on the piston withdrawal problem and numerical results for a closed shock tube. This text will appeal to students, researchers, and professionals in shock wave research and related fields. Students in particular will appreciate the benefits of numerical methods in fluid mechanics and the level of presentation.