Self Similar Problems In Gas Dynamics
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Self Similar Problems In Gas Dynamics
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Author : M. A. Grant
language : en
Publisher:
Release Date : 1975
Self Similar Problems In Gas Dynamics written by M. A. Grant and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.
Self Similar Problems In Gas Dynamics
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Author : Michael Ayrton Grant
language : en
Publisher:
Release Date : 1972
Self Similar Problems In Gas Dynamics written by Michael Ayrton Grant and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with categories.
Dimensional Analysis And Self Similarity Methods For Engineers And Scientists
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Author : Bahman Zohuri
language : en
Publisher:
Release Date : 2015
Dimensional Analysis And Self Similarity Methods For Engineers And Scientists written by Bahman Zohuri and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
· Provides innovative techniques for solving complex nonlinear partial differential equations, previously only available to scientists involved in classified government funded projects. · Goes beyond the traditional Pi (Buckingham) Theorem method to apply dimensional analysis to gas dynamics and thermal hydraulics problems where both laminar and turbulent fluids come into play · Includes specific examples demonstrating how dimensional analysis can shed light on applications from shock wave impact prediction to plasma confinement. · Presents a unique approach to similarity methods by discussing Chaos, Fractals and Arcadia, in addition to the more common Self-Similarity and Fractals Techniques This ground-breaking reference provides an overview of key concepts in dimensional analysis and the scientific approach of similarity methods, including a uniquely robust discussion on self-similarity solutions of the First and Second kinds. The coverage pushes well beyond traditional applications in fluid mechanics and gas dynamics to demonstrate how powerful self-similarity can be in solving complex problems across many diverse fields, using nonlinear Partial Differential Equations (PDEs) by reducing them to Ordinary Differential Equations (ODEs) with a simple traditional analytical solution approach. Of particular interest is the book's coverage of dimensional analysis and self-similarity methods in nuclear and energy engineering from Heat Transfer and Thermal Hydraulic points of view. Numerous practical examples of dimensional analysis problems are presented throughout each chapter, with additional problems presented in each appendix, allowing readers to link the book's theoretical explanations and step-by-step mathematical solutions to practical implementations.
Problems In The Theory Of Point Explosion In Gases
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Author : Viktor Pavlovich Korobeĭnikov
language : en
Publisher: American Mathematical Soc.
Release Date : 1976
Problems In The Theory Of Point Explosion In Gases written by Viktor Pavlovich Korobeĭnikov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.
A Class Of Self Similar Hydrodynamics Test Problems
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Author :
language : en
Publisher:
Release Date : 2010
A Class Of Self Similar Hydrodynamics Test Problems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
We consider self-similar solutions to the gas dynamics equations. One such solution - a spherical geometry Gaussian density profile - has been analyzed in the existing literature, and a connection between it, a linear velocity profile, and a uniform specific internal energy profile has been identified. In this work, we assume the linear velocity profile to construct an entire class of self-similar sol utions in both cylindrical and spherical geometry, of which the Gaussian form is one possible member. After completing the derivation, we present some results in the context of a test problem for compressible flow codes.
Systems Of Quasilinear Equations And Their Applications To Gas Dynamics
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Author : Boris Leonidovich Rozhdestvenski_
language : en
Publisher: American Mathematical Soc.
Release Date : 1983-12-31
Systems Of Quasilinear Equations And Their Applications To Gas Dynamics written by Boris Leonidovich Rozhdestvenski_ and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-12-31 with Science categories.
This book is essentially a new edition, revised and augmented by results of the last decade, of the work of the same title published in 1968 by ``Nauka.'' It is devoted to mathematical questions of gas dynamics. Topics covered include Foundations of the Theory of Systems of Quasilinear Equations of Hyperbolic Type in Two Independent Variables; Classical and Generalized Solutions of One-Dimensional Gas Dynamics; Difference Methods for Solving the Equations of Gas Dynamics; and Generalized Solutions of Systems of Quasilinear Equations of Hyperbolic Type.
The Two Dimensional Riemann Problem In Gas Dynamics
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Author : Jiequan Li
language : en
Publisher: CRC Press
Release Date : 1998-08-21
The Two Dimensional Riemann Problem In Gas Dynamics written by Jiequan Li and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-08-21 with Mathematics categories.
The Riemann problem is the most fundamental problem in the entire field of non-linear hyperbolic conservation laws. Since first posed and solved in 1860, great progress has been achieved in the one-dimensional case. However, the two-dimensional case is substantially different. Although research interest in it has lasted more than a century, it has yielded almost no analytical demonstration. It remains a great challenge for mathematicians. This volume presents work on the two-dimensional Riemann problem carried out over the last 20 years by a Chinese group. The authors explore four models: scalar conservation laws, compressible Euler equations, zero-pressure gas dynamics, and pressure-gradient equations. They use the method of generalized characteristic analysis plus numerical experiments to demonstrate the elementary field interaction patterns of shocks, rarefaction waves, and slip lines. They also discover a most interesting feature for zero-pressure gas dynamics: a new kind of elementary wave appearing in the interaction of slip lines-a weighted Dirac delta shock of the density function. The Two-Dimensional Riemann Problem in Gas Dynamics establishes the rigorous mathematical theory of delta-shocks and Mach reflection-like patterns for zero-pressure gas dynamics, clarifies the boundaries of interaction of elementary waves, demonstrates the interesting spatial interaction of slip lines, and proposes a series of open problems. With applications ranging from engineering to astrophysics, and as the first book to examine the two-dimensional Riemann problem, this volume will prove fascinating to mathematicians and hold great interest for physicists and engineers.
Similarity And Dimensional Methods In Mechanics
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Author : L. I. Sedov
language : en
Publisher: Academic Press
Release Date : 2014-05-12
Similarity And Dimensional Methods In Mechanics written by L. I. Sedov and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Science categories.
Similarity and Dimensional Methods in Mechanics provides a complete development of the basic concepts of dimensional analysis and similarity methods, illustrated by applications to a wide variety of problems in mechanics. This book shows the power of dimensional and similarity methods in solving problems in the theory of explosions and astrophysics. Organized into five chapters, this book begins with an overview of the fundamental ideas behind similarity and dimensional methods. This text then provides a series of examples of application of the methods. Other chapters consider the use of similarity and dimensional analysis in developing fundamental contributions to viscous fluid theory. This book discusses as well the various theories of isotropic turbulence. The final chapter deals with the applications to the theory of the luminosity and internal structure of stars. This book is a valuable resource for students who wish to learn dimensional analysis and similarity methods for the first time. Readers who are connected with the many aspects of gas dynamics, including space technology, astrophysics, and atomic energy will also find this book useful.
Dimensional Analysis Beyond The Pi Theorem
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Author : Bahman Zohuri
language : en
Publisher: Springer
Release Date : 2016-11-02
Dimensional Analysis Beyond The Pi Theorem written by Bahman Zohuri and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-02 with Technology & Engineering categories.
Dimensional Analysis and Physical Similarity are well understood subjects, and the general concepts of dynamical similarity are explained in this book. Our exposition is essentially different from those available in the literature, although it follows the general ideas known as Pi Theorem. There are many excellent books that one can refer to; however, dimensional analysis goes beyond Pi theorem, which is also known as Buckingham’s Pi Theorem. Many techniques via self-similar solutions can bound solutions to problems that seem intractable. A time-developing phenomenon is called self-similar if the spatial distributions of its properties at different points in time can be obtained from one another by a similarity transformation, and identifying one of the independent variables as time. However, this is where Dimensional Analysis goes beyond Pi Theorem into self-similarity, which has represented progress for researchers. In recent years there has been a surge of interest in self-similar solutions of the First and Second kind. Such solutions are not newly discovered; they have been identified and named by Zel’dovich, a famous Russian Mathematician in 1956. They have been used in the context of a variety of problems, such as shock waves in gas dynamics, and filtration through elasto-plastic materials. Self-Similarity has simplified computations and the representation of the properties of phenomena under investigation. It handles experimental data, reduces what would be a random cloud of empirical points to lie on a single curve or surface, and constructs procedures that are self-similar. Variables can be specifically chosen for the calculations.
The Two Dimensional Riemann Problem In Gas Dynamics
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Author : Jiequan Li
language : en
Publisher: Taylor & Francis
Release Date : 2022-02-13
The Two Dimensional Riemann Problem In Gas Dynamics written by Jiequan Li and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-13 with Mathematics categories.
The Riemann problem is the most fundamental problem in the entire field of non-linear hyperbolic conservation laws. Since first posed and solved in 1860, great progress has been achieved in the one-dimensional case. However, the two-dimensional case is substantially different. Although research interest in it has lasted more than a century, it has yielded almost no analytical demonstration. It remains a great challenge for mathematicians. This volume presents work on the two-dimensional Riemann problem carried out over the last 20 years by a Chinese group. The authors explore four models: scalar conservation laws, compressible Euler equations, zero-pressure gas dynamics, and pressure-gradient equations. They use the method of generalized characteristic analysis plus numerical experiments to demonstrate the elementary field interaction patterns of shocks, rarefaction waves, and slip lines. They also discover a most interesting feature for zero-pressure gas dynamics: a new kind of elementary wave appearing in the interaction of slip lines-a weighted Dirac delta shock of the density function. The Two-Dimensional Riemann Problem in Gas Dynamics establishes the rigorous mathematical theory of delta-shocks and Mach reflection-like patterns for zero-pressure gas dynamics, clarifies the boundaries of interaction of elementary waves, demonstrates the interesting spatial interaction of slip lines, and proposes a series of open problems. With applications ranging from engineering to astrophysics, and as the first book to examine the two-dimensional Riemann problem, this volume will prove fascinating to mathematicians and hold great interest for physicists and engineers.