Front Tracking for Hyperbolic Conservation Laws PDF Download

Author: Helge Holden
Publisher: Springer
ISBN: 3662475073
Category : Mathematics
Languages : en
Pages : 521

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Book Description
This is the second edition of a well-received book providing the fundamentals of the theory hyperbolic conservation laws. Several chapters have been rewritten, new material has been added, in particular, a chapter on space dependent flux functions and the detailed solution of the Riemann problem for the Euler equations. 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 of the first edition: "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.

Author: Alberto Bressan
Publisher: Oxford University Press, USA
ISBN: 9780198507000
Category : Mathematics
Languages : en
Pages : 270

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Book Description
This book provides a self-contained introduction to the mathematical theory of hyperbolic systems of conservation laws, with particular emphasis on the study of discontinuous solutions, characterized by the appearance of shock waves. This area has experienced substantial progress in very recent years thanks to the introduction of new techniques, in particular the front tracking algorithm and the semigroup approach. These techniques provide a solution to the long standing open problems of uniqueness and stability of entropy weak solutions. This volume is the first to present a comprehensive account of these new, fundamental advances. It also includes a detailed analysis of the stability and convergence of the front tracking algorithm. A set of problems, with varying difficulty is given at the end of each chapter to verify and expand understanding of the concepts and techniques previously discussed. For researchers, this book will provide an indispensable reference to the state of the art in the field of hyperbolic systems of conservation laws.

Author: Universitetet i Oslo. Institute for Informatics
Publisher:
ISBN: 9788273681256
Category : Conservation laws (Mathematics)
Languages : en
Pages :

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Author: Heinrich Freistuhler
Publisher: CRC Press
ISBN: 9780849306440
Category : Mathematics
Languages : en
Pages : 276

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Book Description
Systems of partial differential equations reflecting conservation laws hold significant relevance to a variety of theoretical and practical applications, including compressible fluid flow, electromagnetism, elasticity theory, and other areas of continuum mechanics. This field of nonlinear analysis is currently experiencing a marked increase in successful research activity. The EU-TMR network "Hyperbolic Systems of Conservation Laws held a summer program offering short courses on the Analysis of Systems of Conservation Laws. This book contains five of the self-contained short courses presented during this program by experts of international reputation. These courses, which address solutions to hyperbolic systems by the front tracking method, non-strictly hyperbolic conservation laws, hyperbolic-elliptic coupled systems, hyperbolic relaxation problems, the stability of nonlinear waves in viscous media and numerics, and more, represent the state of the art of most central aspects of the field.

Author: Philippe G. LeFloch
Publisher: Springer Science & Business Media
ISBN: 9783764366872
Category : Mathematics
Languages : en
Pages : 1010

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Book Description
This book examines the well-posedness theory for nonlinear hyperbolic systems of conservation laws, recently completed by the author together with his collaborators. It covers the existence, uniqueness, and continuous dependence of classical entropy solutions. It also introduces the reader to the developing theory of nonclassical (undercompressive) entropy solutions. The systems of partial differential equations under consideration arise in many areas of continuum physics.

Author: LEVEQUE
Publisher: Birkhäuser
ISBN: 3034851162
Category : Science
Languages : en
Pages : 221

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Book Description
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.

Author: Giuseppe Maria Coclite
Publisher: Springer Nature
ISBN: 9819739845
Category :
Languages : en
Pages : 153

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Book Description

Author: Helge Holden
Publisher: European Mathematical Society
ISBN: 9783037190784
Category : Mathematics
Languages : en
Pages : 238

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Book Description
Operator splitting (or the fractional steps method) is a very common tool to analyze nonlinear partial differential equations both numerically and analytically. By applying operator splitting to a complicated model one can often split it into simpler problems that can be analyzed separately. In this book one studies operator splitting for a family of nonlinear evolution equations, including hyperbolic conservation laws and degenerate convection-diffusion equations. Common for these equations is the prevalence of rough, or non-smooth, solutions, e.g., shocks. Rigorous analysis is presented, showing that both semi-discrete and fully discrete splitting methods converge. For conservation laws, sharp error estimates are provided and for convection-diffusion equations one discusses a priori and a posteriori correction of entropy errors introduced by the splitting. Numerical methods include finite difference and finite volume methods as well as front tracking. The theory is illustrated by numerous examples. There is a dedicated Web page that provides MATLABR codes for many of the examples. The book is suitable for graduate students and researchers in pure and applied mathematics, physics, and engineering.

Author: Mehdi Vahab
Publisher:
ISBN: 9781321213164
Category :
Languages : en
Pages :

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Book Description
This dissertation presents a new high-order front tracking method for two-phase hyperbolic systems of conservation laws separated by a contact discontinuity. A review of existing methods for moving and/or irregular boundaries shows the significance of accurate geometry data and flux calculation near the interface to achieve a high order method. A general method for hyperbolic systems of conservation laws is presented along with the implementations of numerical methods for simulations of gas dynamics in 2-D using the Euler equations. Convergence tests show the new method is second order accurate for smooth solutions and first order in presence of shocks. Also the new method is used for simulation of Richtmyer-Meshkov instability, in which results are in agreement with both theoretical andexperimental approaches.

Author: Jean-michel Coron
Publisher: World Scientific
ISBN: 9813276193
Category : Mathematics
Languages : en
Pages : 395

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Book Description
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.