One Dimensional Hyperbolic Conservation Laws And Their Applications
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One Dimensional Hyperbolic Conservation Laws And Their Applications
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Author : Jean-michel Coron
language : en
Publisher: World Scientific
Release Date : 2019-01-08
One Dimensional Hyperbolic Conservation Laws And Their Applications written by Jean-michel Coron and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-08 with Mathematics categories.
This book is a collection of lecture notes for the LIASFMA Shanghai Summer School on 'One-dimensional Hyperbolic Conservation Laws and Their Applications' which was held during August 16 to August 27, 2015 at Shanghai Jiao Tong University, Shanghai, China. This summer school is one of the activities promoted by Sino-French International Associate Laboratory in Applied Mathematics (LIASFMA in short). LIASFMA was established jointly by eight institutions in China and France in 2014, which is aimed at providing a platform for some of the leading French and Chinese mathematicians to conduct in-depth researches, extensive exchanges, and student training in the field of applied mathematics. This summer school has the privilege of being the first summer school of the newly established LIASFMA, which makes it significant.
Numerical Approximation Of Hyperbolic Systems Of Conservation Laws
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Author : Edwige Godlewski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21
Numerical Approximation Of Hyperbolic Systems Of Conservation Laws written by Edwige Godlewski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-21 with Mathematics categories.
This work is devoted to the theory and approximation of nonlinear hyper bolic systems of conservation laws in one or two space variables. It follows directly a previous publication on hyperbolic systems of conservation laws by the same authors, and we shall make frequent references to Godlewski and Raviart (1991) (hereafter noted G. R. ), though the present volume can be read independently. This earlier publication, apart from a first chap ter, especially covered the scalar case. Thus, we shall detail here neither the mathematical theory of multidimensional scalar conservation laws nor their approximation in the one-dimensional case by finite-difference con servative schemes, both of which were treated in G. R. , but we shall mostly consider systems. The theory for systems is in fact much more difficult and not at all completed. This explains why we shall mainly concentrate on some theoretical aspects that are needed in the applications, such as the solution of the Riemann problem, with occasional insights into more sophisticated problems. The present book is divided into six chapters, including an introductory chapter. For the reader's convenience, we shall resume in this Introduction the notions that are necessary for a self-sufficient understanding of this book -the main definitions of hyperbolicity, weak solutions, and entropy present the practical examples that will be thoroughly developed in the following chapters, and recall the main results concerning the scalar case.
Front Tracking For Hyperbolic Conservation Laws
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Author : Helge Holden
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-08
Front Tracking For Hyperbolic Conservation Laws written by Helge Holden and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-08 with Mathematics categories.
Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a self-contained presentation using front tracking, which is also a numerical method. The multidimensional scalar case and the case of systems on the line are treated in detail. A chapter on finite differences is included. From the reviews: "It is already one of the few best digests on this topic. The present book is an excellent compromise between theory and practice. Students will appreciate the lively and accurate style." D. Serre, MathSciNet "I have read the book with great pleasure, and I can recommend it to experts as well as students. It can also be used for reliable and very exciting basis for a one-semester graduate course." S. Noelle, Book review, German Math. Soc. "Making it an ideal first book for the theory of nonlinear partial differential equations...an excellent reference for a graduate course on nonlinear conservation laws." M. Laforest, Comp. Phys. Comm.
Hyperbolic Problems Theory Numerics Applications
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Author : Heinrich Freistühler
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Hyperbolic Problems Theory Numerics Applications written by Heinrich Freistühler and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics. The mathematical theory of hyperbolic equations has recently made considerable progress. Accurate and efficient numerical schemes for computation have been and are being further developed. This two-volume set of conference proceedings contains about 100 refereed and carefully selected papers. The books are intended for researchers and graduate students in mathematics, science and engineering interested in the most recent results in theory and practice of hyperbolic problems. Applications touched in these proceedings concern one-phase and multiphase fluid flow, phase transitions, shallow water dynamics, elasticity, extended thermodynamics, electromagnetism, classical and relativistic magnetohydrodynamics, cosmology. Contributions to the abstract theory of hyperbolic systems deal with viscous and relaxation approximations, front tracking and wellposedness, stability of shock profiles and multi-shock patterns, traveling fronts for transport equations. Numerically oriented articles study finite difference, finite volume, and finite element schemes, adaptive, multiresolution, and artificial dissipation methods.
Finite Volume Methods For Hyperbolic Problems
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Author : Randall J. LeVeque
language : en
Publisher: Cambridge University Press
Release Date : 2002-08-26
Finite Volume Methods For Hyperbolic Problems written by Randall J. LeVeque and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-26 with Mathematics categories.
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Hyperbolic Conservation Laws And The Compensated Compactness Method
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Author : Yunguang Lu
language : en
Publisher: CRC Press
Release Date : 2002-09-27
Hyperbolic Conservation Laws And The Compensated Compactness Method written by Yunguang Lu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-27 with Mathematics categories.
The method of compensated compactness as a technique for studying hyperbolic conservation laws is of fundamental importance in many branches of applied mathematics. Until now, however, most accounts of this method have been confined to research papers. Offering the first comprehensive treatment, Hyperbolic Conservation Laws and the Compensated Comp
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1995
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Aeronautics categories.
Numerical Methods For Conservation Laws
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Author : LEVEQUE
language : en
Publisher: Birkhäuser
Release Date : 2013-11-11
Numerical Methods For Conservation Laws written by LEVEQUE and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in de veloping, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable un derstanding of the mathematical structure of these equations and their solutions is first required, and Part I of these notes deals with this theory. Part II deals more directly with numerical methods, again with the emphasis on general tools that are of broad use. I have stressed the underlying ideas used in various classes of methods rather than present ing the most sophisticated methods in great detail. My aim was to provide a sufficient background that students could then approach the current research literature with the necessary tools and understanding. vVithout the wonders of TeX and LaTeX, these notes would never have been put together. The professional-looking results perhaps obscure the fact that these are indeed lecture notes. Some sections have been reworked several times by now, but others are still preliminary. I can only hope that the errors are not too blatant. Moreover, the breadth and depth of coverage was limited by the length of these courses, and some parts are rather sketchy.
Godunov Type Schemes
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Author : V. Guinot
language : en
Publisher: Elsevier
Release Date : 2003-01-29
Godunov Type Schemes written by V. Guinot and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-29 with Science categories.
Godunov-type schemes appear as good candidates for the next generation of commercial modelling software packages, the capability of which to handle discontinuous solution will be a basic requirement. It is in the interest of practising engineers and developers to be familiar with the specific features of discontinuous wave propagation problems and to be aware of the possibilities offered by Godunov-type schemes for their solution. This book aims to present the principles of such schemes in a way that is easily understandable to practising engineers.The features of hyperbolic conservation laws and their solutions are presented in the first two chapters. The principles of Godunov-type schemes are outlined in a third chapter. Chapters 4 and 5 cover the application of the original Godunov scheme to scalar laws and to hyperbolic systems of conservation laws respectively. Chapter 6 is devoted to higher-order schemes in one dimension of space. The design of such a scheme is described for the general case and applied to some well-known schemes such as the MUSCL and PPM schemes. Chapter 7 focuses on multidimensional problems. The classical alternate directions and finite volume approaches are presented together with the wave splitting technique that is described in depth with an application to two-dimensional systems. Chapter 8 deals with large-time step algorithms. These include front tracking-based methods, explicit-implicit techniques and the time-line interpolation technique. Three appendices provide notions on accuracy and stability issues, Riemann solvers and the user instructions for the computational codes provided in the enclosed CD-ROM.
Handbook Of Numerical Methods For Hyperbolic Problems
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Author : Remi Abgrall
language : en
Publisher: Elsevier
Release Date : 2016-11-17
Handbook Of Numerical Methods For Hyperbolic Problems written by Remi Abgrall and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-17 with Mathematics categories.
Handbook of Numerical Methods for Hyperbolic Problems explores the changes that have taken place in the past few decades regarding literature in the design, analysis and application of various numerical algorithms for solving hyperbolic equations. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and readily understand their relative advantages and limitations. - Provides detailed, cutting-edge background explanations of existing algorithms and their analysis - Ideal for readers working on the theoretical aspects of algorithm development and its numerical analysis - Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or readers involved in applications - Written by leading subject experts in each field who provide breadth and depth of content coverage