The Method of Fractional Steps PDF Download
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Author: Nikolaj N. Yanenko
Publisher: Springer Science & Business Media
ISBN: 3642651089
Category : Mathematics
Languages : en
Pages : 169
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Book Description
The method of. fractional steps, known familiarly as the method oi splitting, is a remarkable technique, developed by N. N. Yanenko and his collaborators, for solving problems in theoretical mechanics numerically. It is applicable especially to potential problems, problems of elasticity and problems of fluid dynamics. Most of the applications at the present time have been to incompressible flow with free bound aries and to viscous flow at low speeds. The method offers a powerful means of solving the Navier-Stokes equations and the results produced so far cover a range of Reynolds numbers far greater than that attained in earlier methods. Further development of the method should lead to complete numerical solutions of many of the boundary layer and wake problems which at present defy satisfactory treatment. As noted by the author very few applications of the method have yet been made to problems in solid mechanics and prospects for answers both in this field and other areas such as heat transfer are encouraging. As the method is perfected it is likely to supplant traditional relaxation methods and finite element methods, especially with the increase in capability of large scale computers. The literal translation was carried out by T. Cheron with financial support of the Northrop Corporation. The editing of the translation was undertaken in collaboration with N. N. Yanenko and it is a plea sure to acknowledge his patient help and advice in this project. The edited manuscript was typed, for the most part, by Mrs.
Author: Nikolaj N. Yanenko
Publisher: Springer Science & Business Media
ISBN: 3642651089
Category : Mathematics
Languages : en
Pages : 169
Get Book Here
Book Description
The method of. fractional steps, known familiarly as the method oi splitting, is a remarkable technique, developed by N. N. Yanenko and his collaborators, for solving problems in theoretical mechanics numerically. It is applicable especially to potential problems, problems of elasticity and problems of fluid dynamics. Most of the applications at the present time have been to incompressible flow with free bound aries and to viscous flow at low speeds. The method offers a powerful means of solving the Navier-Stokes equations and the results produced so far cover a range of Reynolds numbers far greater than that attained in earlier methods. Further development of the method should lead to complete numerical solutions of many of the boundary layer and wake problems which at present defy satisfactory treatment. As noted by the author very few applications of the method have yet been made to problems in solid mechanics and prospects for answers both in this field and other areas such as heat transfer are encouraging. As the method is perfected it is likely to supplant traditional relaxation methods and finite element methods, especially with the increase in capability of large scale computers. The literal translation was carried out by T. Cheron with financial support of the Northrop Corporation. The editing of the translation was undertaken in collaboration with N. N. Yanenko and it is a plea sure to acknowledge his patient help and advice in this project. The edited manuscript was typed, for the most part, by Mrs.
Author: C.B. Vreugdenhil
Publisher: Springer Science & Business Media
ISBN: 9401583544
Category : Science
Languages : en
Pages : 273
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Book Description
A wide variety of problems are associated with the flow of shallow water, such as atmospheric flows, tides, storm surges, river and coastal flows, lake flows, tsunamis. Numerical simulation is an effective tool in solving them and a great variety of numerical methods are available. The first part of the book summarizes the basic physics of shallow-water flow needed to use numerical methods under various conditions. The second part gives an overview of possible numerical methods, together with their stability and accuracy properties as well as with an assessment of their performance under various conditions. This enables the reader to select a method for particular applications. Correct treatment of boundary conditions (often neglected) is emphasized. The major part of the book is about two-dimensional shallow-water equations but a discussion of the 3-D form is included. The book is intended for researchers and users of shallow-water models in oceanographic and meteorological institutes, hydraulic engineering and consulting. It also provides a major source of information for applied and numerical mathematicians.
Author: William F. Ames
Publisher: Academic Press
ISBN: 0080571301
Category : Mathematics
Languages : en
Pages : 467
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Book Description
This volume is designed as an introduction to the concepts of modern numerical analysis as they apply to partial differential equations. The book contains many practical problems and their solutions, but at the same time, strives to expose the pitfalls--such as overstability, consistency requirements, and the danger of extrapolation to nonlinear problems methods used on linear problems. Numerical Methods for Partial Differential Equations, Third Edition reflects the great accomplishments that have taken place in scientific computation in the fifteen years since the Second Edition was published. This new edition is a drastic revision of the previous one, with new material on boundary elements, spectral methods, the methods of lines, and invariant methods. At the same time, the new edition retains the self-contained nature of the older version, and shares the clarity of its exposition and the integrity of its presentation. Material on finite elements and finite differences have been merged, and now constitute equal partners Additional material has been added on boundary elements, spectral methods, the method of lines, and invariant methods References have been updated, and reflect the additional material Self-contained nature of the Second Edition has been maintained Very suitable for PDE courses
Author: John P. Boyd
Publisher: Courier Corporation
ISBN: 0486141926
Category : Mathematics
Languages : en
Pages : 690
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Book Description
Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.
Author: Roger Temam
Publisher: American Mathematical Soc.
ISBN: 0821827375
Category : Mathematics
Languages : en
Pages : 426
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Book Description
Originally published in 1977, the book is devoted to the theory and numerical analysis of the Navier-Stokes equations for viscous incompressible fluid. On the theoretical side, results related to the existence, the uniqueness, and, in some cases, the regularity of solutions are presented. On the numerical side, various approaches to the approximation of Navier-Stokes problems by discretization are considered, such as the finite dereference method, the finite element method, and the fractional steps method. The problems of stability and convergence for numerical methods are treated as completely as possible. The new material in the present book (as compared to the preceding 1984 edition) is an appendix reproducing a survey article written in 1998. This appendix touches upon a few aspects not addressed in the earlier editions, in particular a short derivation of the Navier-Stokes equations from the basic conservation principles in continuum mechanics, further historical perspectives, and indications on new developments in the area. The appendix also surveys some aspects of the related Euler equations and the compressible Navier-Stokes equations. The book is written in the style of a textbook and the author has attempted to make the treatment self-contained. It can be used as a textbook or a reference book for researchers. Prerequisites for reading the book include some familiarity with the Navier-Stokes equations and some knowledge of functional analysis and Sololev spaces.
Author: Jean Donea
Publisher: John Wiley & Sons
ISBN: 9780471496663
Category : Science
Languages : en
Pages : 366
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Book Description
Die Finite-Elemente-Methode, eines der wichtigsten in der Technik verwendeten numerischen Näherungsverfahren, wird hier gründlich und gut verständlich, aber ohne ein Zuviel an mathematischem Formalismus abgehandelt. Insbesondere geht es um die Anwendung der Methode auf Strömungsprobleme. Alle wesentlichen aktuellen Forschungsergebnisse wurden in den Band aufgenommen; viele davon sind bisher nur verstreut in der Originalliteratur zu finden.
Author:
Publisher: Elsevier
ISBN: 0080870279
Category : Computers
Languages : en
Pages : 483
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Book Description
Numerical Methods for Transport and Hydraulic Processes
Author: Steven J. Fenves
Publisher: Elsevier
ISBN: 1483272540
Category : Technology & Engineering
Languages : en
Pages : 698
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Book Description
Numerical and Computer Methods in Structural Mechanics is a compendium of papers that deals with the numerical methods in structural mechanics, computer techniques, and computer capabilities. Some papers discus the analytical basis of the computer technique most widely used in software, that is, the finite element method. This method includes the convergence (in terms of variation principles) isoparametrics, hybrid models, and incompatible displacement models. Other papers explain the storage or retrieval of data, as well as equation-solving algorithms. Other papers describe general-purpose structural mechanics programs, alternatives to, and extension of the usual finite element approaches. Another paper explores nonlinear, dynamic finite element problems, and a direct physical approach to determine finite difference models. Special papers explain structural mechanics used in computing, particularly, those related to integrated data bases, such as in the Structures Oriented Exchange System of the Office of Naval Research and the integrated design of tanker structures. Other papers describe software and hardware capabilities, for example, in ship design, fracture mechanics, biomechanics, and crash safety. The text is suitable for programmers, computer engineers, researchers, and scientists involved in materials and industrial design.
Author: Boling Guo
Publisher: World Scientific
ISBN: 9814667064
Category : Mathematics
Languages : en
Pages : 347
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Book Description
This book aims to introduce some new trends and results on the study of the fractional differential equations, and to provide a good understanding of this field to beginners who are interested in this field, which is the authors' beautiful hope.This book describes theoretical and numerical aspects of the fractional partial differential equations, including the authors' researches in this field, such as the fractional Nonlinear Schrödinger equations, fractional Landau-Lifshitz equations and fractional Ginzburg-Landau equations. It also covers enough fundamental knowledge on the fractional derivatives and fractional integrals, and enough background of the fractional PDEs.
Author: L. Quartapelle
Publisher: Birkhäuser
ISBN: 3034885792
Category : Science
Languages : en
Pages : 296
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Book Description
This book presents different formulations of the equations governing incompressible viscous flows, in the form needed for developing numerical solution procedures. The conditions required to satisfy the no-slip boundary conditions in the various formulations are discussed in detail. Rather than focussing on a particular spatial discretization method, the text provides a unitary view of several methods currently in use for the numerical solution of incompressible Navier-Stokes equations, using either finite differences, finite elements or spectral approximations. For each formulation, a complete statement of the mathematical problem is provided, comprising the various boundary, possibly integral, and initial conditions, suitable for any theoretical and/or computational development of the governing equations. The text is suitable for courses in fluid mechanics and computational fluid dynamics. It covers that part of the subject matter dealing with the equations for incompressible viscous flows and their determination by means of numerical methods. A substantial portion of the book contains new results and unpublished material.
