Range And Null Space Finite Element Methods For Viscous Incompressible Flow
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Finite Element Methods for Viscous Incompressible Flows
Author | : Max D. Gunzburger |
Publisher | : Elsevier |
Total Pages | : 292 |
Release | : 2012-12-02 |
Genre | : Technology & Engineering |
ISBN | : 0323139825 |
Finite Element Methods for Viscous Incompressible Flows examines mathematical aspects of finite element methods for the approximate solution of incompressible flow problems. The principal goal is to present some of the important mathematical results that are relevant to practical computations. In so doing, useful algorithms are also discussed. Although rigorous results are stated, no detailed proofs are supplied; rather, the intention is to present these results so that they can serve as a guide for the selection and, in certain respects, the implementation of algorithms.
Incompressible Flow and the Finite Element Method: Incompressible Flow and the Finite Element Method & Advection-Diffusion and Isothermal Laminar Flow (Combined Edition)
Author | : P. M. Gresho |
Publisher | : |
Total Pages | : 1072 |
Release | : 1998-06-18 |
Genre | : Mathematics |
ISBN | : |
This comprehensive reference work covers all the important details regarding the application of the finite element method to incompressible flows. It addresses the theoretical background and the detailed development of appropriate numerical methods applied to the solution of a wide range of incompressible flows, beginning with extensive coverage of the advection-diffusion equation in volume one. For both this equation and the equations of principal interest - the Navier-Stokes equations, covered in detail in volume two - detailed discussion of both the continuous and discrete equations is presented, as well as explanations of how to properly march the time-dependent equations using smart implicit methods. Boundary and initial conditions, so important in applications, are carefully described and discussed, including well-posedness. The important role played by the pressure, so confusing in the past, is carefully explained. Together, this two volume work explains and emphasizes consistency in six areas: · consistent mass matrix · consistent pressure Poisson equation · consistent penalty methods · consistent normal direction · consistent heat flux · consistent forces Fully indexed and referenced, this book is an essential reference tool for all researchers, students and applied scientists in incompressible fluid mechanics.
Finite Element Methods for Incompressible Flow Problems
Author | : Volker John |
Publisher | : Springer |
Total Pages | : 816 |
Release | : 2016-10-27 |
Genre | : Mathematics |
ISBN | : 3319457500 |
This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.
Incompressible Flow and the Finite Element Method, Volume 2
Author | : P. M. Gresho |
Publisher | : Wiley |
Total Pages | : 630 |
Release | : 2000-06-22 |
Genre | : Science |
ISBN | : 9780471492504 |
This comprehensive two-volume reference covers the application of the finite element method to incompressible flows in fluid mechanics, addressing the theoretical background and the development of appropriate numerical methods applied to their solution. Volume One provides extensive coverage of the prototypical fluid mechanics equation: the advection-diffusion equation. For both this equation and the equations of principal interest - the Navier-Stokes equations (covered in detail in Volume Two) - a discussion of both the continuous and discrete equations is presented, as well as explanations of how to properly march the time-dependent equations using smart implicit methods. Boundary and initial conditions, so important in applications, are carefully described and discussed, including well-posedness. The important role played by the pressure, so confusing in the past, is carefully explained. The book explains and emphasizes consistency in six areas: * consistent mass matrix * consistent pressure Poisson equation * consistent penalty methods * consistent normal direction * consistent heat flux * consistent forces Fully indexed and referenced, this book is an essential reference tool for all researchers, students and applied scientists in incompressible fluid mechanics.
Finite Element Methods for Flow Problems
Author | : Jean Donea |
Publisher | : John Wiley & Sons |
Total Pages | : 366 |
Release | : 2003-06-02 |
Genre | : Science |
ISBN | : 9780471496663 |
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.
Finite Element Techniques for Fluid Flow
Author | : J. J. Connor |
Publisher | : Newnes |
Total Pages | : 321 |
Release | : 2013-09-11 |
Genre | : Technology & Engineering |
ISBN | : 1483161161 |
Finite Element Techniques for Fluid Flow describes the advances in the applications of finite element techniques to fluid mechanics. Topics covered range from weighted residual and variational methods to interpolation functions, inviscid fluids, and flow through porous media. The basic principles and governing equations of fluid mechanics as well as problems related to dispersion and shallow water circulation are also discussed. This text is comprised of nine chapters; the first of which explains some basic definitions and properties as well as the basic principles of weighted residual and variational methods. The reader is then introduced to the simple finite element concepts and models, and gradually to more complex applications. The chapters that follow focus on the governing equations of fluid flow, the solutions to potential type problems, and viscous flow problems in porous media. The solutions to more specialized problems are also presented. This book also considers how circulation problems can be tackled using finite elements, presents a solution to the mass transfer equation, and concludes with an explanation of how to solve general transient incompressible flows. This source will be of use to engineers, applied mathematicians, physicists, self-taught students, and research workers.
Mathematical Aspects of Finite Element Methods for Incompressible Viscous Flows
Author | : M. D. Gunzburger |
Publisher | : |
Total Pages | : 52 |
Release | : 1986 |
Genre | : |
ISBN | : |
We survey some mathematical aspects of finite element methods for incompressible viscous flows, concentrating on the steady primitive variable formulation. We address the discretization of a weak formulation of the Navier Stokes equations; we then consider the div-stability condition, whose satisfaction insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.
Incompressible Flow and the Finite Element Method, 2 Volume Set
Author | : P. M. Gresho |
Publisher | : Wiley |
Total Pages | : 0 |
Release | : 2000-07-26 |
Genre | : Science |
ISBN | : 9780471492689 |
This comprehensive reference work covers all the important details regarding the application of the finite element method to incompressible flows. It addresses the theoretical background and the detailed development of appropriate numerical methods applied to the solution of a wide range of incompressible flows, beginning with extensive coverage of the advection-diffusion equation in volume one. For both this equation and the equations of principal interest - the Navier-Stokes equations, covered in detail in volume two - detailed discussion of both the continuous and discrete equations is presented, as well as explanations of how to properly march the time-dependent equations using smart implicit methods. Boundary and initial conditions, so important in applications, are carefully described and discussed, including well-posedness. The important role played by the pressure, so confusing in the past, is carefully explained. Together, this two volume work explains and emphasizes consistency in six areas: * consistent mass matrix * consistent pressure Poisson equation * consistent penalty methods * consistent normal direction * consistent heat flux * consistent forces Fully indexed and referenced, this book is an essential reference tool for all researchers, students and applied scientists in incompressible fluid mechanics.