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The Method Of Fractional Steps
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Book Synopsis The Method of Fractional Steps by : Nikolaj N. Yanenko
Download or read book The Method of Fractional Steps written by Nikolaj N. Yanenko and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The method of fractional steps by : N. N. Janenko
Download or read book The method of fractional steps written by N. N. Janenko and published by . This book was released on 1971 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Method of Fractional Steps : the Solution of Problems of Mathematical Physics in Several Variables by : Melvil Dewey
Download or read book The Method of Fractional Steps : the Solution of Problems of Mathematical Physics in Several Variables written by Melvil Dewey and published by . This book was released on 1971 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Navier-Stokes Equations by : Roger Temam
Download or read book Navier-Stokes Equations written by Roger Temam and published by American Mathematical Soc.. This book was released on 2001-04-10 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Lagrangian Fractional Step Method for the Incompressible Navier-Stokes Equations by : Christoph Borgers
Download or read book A Lagrangian Fractional Step Method for the Incompressible Navier-Stokes Equations written by Christoph Borgers and published by Sagwan Press. This book was released on 2018-02-07 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. 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. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. 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.
Book Synopsis A fractional step method for regularized Navier Stokes equations by : Werner Varnhorn
Download or read book A fractional step method for regularized Navier Stokes equations written by Werner Varnhorn and published by . This book was released on 1991 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Chebyshev and Fourier Spectral Methods by : John P. Boyd
Download or read book Chebyshev and Fourier Spectral Methods written by John P. Boyd and published by Courier Corporation. This book was released on 2013-06-05 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 A Fractional Step Method for the Solution of Navier-stokes Equations by : Mariano Vázquez
Download or read book A Fractional Step Method for the Solution of Navier-stokes Equations written by Mariano Vázquez and published by . This book was released on 1996 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Lagrangian Fractional Step Method for the Incompressible Navier-Stokes Equations by : Christoph Borgers
Download or read book A Lagrangian Fractional Step Method for the Incompressible Navier-Stokes Equations written by Christoph Borgers and published by . This book was released on 2015-08-04 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from A Lagrangian Fractional Step Method for the Incompressible Navier-Stokes Equations: October 1985 We develop a modification of Peskin's Lagrangian fractional step method for the incompressible Navier-Stokes equations. This new method is substantially more efficient than the one originally proposed by Peskin. On a grid with N points, the work per time step is proportional to NlogN. This gain in efficiency is accomplished by modifying the splitting and by using a multigrid method for the solution of the resulting systems of equations. The method uses finite difference operators constructed with the aid of Voronoi diagrams. We have implemented it on a periodic domain in the plane. We describe an efficient algorithm for the numerical construction of periodic Voronoi diagrams in the plane. We believe that this algorithm can easily be generalized to higher space dimensions. We report on numerical experiments with our method. We solve test problems with known solutions, and we compute a flow evolving from an initial vortex blob. Our results indicate that the method is convergent of first order. As an application of our method, we present a fully Lagrangian variant of Peskin's algorithm for the treatment of elastic boundaries immersed in the fluid, and we report on numerical results obtained with this algorithm. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Book Synopsis A Fractional-step Method for Solving 3-D Time-domain Maxwell Equations by : J. S. Shang
Download or read book A Fractional-step Method for Solving 3-D Time-domain Maxwell Equations written by J. S. Shang and published by . This book was released on 1993 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Fractional Step Method for the Solution of the Compressible Navier-stokes Equations by : Ramon Codina Rovira
Download or read book A Fractional Step Method for the Solution of the Compressible Navier-stokes Equations written by Ramon Codina Rovira and published by . This book was released on 1997 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Application of a Fractional-step Method to Incompressible Navier-Stokes Equation by :
Download or read book Application of a Fractional-step Method to Incompressible Navier-Stokes Equation written by and published by . This book was released on 1984 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Analysis and Optimal Control of Phase-Field Transition System: Fractional Steps Methods by : Costica Morosanu
Download or read book Analysis and Optimal Control of Phase-Field Transition System: Fractional Steps Methods written by Costica Morosanu and published by Bentham Science Publishers. This book was released on 2011-04-27 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: "All developments in mathematics and computer science facilitate development of industrial applications. This e-book approaches the subject in a profoundly interdisciplinary manner.The spectrum of subjects covered in this e-book includes mathematics, comp"
Book Synopsis On the Accuracy of Fractional Step Method for Conservation Laws by : Zhen-huan Teng
Download or read book On the Accuracy of Fractional Step Method for Conservation Laws written by Zhen-huan Teng and published by . This book was released on 1991 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fractional Differential Equations by : Igor Podlubny
Download or read book Fractional Differential Equations written by Igor Podlubny and published by Elsevier. This book was released on 1998-10-27 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'. This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models. In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research. A reader will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems, analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications. A unique survey of many applications of fractional calculus Presents basic theory Includes a unified presentation of selected classical results, which are important for applications Provides many examples Contains a separate chapter of fractional order control systems, which opens new perspectives in control theory The first systematic consideration of Caputo's fractional derivative in comparison with other selected approaches Includes tables of fractional derivatives, which can be used for evaluation of all considered types of fractional derivatives
Book Synopsis Fractional Calculus: Models And Numerical Methods (Second Edition) by : Juan J Trujillo
Download or read book Fractional Calculus: Models And Numerical Methods (Second Edition) written by Juan J Trujillo and published by World Scientific. This book was released on 2016-09-15 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods. Moreover, we will introduce some applied topics, in particular fractional variational methods which are used in physics, engineering or economics. We will also discuss the relationship between semi-Markov continuous-time random walks and the space-time fractional diffusion equation, which generalizes the usual theory relating random walks to the diffusion equation. These methods can be applied in finance, to model tick-by-tick (log)-price fluctuations, in insurance theory, to study ruin, as well as in macroeconomics as prototypical growth models.All these topics are complementary to what is dealt with in existing books on fractional calculus and its applications. This book will keep in mind the trade-off between full mathematical rigor and the needs of readers coming from different applied areas of science and engineering. In particular, the numerical methods listed in the book are presented in a readily accessible way that immediately allows the readers to implement them on a computer in a programming language of their choice.The second edition of the book has been expanded and now includes a discussion of additional, newly developed numerical methods for fractional calculus and a chapter on the application of fractional calculus for modeling processes in the life sciences.
