Navier-Stokes Equations
Navier-Stokes Equations

Author: Roger Temam

Publisher: American Mathematical Soc.

Published: 2001-04-10

Total Pages: 426

ISBN-13: 0821827375

DOWNLOAD EBOOK

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.

Navier—Stokes Equations
Navier—Stokes Equations

Author: Roger Temam

Publisher: Elsevier

Published: 2016-06-03

Total Pages: 539

ISBN-13: 1483256855

DOWNLOAD EBOOK

Navier-Stokes Equations: Theory and Numerical Analysis focuses on the processes, methodologies, principles, and approaches involved in Navier-Stokes equations, computational fluid dynamics (CFD), and mathematical analysis to which CFD is grounded. The publication first takes a look at steady-state Stokes equations and steady-state Navier-Stokes equations. Topics include bifurcation theory and non-uniqueness results, discrete inequalities and compactness theorems, existence and uniqueness theorems, discretization of Stokes equations, existence and uniqueness for the Stokes equations, and function spaces. The text then examines the evolution of Navier-Stokes equations, including linear case, compactness theorems, alternate proof of existence by semi-discretization, and discretization of the Navier-Stokes equations. The book ponders on the approximation of the Navier-Stokes equations by the projection and compressibility methods; properties of the curl operator and application to the steady-state Navier-Stokes equations; and implementation of non-conforming linear finite elements. The publication is a valuable reference for researchers interested in the theory and numerical analysis of Navier-Stokes equations.

Finite Element Methods for Navier-Stokes Equations
Finite Element Methods for Navier-Stokes Equations

Author: Vivette Girault

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 386

ISBN-13: 3642616232

DOWNLOAD EBOOK

The material covered by this book has been taught by one of the authors in a post-graduate course on Numerical Analysis at the University Pierre et Marie Curie of Paris. It is an extended version of a previous text (cf. Girault & Raviart [32J) published in 1979 by Springer-Verlag in its series: Lecture Notes in Mathematics. In the last decade, many engineers and mathematicians have concentrated their efforts on the finite element solution of the Navier-Stokes equations for incompressible flows. The purpose of this book is to provide a fairly comprehen sive treatment of the most recent developments in that field. To stay within reasonable bounds, we have restricted ourselves to the case of stationary prob lems although the time-dependent problems are of fundamental importance. This topic is currently evolving rapidly and we feel that it deserves to be covered by another specialized monograph. We have tried, to the best of our ability, to present a fairly exhaustive treatment of the finite element methods for inner flows. On the other hand however, we have entirely left out the subject of exterior problems which involve radically different techniques, both from a theoretical and from a practical point of view. Also, we have neither discussed the implemen tation of the finite element methods presented by this book, nor given any explicit numerical result. This field is extensively covered by Peyret & Taylor [64J and Thomasset [82].

Initial-boundary Value Problems and the Navier-Stokes Equations
Initial-boundary Value Problems and the Navier-Stokes Equations

Author: Heinz-Otto Kreiss

Publisher: SIAM

Published: 1989-01-01

Total Pages: 408

ISBN-13: 0898719135

DOWNLOAD EBOOK

Annotation This book provides an introduction to the vast subject of initial and initial-boundary value problems for PDEs, with an emphasis on applications to parabolic and hyperbolic systems. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. Researchers and graduate students in applied mathematics and engineering will find Initial-Boundary Value Problems and the Navier-Stokes Equations invaluable. The subjects addressed in the book, such as the well-posedness of initial-boundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. There are many new results, in particular on the Navier-Stokes equations. The direct approach to the subject still gives a valuable introduction to an important area of applied analysis.

Numerical Treatment of the Navier-Stokes Equations
Numerical Treatment of the Navier-Stokes Equations

Author: Wolfgang Hackbusch

Publisher: Vieweg+teubner Verlag

Published: 1990

Total Pages: 184

ISBN-13:

DOWNLOAD EBOOK

The most frequently used method for the numerical integration of parabolic differential equa­ tions is the method of lines, where one first uses a discretization of space derivatives by finite differences or finite elements and then uses some time-stepping method for the the solution of resulting system of ordinary differential equations. Such methods are, at least conceptually, easy to perform. However, they can be expensive if steep gradients occur in the solution, stability must be controlled, and the global error control can be troublesome. This paper considers a simultaneaus discretization of space and time variables for a one-dimensional parabolic equation on a relatively long time interval, called 'time-slab'. The discretization is repeated or adjusted for following 'time-slabs' using continuous finite element approximations. In such a method we utilize the efficiency of finite elements by choosing a finite element mesh in the time-space domain where the finite element mesh has been adjusted to steep gradients of the solution both with respect to the space and the time variables. In this way we solve all the difficulties with the classical approach since stability, discretization error estimates and global error control are automatically satisfied. Such a method has been discussed previously in [3] and [4]. The related boundary value techniques or global time integration for systems of ordinary differential equations have been discussed in several papers, see [12] and the references quoted therein.

Numerical Solution of the Incompressible Navier-Stokes Equations
Numerical Solution of the Incompressible Navier-Stokes Equations

Author: L. Quartapelle

Publisher: Birkhäuser

Published: 2013-03-07

Total Pages: 296

ISBN-13: 3034885792

DOWNLOAD EBOOK

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.