Implementation of Finite Element Methods for Navier-Stokes Equations

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Publisher : Springer Science & Business Media
ISBN 13 : 3642870473
Total Pages : 168 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Implementation of Finite Element Methods for Navier-Stokes Equations by : F. Thomasset

Download or read book Implementation of Finite Element Methods for Navier-Stokes Equations written by F. Thomasset and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: In structure mechanics analysis, finite element methods are now well estab lished and well documented techniques; their advantage lies in a higher flexibility, in particular for: (i) The representation of arbitrary complicated boundaries; (ii) Systematic rules for the developments of stable numerical schemes ap proximating mathematically wellposed problems, with various types of boundary conditions. On the other hand, compared to finite difference methods, this flexibility is paid by: an increased programming complexity; additional storage require ment. The application of finite element methods to fluid mechanics has been lagging behind and is relatively recent for several types of reasons: (i) Historical reasons: the early methods were invented by engineers for the analysis of torsion, flexion deformation of bearns, plates, shells, etc ... (see the historics in Strang and Fix (1972) or Zienckiewicz (1977». (ii) Technical reasons: fluid flow problems present specific difficulties: strong gradients,l of the velocity or temperature for instance, may occur which a finite mesh is unable to properly represent; a remedy lies in the various upwind finite element schemes which recently turned up, and which are reviewed in chapter 2 (yet their effect is just as controversial as in finite differences). Next, waves can propagate (e.g. in ocean dynamics with shallowwaters equations) which will be falsely distorted by a finite non regular mesh, as Kreiss (1979) pointed out. We are concerned in this course with the approximation of incompressible, viscous, Newtonian fluids, i.e. governed by N avier Stokes equations.

Contributions to Current Challenges in Mathematical Fluid Mechanics

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Publisher : Springer Science & Business Media
ISBN 13 : 9783764371043
Total Pages : 164 pages
Book Rating : 4.3/5 (71 download)

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Book Synopsis Contributions to Current Challenges in Mathematical Fluid Mechanics by : Giovanni P. Galdi

Download or read book Contributions to Current Challenges in Mathematical Fluid Mechanics written by Giovanni P. Galdi and published by Springer Science & Business Media. This book was released on 2004-07-23 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of five research articles, each dedicated to a significant topic in the mathematical theory of the Navier-Stokes equations, for compressible and incompressible fluids, and to related questions. All results given here are new and represent a noticeable contribution to the subject. One of the most famous predictions of the Kolmogorov theory of turbulence is the so-called Kolmogorov-obukhov five-thirds law. As is known, this law is heuristic and, to date, there is no rigorous justification. The article of A. Biryuk deals with the Cauchy problem for a multi-dimensional Burgers equation with periodic boundary conditions. Estimates in suitable norms for the corresponding solutions are derived for "large" Reynolds numbers, and their relation with the Kolmogorov-Obukhov law are discussed. Similar estimates are also obtained for the Navier-Stokes equation. In the late sixties J. L. Lions introduced a "perturbation" of the Navier Stokes equations in which he added in the linear momentum equation the hyper dissipative term (-Ll),Bu, f3 ~ 5/4, where Ll is the Laplace operator. This term is referred to as an "artificial" viscosity. Even though it is not physically moti vated, artificial viscosity has proved a useful device in numerical simulations of the Navier-Stokes equations at high Reynolds numbers. The paper of of D. Chae and J. Lee investigates the global well-posedness of a modification of the Navier Stokes equation similar to that introduced by Lions, but where now the original dissipative term -Llu is replaced by (-Ll)O:u, 0 S Ct

Spectral Methods in Fluid Dynamics

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Publisher : Springer Science & Business Media
ISBN 13 : 3642841082
Total Pages : 582 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Spectral Methods in Fluid Dynamics by : Claudio Canuto

Download or read book Spectral Methods in Fluid Dynamics written by Claudio Canuto and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigorous theory. The computational side vigorously since the early 1970s, especially in computationally intensive of the more spectacular applications are applications in fluid dynamics. Some of the power of these discussed here, first in general terms as examples of the methods have been methods and later in great detail after the specifics covered. This book pays special attention to those algorithmic details which are essential to successful implementation of spectral methods. The focus is on algorithms for fluid dynamical problems in transition, turbulence, and aero dynamics. This book does not address specific applications in meteorology, partly because of the lack of experience of the authors in this field and partly because of the coverage provided by Haltiner and Williams (1980). The success of spectral methods in practical computations has led to an increasing interest in their theoretical aspects, especially since the mid-1970s. Although the theory does not yet cover the complete spectrum of applications, the analytical techniques which have been developed in recent years have facilitated the examination of an increasing number of problems of practical interest. In this book we present a unified theory of the mathematical analysis of spectral methods and apply it to many of the algorithms in current use.

Computational Structural Mechanics & Fluid Dynamics

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Publisher : Elsevier
ISBN 13 : 1483287041
Total Pages : 467 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Computational Structural Mechanics & Fluid Dynamics by : A.K. Noor

Download or read book Computational Structural Mechanics & Fluid Dynamics written by A.K. Noor and published by Elsevier. This book was released on 2013-10-22 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational structural mechanics (CSM) and computational fluid dynamics (CFD) have emerged in the last two decades as new disciplines combining structural mechanics and fluid dynamics with approximation theory, numerical analysis and computer science. Their use has transformed much of theoretical mechanics and abstract science into practical and essential tools for a multitude of technological developments which affect many facets of our life. This collection of over 40 papers provides an authoritative documentation of major advances in both CSM and CFD, helping to identify future directions of development in these rapidly changing fields. Key areas covered are fluid structure interaction and aeroelasticity, CFD technology and reacting flows, micromechanics, stability and eigenproblems, probabilistic methods and chaotic dynamics, perturbation and spectral methods, element technology (finite volume, finite elements and boundary elements), adaptive methods, parallel processing machines and applications, and visualization, mesh generation and artificial intelligence interfaces.

Spectral Methods in Fluid Dynamics

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Publisher :
ISBN 13 :
Total Pages : 592 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Spectral Methods in Fluid Dynamics by : C. Canuto

Download or read book Spectral Methods in Fluid Dynamics written by C. Canuto and published by . This book was released on 1988 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Single-grid Spectral Collocation for the Navier-Stokes Equations

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Publisher :
ISBN 13 :
Total Pages : 54 pages
Book Rating : 4.:/5 (317 download)

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Book Synopsis Single-grid Spectral Collocation for the Navier-Stokes Equations by : Christine Bernardi

Download or read book Single-grid Spectral Collocation for the Navier-Stokes Equations written by Christine Bernardi and published by . This book was released on 1988 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Publications Du Laboratoire D'analyse Numérique

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Publisher :
ISBN 13 :
Total Pages : 444 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Publications Du Laboratoire D'analyse Numérique by :

Download or read book Publications Du Laboratoire D'analyse Numérique written by and published by . This book was released on 1991 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Vortex Dynamics and Vortex Methods

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821896969
Total Pages : 776 pages
Book Rating : 4.8/5 (969 download)

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Book Synopsis Vortex Dynamics and Vortex Methods by : Christopher Radcliff Anderson

Download or read book Vortex Dynamics and Vortex Methods written by Christopher Radcliff Anderson and published by American Mathematical Soc.. This book was released on 1991-12-23 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding vortex dynamics is the key to understanding much of fluid dynamics. For this reason, many researchers, using a great variety of different approaches--analytical, computational, and experimental--have studied the dynamics of vorticity. The AMS-SIAM Summer Seminar on Vortex Dynamics and Vortex Methods, held in June 1990 at the University of Washington in Seattle, brought together experts with a broad range of viewpoints and areas of specialization. This volume contains the proceedings from that seminar. The focus here is on the numerical computation of high Reynolds number incompressible flows. Also included is a smaller selection of important experimental results and analytic treatments. Many of the articles contain valuable introductory and survey material as well as open problems. Readers will appreciate this volume for its coverage of a wide variety of numerical, analytical, and experimental tools and for its treatment of interesting important discoveries made with these tools.

Parallel Computational Fluid Dynamics 2000

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Publisher : Gulf Professional Publishing
ISBN 13 : 0080538401
Total Pages : 601 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Parallel Computational Fluid Dynamics 2000 by : C.B. Jenssen

Download or read book Parallel Computational Fluid Dynamics 2000 written by C.B. Jenssen and published by Gulf Professional Publishing. This book was released on 2001-04-27 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: Parallel CFD 2000, the Twelfth in an International series of meetings featuring computational fluid dynamics research on parallel computers, was held May 22-25, 2000 in Trondheim, Norway.Following the trend of the past conferences, areas such as numerical schemes and algorithms, tools and environments, load balancing, as well as interdisciplinary topics and various kinds of industrial applications were all well represented in the work presented. In addition, for the first time in the Parallel CFD conference series, the organizing committee chose to draw special attention to certain subject areas by organizing a number of special sessions.We feel the emphasis of the papers presented at the conference reflect the direction of the research within parallel CFD at the beginning of the new millennium. It seems to be a clear tendency towards increased industrial exploitation of parallel CFD. Several presentations also demonstrated how new insight is being achieved from complex simulations, and how powerful parallel computers now make it possible to use CFD within a broader interdisciplinary setting.Obviously, successful application of parallel CFD still rests on the underlying fundamental principles. Therefore, numerical algorithms, development tools, and parallelization techniques are still as important as when parallel CFD was in is infancy. Furthermore, the novel concepts of affordable parallel computing as well as metacomputing show that exciting developments are still taking place.As is often pointed out however, the real power of parallel CFD comes from the combination of all the disciplines involved: Physics, mathematics, and computer science. This is probably one of the principal reasons for the continued popularity of the Parallel CFD Conferences series, as well as the inspiration behind much of the excellent work carried out on the subject. We hope that the papers in this book, both on an individual basis and as a whole, will contribute to that inspiration. Further details of Parallel CFD'99, as well as other conferences in this series, are available at http://www.parcfd.org

Numerical Approximation of Partial Differential Equations

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Publisher : Springer Science & Business Media
ISBN 13 : 3540852689
Total Pages : 551 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Numerical Approximation of Partial Differential Equations by : Alfio Quarteroni

Download or read book Numerical Approximation of Partial Differential Equations written by Alfio Quarteroni and published by Springer Science & Business Media. This book was released on 2009-02-11 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Everything is more simple than one thinks but at the same time more complex than one can understand Johann Wolfgang von Goethe To reach the point that is unknown to you, you must take the road that is unknown to you St. John of the Cross This is a book on the numerical approximation ofpartial differential equations (PDEs). Its scope is to provide a thorough illustration of numerical methods (especially those stemming from the variational formulation of PDEs), carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is our primary concern. Many kinds of problems are addressed: linear and nonlinear, steady and time-dependent, having either smooth or non-smooth solutions. Besides model equations, we consider a number of (initial-) boundary value problems of interest in several fields of applications. Part I is devoted to the description and analysis of general numerical methods for the discretization of partial differential equations. A comprehensive theory of Galerkin methods and its variants (Petrov Galerkin and generalized Galerkin), as wellas ofcollocationmethods, is devel oped for the spatial discretization. This theory is then specified to two numer ical subspace realizations of remarkable interest: the finite element method (conforming, non-conforming, mixed, hybrid) and the spectral method (Leg endre and Chebyshev expansion).

Reviews in Numerical Analysis, 1980-86

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Publisher :
ISBN 13 :
Total Pages : 648 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Reviews in Numerical Analysis, 1980-86 by :

Download or read book Reviews in Numerical Analysis, 1980-86 written by and published by . This book was released on 1987 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: These five volumes bring together a wealth of bibliographic information in the area of numerical analysis. Containing over 17,600 reviews of articles, books, and conference proceedings, these volumes represent all the numerical analysis entries that appeared in Mathematical Reviews between 1980 and 1986. Author and key indexes appear at the end of volume 5.

ESAIM.

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Publisher :
ISBN 13 :
Total Pages : 674 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis ESAIM. by :

Download or read book ESAIM. written by and published by . This book was released on 2005 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Spectral and High Order Methods for Partial Differential Equations

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Publisher : North Holland
ISBN 13 :
Total Pages : 532 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Spectral and High Order Methods for Partial Differential Equations by : C. Canuto

Download or read book Spectral and High Order Methods for Partial Differential Equations written by C. Canuto and published by North Holland. This book was released on 1990 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decade high order methods for scientific computing have been attracting increasing interest. This trend has been generated by the need for a higher accuracy in the numerical simulation of more and more complex scientific and technological problems; it is backed up by sound mathematical research, and propelled by the availability of faster supercomputers. Spectral methods have now become the methods preferred in the prediction of many highly structured phenomena. The h-p version of the finite element method has proven extremely effective in handling singularities in structural mechanics. Finite differences have been demonstrated capable of blending flexibility and accuracy in applications to non-smooth problems. Although these and other high order methods originated from different, sometimes even opposite philosophies, they exhibit common features, and share a large part of the methodologies for their mathematical investigation and their algorithmic implementation. The technical content of the 14 invited and 30 general papers presented in this volume reflect the high standard of current research being achieved in this field.

International Aerospace Abstracts

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ISBN 13 :
Total Pages : 982 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis International Aerospace Abstracts by :

Download or read book International Aerospace Abstracts written by and published by . This book was released on 1979 with total page 982 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Canadian Journal of Physics

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Publisher :
ISBN 13 :
Total Pages : 570 pages
Book Rating : 4.:/5 (334 download)

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Book Synopsis Canadian Journal of Physics by :

Download or read book Canadian Journal of Physics written by and published by . This book was released on 2004 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Reviews

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Publisher :
ISBN 13 :
Total Pages : 868 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 1994 with total page 868 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Government Reports Annual Index

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ISBN 13 :
Total Pages : 1832 pages
Book Rating : 4.:/5 (3 download)

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Book Synopsis Government Reports Annual Index by :

Download or read book Government Reports Annual Index written by and published by . This book was released on 1993 with total page 1832 pages. Available in PDF, EPUB and Kindle. Book excerpt: