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Godunov Methods
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Download or read book Godunov Methods written by E.F. Toro and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 1050 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited review book on Godunov methods contains 97 articles, all of which were presented at the international conference on Godunov Methods: Theory and Applications, held at Oxford in October 1999, to commemo rate the 70th birthday of the Russian mathematician Sergei K. Godunov. The meeting enjoyed the participation of 140 scientists from 20 countries; one of the participants commented: everyone is here, meaning that virtu ally everybody who had made a significant contribution to the general area of numerical methods for hyperbolic conservation laws, along the lines first proposed by Godunov in the fifties, was present at the meeting. Sadly, there were important absentees, who due to personal circumstance could not at tend this very exciting gathering. The central theme o{ the meeting, and of this book, was numerical methods for hyperbolic conservation laws fol lowing Godunov's key ideas contained in his celebrated paper of 1959. But Godunov's contributions to science are not restricted to Godunov's method.
Book Synopsis Riemann Solvers and Numerical Methods for Fluid Dynamics by : Eleuterio F. Toro
Download or read book Riemann Solvers and Numerical Methods for Fluid Dynamics written by Eleuterio F. Toro and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: High resolution upwind and centered methods are today a mature generation of computational techniques applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dynamics (CFD) being the most prominent up to now. This textbook gives a comprehensive, coherent and practical presentation of this class of techniques. The book is designed to provide readers with an understanding of the basic concepts, some of the underlying theory, the ability to critically use the current research papers on the subject, and, above all, with the required information for the practical implementation of the methods. Applications include: compressible, steady, unsteady, reactive, viscous, non-viscous and free surface flows.
Book Synopsis Riemann Solvers and Numerical Methods for Fluid Dynamics by : Eleuterio F. Toro
Download or read book Riemann Solvers and Numerical Methods for Fluid Dynamics written by Eleuterio F. Toro and published by Springer Science & Business Media. This book was released on 2009-04-21 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt: High resolution upwind and centered methods are a mature generation of computational techniques. They are applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dynamics (CFD) being the most prominent up to now. This textbook gives a comprehensive, coherent and practical presentation of this class of techniques. For its third edition the book has been thoroughly revised to contain new material.
Book Synopsis High-Resolution Methods for Incompressible and Low-Speed Flows by : D. Drikakis
Download or read book High-Resolution Methods for Incompressible and Low-Speed Flows written by D. Drikakis and published by Springer Science & Business Media. This book was released on 2004-09-21 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of incompressible ?ows is vital to many areas of science and te- nology. This includes most of the ?uid dynamics that one ?nds in everyday life from the ?ow of air in a room to most weather phenomena. Inundertakingthesimulationofincompressible?uid?ows,oneoftentakes many issues for granted. As these ?ows become more realistic, the problems encountered become more vexing from a computational point-of-view. These range from the benign to the profound. At once, one must contend with the basic character of incompressible ?ows where sound waves have been analytically removed from the ?ow. As a consequence vortical ?ows have been analytically “preconditioned,” but the ?ow has a certain non-physical character (sound waves of in?nite velocity). At low speeds the ?ow will be deterministic and ordered, i.e., laminar. Laminar ?ows are governed by a balance between the inertial and viscous forces in the ?ow that provides the stability. Flows are often characterized by a dimensionless number known as the Reynolds number, which is the ratio of inertial to viscous forces in a ?ow. Laminar ?ows correspond to smaller Reynolds numbers. Even though laminar ?ows are organized in an orderly manner, the ?ows may exhibit instabilities and bifurcation phenomena which may eventually lead to transition and turbulence. Numerical modelling of suchphenomenarequireshighaccuracyandmostimportantlytogaingreater insight into the relationship of the numerical methods with the ?ow physics.
Download or read book Review of Godunov Methods written by and published by . This book was released on 1996 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Level Set Methods and Dynamic Implicit Surfaces by : Stanley Osher
Download or read book Level Set Methods and Dynamic Implicit Surfaces written by Stanley Osher and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very hot area with a wide range of applications; Gives complete numerical analysis and recipes, which will enable readers to quickly apply the techniques to real problems; Includes two new techniques pioneered by Osher and Fedkiw; Osher and Fedkiw are internationally well-known researchers in this area
Download or read book Godunov-type Schemes written by V. Guinot and published by Elsevier. This book was released on 2003-01-29 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Finite Volume Methods for Hyperbolic Problems by : Randall J. LeVeque
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.
Book Synopsis Finite Volume Methods for Hyperbolic Problems by : Randall J. LeVeque
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: Publisher Description
Book Synopsis Computational Methods for Fluid Flow by : Roger Peyret
Download or read book Computational Methods for Fluid Flow written by Roger Peyret and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: In developing this book, we decided to emphasize applications and to provide methods for solving problems. As a result, we limited the mathematical devel opments and we tried as far as possible to get insight into the behavior of numerical methods by considering simple mathematical models. The text contains three sections. The first is intended to give the fundamen tals of most types of numerical approaches employed to solve fluid-mechanics problems. The topics of finite differences, finite elements, and spectral meth ods are included, as well as a number of special techniques. The second section is devoted to the solution of incompressible flows by the various numerical approaches. We have included solutions of laminar and turbulent-flow prob lems using finite difference, finite element, and spectral methods. The third section of the book is concerned with compressible flows. We divided this last section into inviscid and viscous flows and attempted to outline the methods for each area and give examples.
Book Synopsis Non-Newtonian Fluid Mechanics and Complex Flows by : Angiolo Farina
Download or read book Non-Newtonian Fluid Mechanics and Complex Flows written by Angiolo Farina and published by Springer. This book was released on 2018-06-25 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a series of challenging mathematical problems which arise in the modeling of Non-Newtonian fluid dynamics. It focuses in particular on the mathematical and physical modeling of a variety of contemporary problems, and provides some results. The flow properties of Non-Newtonian fluids differ in many ways from those of Newtonian fluids. Many biological fluids (blood, for instance) exhibit a non-Newtonian behavior, as do many naturally occurring or technologically relevant fluids such as molten polymers, oil, mud, lava, salt solutions, paint, and so on. The term "complex flows" usually refers to those fluids presenting an "internal structure" (fluid mixtures, solutions, multiphase flows, and so on). Modern research on complex flows has increased considerably in recent years due to the many biological and industrial applications.
Book Synopsis Computational Methods In Engineering: Advances & Applications - Proceedings Of The International Conference (In 2 Volumes) by : Khin-yong Lam
Download or read book Computational Methods In Engineering: Advances & Applications - Proceedings Of The International Conference (In 2 Volumes) written by Khin-yong Lam and published by World Scientific. This book was released on 1992-10-29 with total page 1556 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Methods for Conservation Laws by : LEVEQUE
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.
Book Synopsis Viscous Profiles and Numerical Methods for Shock Waves by : Michael Shearer
Download or read book Viscous Profiles and Numerical Methods for Shock Waves written by Michael Shearer and published by SIAM. This book was released on 1991-01-01 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: One strongly represented theme is the power of ideas from dynamical systems that are being adapted and developed in the context of shock waves.
Book Synopsis Lecture Notes on Numerical Methods for Hyperbolic Equations by : Elena Vázquez-Cendón
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
Book Synopsis Splitting Methods for Partial Differential Equations with Rough Solutions by : Helge Holden
Download or read book Splitting Methods for Partial Differential Equations with Rough Solutions written by Helge Holden and published by European Mathematical Society. This book was released on 2010 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Methods in Fluid Dynamics by : Maurice Holt
Download or read book Numerical Methods in Fluid Dynamics written by Maurice Holt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews of the first edition: "This book is directed to graduate students and research workers interested in the numerical solution of problems of fluid dynamics, primarily those arising in high speed flow. ...The book is well arranged, logically presented and well illustrated. It contains several FORTRAN programms with which students could experiment ... It is a practical book, with emphasis on methods and their implementation. It is an excellent text for the fruitful research area it covers, and is highly recommended". Journal of Fluid Mechanics #1 From the reviews of the second edition: "The arrangement of chapters in the book remains practically the same as that in the first editon (1977), except for the inclusion of Glimm's method ... This book is higly recommended for both graduate students and researchers." Applied Mechanics Reviews #1
