The Method Of Fractional Steps

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The Method Of Fractional Steps

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Author : Nikolaj N. Yanenko
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

The Method Of Fractional Steps written by Nikolaj N. Yanenko and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Die Zwischenschrittmethode Zur L Sung Mehrdimensionaler Probleme Der Mathematischen Physik

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Author : Nikolai͏̈ Nikolaevitch Yanenko
language : en
Publisher:
Release Date : 1969

Die Zwischenschrittmethode Zur L Sung Mehrdimensionaler Probleme Der Mathematischen Physik written by Nikolai͏̈ Nikolaevitch Yanenko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Mathematical physics categories.

Chebyshev And Fourier Spectral Methods

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Author : John P. Boyd
language : en
Publisher: Courier Corporation
Release Date : 2013-06-05

Chebyshev And Fourier Spectral Methods written by John P. Boyd and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-05 with Mathematics categories.

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.

Numerical Methods For Shallow Water Flow

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Author : C.B. Vreugdenhil
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Numerical Methods For Shallow Water Flow written by C.B. Vreugdenhil and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Science categories.

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.

Numerical Methods For Partial Differential Equations

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Author : William F. Ames
language : en
Publisher: Academic Press
Release Date : 2014-05-10

Numerical Methods For Partial Differential Equations written by William F. Ames and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.

Numerical Methods for Partial Differential Equations, Second Edition deals with the use of numerical methods to solve partial differential equations. In addition to numerical fluid mechanics, hopscotch and other explicit-implicit methods are also considered, along with Monte Carlo techniques, lines, fast Fourier transform, and fractional steps methods. Comprised of six chapters, this volume begins with an introduction to numerical calculation, paying particular attention to the classification of equations and physical problems, asymptotics, discrete methods, and dimensionless forms. Subsequent chapters focus on parabolic and hyperbolic equations, elliptic equations, and special topics ranging from singularities and shocks to Navier-Stokes equations and Monte Carlo methods. The final chapter discuss the general concepts of weighted residuals, with emphasis on orthogonal collocation and the Bubnov-Galerkin method. The latter procedure is used to introduce finite elements. This book should be a valuable resource for students and practitioners in the fields of computer science and applied mathematics.

Numerical Methods For Transport And Hydraulic Processes

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Author :
language : en
Publisher: Elsevier
Release Date : 1988-06-01

Numerical Methods For Transport And Hydraulic Processes written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-06-01 with Computers categories.

Numerical Methods for Transport and Hydraulic Processes

Computer Aided Analysis Of Difference Schemes For Partial Differential Equations

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Author : Victor G. Ganzha
language : en
Publisher: John Wiley & Sons
Release Date : 2011-03-01

Computer Aided Analysis Of Difference Schemes For Partial Differential Equations written by Victor G. Ganzha and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-01 with Science categories.

Advances in computer technology have conveniently coincided withtrends in numerical analysis toward increased complexity ofcomputational algorithms based on finite difference methods. It isno longer feasible to perform stability investigation of thesemethods manually--and no longer necessary. As this book shows,modern computer algebra tools can be combined with methods fromnumerical analysis to generate programs that will do the jobautomatically. Comprehensive, timely, and accessible--this is the definitivereference on the application of computerized symbolic manipulationsfor analyzing the stability of a wide range of difference schemes.In particular, it deals with those schemes that are used to solvecomplex physical problems in areas such as gas dynamics, heat andmass transfer, catastrophe theory, elasticity, shallow watertheory, and more. Introducing many new applications, methods, and concepts,Computer-Aided Analysis of Difference Schemes for PartialDifferential Equations * Shows how computational algebra expedites the task of stabilityanalysis--whatever the approach to stability investigation * Covers ten different approaches for each stability method * Deals with the specific characteristics of each method and itsapplication to problems commonly encountered by numerical modelers * Describes all basic mathematical formulas that are necessary toimplement each algorithm * Provides each formula in several global algebraic symboliclanguages, such as MAPLE, MATHEMATICA, and REDUCE * Includes numerous illustrations and thought-provoking examplesthroughout the text For mathematicians, physicists, and engineers, as well as forpostgraduate students, and for anyone involved with numericsolutions for real-world physical problems, this book provides avaluable resource, a helpful guide, and a head start ondevelopments for the twenty-first century.

The Method Of Fractional Steps The Solution Of Problems Of Mathematical Physics In Several Variables

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Author : Melvil Dewey
language : en
Publisher:
Release Date : 1971

The Method Of Fractional Steps The Solution Of Problems Of Mathematical Physics In Several Variables written by Melvil Dewey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with categories.

Finite Element Methods For Flow Problems

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Author : Jean Donea
language : en
Publisher: John Wiley & Sons
Release Date : 2003-06-02

Finite Element Methods For Flow Problems written by Jean Donea and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-02 with Science categories.

In recent years there have been significant developments in the development of stable and accurate finite element procedures for the numerical approximation of a wide range of fluid mechanics problems. Taking an engineering rather than a mathematical bias, this valuable reference resource details the fundamentals of stabilised finite element methods for the analysis of steady and time-dependent fluid dynamics problems. Organised into six chapters, this text combines theoretical aspects and practical applications and offers coverage of the latest research in several areas of computational fluid dynamics. * Coverage includes new and advanced topics unavailable elsewhere in book form * Collection in one volume of the widely dispersed literature reporting recent progress in this field * Addresses the key problems and offers modern, practical solutions Due to the balance between the concise explanation of the theory and the detailed description of modern practical applications, this text is suitable for a wide audience including academics, research centres and government agencies in aerospace, automotive and environmental engineering.

Numerical Solution Of The Incompressible Navier Stokes Equations

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Author : L. Quartapelle
language : en
Publisher: Birkhäuser
Release Date : 2013-03-07

Numerical Solution Of The Incompressible Navier Stokes Equations written by L. Quartapelle and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Social Science categories.

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.