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Analysis of Systems of Conservation Laws

1998-12-30 Mathematics
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Release : 1998-12-30
Genre : Mathematics
Kind : eBook
Book Rating : 440/5 ( reviews)

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Book Synopsis Analysis of Systems of Conservation Laws by : Heinrich Freistuhler

Download or read book Analysis of Systems of Conservation Laws written by Heinrich Freistuhler. This book was released on 1998-12-30. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analysis of Systems of Conservation Laws

1998-10
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Release : 1998-10
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Kind : eBook
Book Rating : 358/5 ( reviews)

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Book Synopsis Analysis of Systems of Conservation Laws by : Heinrich Freistuehler

Download or read book Analysis of Systems of Conservation Laws written by Heinrich Freistuehler. This book was released on 1998-10. Available in PDF, EPUB and Kindle. Book excerpt:

Systems of Conservation Laws 1

1999-05-27 Mathematics
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Release : 1999-05-27
Genre : Mathematics
Kind : eBook
Book Rating : 414/5 ( reviews)

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Book Synopsis Systems of Conservation Laws 1 by : Denis Serre

Download or read book Systems of Conservation Laws 1 written by Denis Serre. This book was released on 1999-05-27. Available in PDF, EPUB and Kindle. Book excerpt: Systems of conservation laws arise naturally in physics and chemistry. To understand them and their consequences (shock waves, finite velocity wave propagation) properly in mathematical terms requires, however, knowledge of a broad range of topics. This book sets up the foundations of the modern theory of conservation laws, describing the physical models and mathematical methods, leading to the Glimm scheme. Building on this the author then takes the reader to the current state of knowledge in the subject. The maximum principle is considered from the viewpoint of numerical schemes and also in terms of viscous approximation. Small waves are studied using geometrical optics methods. Finally, the initial-boundary problem is considered in depth. Throughout, the presentation is reasonably self-contained, with large numbers of exercises and full discussion of all the ideas. This will make it ideal as a text for graduate courses in the area of partial differential equations.

Numerical Methods for Conservation Laws

2018-01-30 Science
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Release : 2018-01-30
Genre : Science
Kind : eBook
Book Rating : 107/5 ( reviews)

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Book Synopsis Numerical Methods for Conservation Laws by : Jan S. Hesthaven

Download or read book Numerical Methods for Conservation Laws written by Jan S. Hesthaven. This book was released on 2018-01-30. Available in PDF, EPUB and Kindle. Book excerpt: Conservation laws are the mathematical expression of the principles of conservation and provide effective and accurate predictive models of our physical world. Although intense research activity during the last decades has led to substantial advances in the development of powerful computational methods for conservation laws, their solution remains a challenge and many questions are left open; thus it is an active and fruitful area of research. Numerical Methods for Conservation Laws: From Analysis to Algorithms offers the first comprehensive introduction to modern computational methods and their analysis for hyperbolic conservation laws, building on intense research activities for more than four decades of development; discusses classic results on monotone and finite difference/finite volume schemes, but emphasizes the successful development of high-order accurate methods for hyperbolic conservation laws; addresses modern concepts of TVD and entropy stability, strongly stable Runge-Kutta schemes, and limiter-based methods before discussing essentially nonoscillatory schemes, discontinuous Galerkin methods, and spectral methods; explores algorithmic aspects of these methods, emphasizing one- and two-dimensional problems and the development and analysis of an extensive range of methods; includes MATLAB software with which all main methods and computational results in the book can be reproduced; and demonstrates the performance of many methods on a set of benchmark problems to allow direct comparisons. Code and other supplemental material will be available online at publication.

Numerical Approximation of Hyperbolic Systems of Conservation Laws

2021-08-28 Mathematics
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Release : 2021-08-28
Genre : Mathematics
Kind : eBook
Book Rating : 448/5 ( reviews)

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Book Synopsis Numerical Approximation of Hyperbolic Systems of Conservation Laws by : Edwige Godlewski

Download or read book Numerical Approximation of Hyperbolic Systems of Conservation Laws written by Edwige Godlewski. This book was released on 2021-08-28. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the theory and approximation by finite volume methods of nonlinear hyperbolic 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. Since the earlier work concentrated on the mathematical theory of multidimensional scalar conservation laws, this book will focus on systems and the theoretical aspects which are needed in the applications, such as the solution of the Riemann problem and further insights into more sophisticated problems, with special attention to the system of gas dynamics. This new edition includes more examples such as MHD and shallow water, with an insight on multiphase flows. Additionally, the text includes source terms and well-balanced/asymptotic preserving schemes, introducing relaxation schemes and addressing problems related to resonance and discontinuous fluxes while adding details on the low Mach number situation.

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