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Author: E.F. Toro Publisher: Springer Science & Business Media ISBN: 1461506638 Category : Computers Languages : en Pages : 1050
Book Description
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.
Author: E.F. Toro Publisher: Springer Science & Business Media ISBN: 1461506638 Category : Computers Languages : en Pages : 1050
Book Description
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.
Author: Eleuterio F. Toro Publisher: Springer Science & Business Media ISBN: 366203915X Category : Technology & Engineering Languages : en Pages : 635
Book Description
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.
Author: V. Guinot Publisher: Elsevier ISBN: 0080532586 Category : Science Languages : en Pages : 509
Book Description
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.
Author: E.F. Toro Publisher: Springer ISBN: 9780306466014 Category : Computers Languages : en Pages : 1077
Book Description
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.
Author: Eleuterio F. Toro Publisher: Springer Science & Business Media ISBN: 3540498346 Category : Technology & Engineering Languages : en Pages : 724
Book Description
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.
Author: Michael Shearer Publisher: SIAM ISBN: 9780898712834 Category : Science Languages : en Pages : 272
Book Description
One strongly represented theme is the power of ideas from dynamical systems that are being adapted and developed in the context of shock waves.
Author: D. Drikakis Publisher: Springer Science & Business Media ISBN: 9783540221364 Category : Science Languages : en Pages : 646
Book Description
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.
Author: Randall J. LeVeque Publisher: Cambridge University Press ISBN: 1139434187 Category : Mathematics Languages : en Pages : 582
Book Description
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.