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Author : Robert Byron Lowrie
Publisher :
ISBN 13 :
Total Pages : 412 pages
Book Rating : 4.3/5 (91 download)
Download or read book Compact Higher-order Numerical Methods for Hyperbolic Conservation Laws written by Robert Byron Lowrie and published by . This book was released on 1996 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Remi Abgrall
Publisher : Elsevier
ISBN 13 : 0444637958
Total Pages : 668 pages
Book Rating : 4.4/5 (446 download)
Download or read book Handbook of Numerical Methods for Hyperbolic Problems written by Remi Abgrall and published by Elsevier. This book was released on 2016-11-17 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author : LEVEQUE
Publisher : Birkhäuser
ISBN 13 : 3034851162
Total Pages : 221 pages
Book Rating : 4.0/5 (348 download)
Download or read book Numerical Methods for Conservation Laws written by LEVEQUE and published by Birkhäuser. This book was released on 2013-11-11 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Elena Vázquez-Cendón
Publisher : CRC Press
ISBN 13 : 0203590627
Total Pages : 144 pages
Book Rating : 4.2/5 (35 download)
Download or read book Lecture Notes on Numerical Methods for Hyperbolic Equations written by Elena Vázquez-Cendón and published by CRC Press. This book was released on 2011-05-23 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the lecture notes of the Short Course on Numerical Methods for Hyperbolic Equations (Faculty of Mathematics, University of Santiago de Compostela, Spain, 2-4 July 2011). The course was organized in recognition of Prof. Eleuterio Toro‘s contribution to education and training on numerical methods for partial differential equation
Author : Randall J. LeVeque
Publisher : Cambridge University Press
ISBN 13 : 1139434187
Total Pages : 582 pages
Book Rating : 4.1/5 (394 download)
Download or read book Finite Volume Methods for Hyperbolic Problems written by Randall J. LeVeque and published by Cambridge University Press. This book was released on 2002-08-26 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.
Author : Elena Vázquez-Cendón
Publisher : CRC Press
ISBN 13 : 041562150X
Total Pages : 436 pages
Book Rating : 4.4/5 (156 download)
Download or read book Numerical Methods for Hyperbolic Equations written by Elena Vázquez-Cendón and published by CRC Press. This book was released on 2012-11-05 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Methods for Hyperbolic Equations is a collection of 49 articles presented at the International Conference on Numerical Methods for Hyperbolic Equations: Theory and Applications (Santiago de Compostela, Spain, 4-8 July 2011). The conference was organized to honour Professor Eleuterio Toro in the month of his 65th birthday. The topics covered include: • Recent advances in the numerical computation of environmental conservation laws with source terms • Multiphase flow and porous media • Numerical methods in astrophysics • Seismology and geophysics modelling • High order methods for hyperbolic conservation laws • Numerical methods for reactive flows • Finite volume and discontinous Galerkin schemes for stiff source term problems • Methods and models for biomedical problems • Numerical methods for reactive flows The research interest of Eleuterio Toro, born in Chile on 16th July 1946, is reflected in Numerical Methods for Hyperbolic Equations, and focuses on: numerical methods for partial differential equations, with particular emphasis on methods for hyperbolic equations; design and application of new algorithms; hyperbolic partial differential equations as mathematical models of various types of processes; mathematical modelling and simulation of physico/chemical processes that include wave propagation phenomena; modelling of multiphase flows; application of models and methods to real problems. Eleuterio Toro received several honours and distinctions, including the honorary title OBE from Queen Elizabeth II (Buckingham Palace, London 2000); Distinguished Citizen of the City of Carahue (Chile, 2001); Life Fellow, Claire Hall, University of Cambridge (UK, 2003); Fellow of the Indian Society for Shock Wave Research (Bangalore, 2005); Doctor Honoris Causa (Universidad de Santiago de Chile, 2008); William Penney Fellow, University of Cambridge (UK, 2010); Doctor Honoris Causa (Universidad de la Frontera, Chile, 2012). Professor Toro is author of two books, editor of two books and author of more than 260 research works. In the last ten years he has been invited and keynote speaker in more than 100 scientific events. Professor Toro has held many visiting appointments round the world, which include several European countries, Japan, China and USA.
Author : Remi Abgrall
Publisher : Elsevier
ISBN 13 : 044463911X
Total Pages : 612 pages
Book Rating : 4.4/5 (446 download)
Download or read book Handbook of Numerical Methods for Hyperbolic Problems written by Remi Abgrall and published by Elsevier. This book was released on 2017-01-16 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook on Numerical Methods for Hyperbolic Problems: Applied and Modern Issues details the large amount of literature in the design, analysis, and application of various numerical algorithms for solving hyperbolic equations that has been produced in the last several decades. 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 become familiar with their relative advantages and limitations. Provides detailed, cutting-edge background explanations of existing algorithms and their analysis Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or those involved in applications Written by leading subject experts in each field, the volumes provide breadth and depth of content coverage
Author : Giacomo Albi
Publisher : Springer Nature
ISBN 13 : 3031298756
Total Pages : 241 pages
Book Rating : 4.0/5 (312 download)
Download or read book Advances in Numerical Methods for Hyperbolic Balance Laws and Related Problems written by Giacomo Albi and published by Springer Nature. This book was released on 2023-06-02 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: A broad range of phenomena in science and technology can be described by non-linear partial differential equations characterized by systems of conservation laws with source terms. Well known examples are hyperbolic systems with source terms, kinetic equations, and convection-reaction-diffusion equations. This book collects research advances in numerical methods for hyperbolic balance laws and kinetic equations together with related modelling aspects. All the contributions are based on the talks of the speakers of the Young Researchers’ Conference “Numerical Aspects of Hyperbolic Balance Laws and Related Problems”, hosted at the University of Verona, Italy, in December 2021.
Author : Randall J. LeVeque
Publisher :
ISBN 13 :
Total Pages : 30 pages
Book Rating : 4.:/5 (317 download)
Download or read book A Study of Numerical Methods for Hyperbolic Conservation Laws with Stiff Source Terms written by Randall J. LeVeque and published by . This book was released on 1988 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Orhan Mehmetoglu
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (818 download)
Download or read book Stability and Convergence of High Order Numerical Methods for Nonlinear Hyperbolic Conservation Laws written by Orhan Mehmetoglu and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently there have been numerous advances in the development of numerical algorithms to solve conservation laws. Even though the analytical theory (existence-uniqueness) is complete in the case of scalar conservation laws, there are many numerically robust methods for which the question of convergence and error estimates are still open. Usually high order schemes are constructed to be Total Variation Diminishing (TVD) which only guarantees convergence of such schemes to a weak solution. The standard approach in proving convergence to the entropy solution is to try to establish cell entropy inequalities. However, this typically requires additional non-homogeneous limitations on the numerical method, which reduces the modified scheme to first order when the mesh is refined. There are only a few results on the convergence which do not impose such limitations and all of them assume some smoothness on the initial data in addition to L[^infinity] bound. The Nessyahu-Tadmor (NT) scheme is a typical example of a high order scheme. It is a simple yet robust second order non-oscillatory scheme, which relies on a non-linear piecewise linear reconstruction. A standard reconstruction choice is based on the so-called minmod limiter which gives a maximum principle for the scheme. Unfortunately, this limiter reduces the reconstruction to first order at local extrema. Numerical evidence suggests that this limitation is not necessary. By using MAPR-like limiters, one can allow local nonlinear reconstructions which do not reduce to first order at local extrema. However, use of such limiters requires a new approach when trying to prove a maximum principle for the scheme. It is also well known that the NT scheme does not satisfy the so-called strict cell entropy inequalities, which is the main difficulty in proving convergence to the entropy solution. In this work, the NT scheme with MAPR-like limiters is considered. A maximum principle result for a conservation law with any Lipschitz flux and also with any k-monotone flux is proven. Using this result it is also proven that in the case of strictly convex flux, the NT scheme with a properly selected MAPR-like limiter satisfies an one-sided Lipschitz stability estimate. As a result, convergence to the unique entropy solution when the initial data satisfies the so-called one-sided Lipschitz condition is obtained. Finally, compensated compactness arguments are employed to prove that for any bounded initial data, the NT scheme based on a MAPR-like limiter converges strongly on compact sets to the unique entropy solution of the conservation law with a strictly convex flux.
Author : A Harten
Publisher : Legare Street Press
ISBN 13 : 9781019952320
Total Pages : 0 pages
Book Rating : 4.9/5 (523 download)
Download or read book High Resolution Schemes for Hyperbolic Conservation Laws written by A Harten and published by Legare Street Press. This book was released on 2023-07-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: High Resolution Schemes for Hyperbolic Conservation Laws is a technical monograph on numerical methods for solving partial differential equations. Author A Harten analyzes a range of high-resolution schemes for hyperbolic conservation laws, offering insights into their accuracy, stability, and computational efficiency. This book will be of interest to computational scientists and mathematicians working in the field of numerical analysis. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Author : Jan S. Hesthaven
Publisher : SIAM
ISBN 13 : 1611975107
Total Pages : 571 pages
Book Rating : 4.6/5 (119 download)
Download or read book Numerical Methods for Conservation Laws written by Jan S. Hesthaven and published by SIAM. This book was released on 2018-01-30 with total page 571 pages. 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.
Author : Dietmar Kröner
Publisher : John Wiley & Sons
ISBN 13 :
Total Pages : 528 pages
Book Rating : 4.3/5 (91 download)
Download or read book Numerical Schemes for Conservation Laws written by Dietmar Kröner and published by John Wiley & Sons. This book was released on 1997 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : François Bouchut
Publisher : Springer Science & Business Media
ISBN 13 : 9783764366650
Total Pages : 148 pages
Book Rating : 4.3/5 (666 download)
Download or read book Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws written by François Bouchut and published by Springer Science & Business Media. This book was released on 2004-06-25 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The schemes are analyzed regarding their nonlinear stability Recently developed entropy schemes are presented A formalism is introduced for source terms
Author : Richard Bissell Pember
Publisher :
ISBN 13 :
Total Pages : 246 pages
Book Rating : 4.:/5 (33 download)
Download or read book Numerical Methods for Hyperbolic Conservation Laws with Stiff Relaxation written by Richard Bissell Pember and published by . This book was released on 1992 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 54 pages
Book Rating : 4.:/5 (317 download)
Download or read book Second- and Third-order Upwind Difference Schemes for Hyperbolic Conservation Laws written by and published by . This book was released on 1984 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Constantine M. Dafermos
Publisher : Springer Science & Business Media
ISBN 13 : 3540290893
Total Pages : 636 pages
Book Rating : 4.5/5 (42 download)
Download or read book Hyperbolic Conservation Laws in Continuum Physics written by Constantine M. Dafermos and published by Springer Science & Business Media. This book was released on 2006-01-16 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a lucid and authoritative exposition of the mathematical theory of hyperbolic system laws. The second edition contains a new chapter recounting exciting recent developments on the vanishing viscosity method. Numerous new sections introduce newly derived results. From the reviews: "The author is known as one of the leading experts in the field. His masterly written book is, surely, the most complete exposition in the subject of conservations laws." --Zentralblatt MATH
