The Three-Dimensional Navier-Stokes Equations

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Publisher : Cambridge University Press
ISBN 13 : 1107019664
Total Pages : 487 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis The Three-Dimensional Navier-Stokes Equations by : James C. Robinson

Download or read book The Three-Dimensional Navier-Stokes Equations written by James C. Robinson and published by Cambridge University Press. This book was released on 2016-09-07 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible treatment of the main results in the mathematical theory of the Navier-Stokes equations, primarily aimed at graduate students.

The Navier-Stokes Equations

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Author :
Publisher : Springer Science & Business Media
ISBN 13 : 3034805519
Total Pages : 376 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis The Navier-Stokes Equations by : Hermann Sohr

Download or read book The Navier-Stokes Equations written by Hermann Sohr and published by Springer Science & Business Media. This book was released on 2012-12-13 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary objective of this monograph is to develop an elementary and se- containedapproachtothemathematicaltheoryofaviscousincompressible?uid n in a domain ? of the Euclidean spaceR , described by the equations of Navier- Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers’ convenience, in the ?rst two chapters we collect, without proof some fundamental properties of Sobolev spaces, distributions, operators, etc. Another important objective is to formulate the theory for a completely general domain ?. In particular, the theory applies to arbitrary unbounded, non-smooth domains. For this reason, in the nonlinear case, we have to restrict ourselves to space dimensions n=2,3 that are also most signi?cant from the physical point of view. For mathematical generality, we will develop the l- earized theory for all n? 2. Although the functional-analytic approach developed here is, in principle, known to specialists, its systematic treatment is not available, and even the diverseaspectsavailablearespreadoutintheliterature.However,theliterature is very wide, and I did not even try to include a full list of related papers, also because this could be confusing for the student. In this regard, I would like to apologize for not quoting all the works that, directly or indirectly, have inspired this monograph.

Finite Element Methods for Navier-Stokes Equations

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Publisher : Springer Science & Business Media
ISBN 13 : 3642616232
Total Pages : 386 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Finite Element Methods for Navier-Stokes Equations by : Vivette Girault

Download or read book Finite Element Methods for Navier-Stokes Equations written by Vivette Girault and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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].

Handbook of Mathematical Fluid Dynamics

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Publisher : Elsevier
ISBN 13 : 0080472915
Total Pages : 687 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Handbook of Mathematical Fluid Dynamics by : S. Friedlander

Download or read book Handbook of Mathematical Fluid Dynamics written by S. Friedlander and published by Elsevier. This book was released on 2004-10-06 with total page 687 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.

Numerical Simulation of 3-D Incompressible Unsteady Viscous Laminar Flows

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Publisher : Vieweg+Teubner Verlag
ISBN 13 : 3663002217
Total Pages : 234 pages
Book Rating : 4.6/5 (63 download)

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Book Synopsis Numerical Simulation of 3-D Incompressible Unsteady Viscous Laminar Flows by : Michel Deville

Download or read book Numerical Simulation of 3-D Incompressible Unsteady Viscous Laminar Flows written by Michel Deville and published by Vieweg+Teubner Verlag. This book was released on 2013-03-09 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: The GAMM-Commi ttee for Numerical Methods in Fluid Mechanics (GAMM-Fachausschuss für Numerische Methoden in der Strömungsmechanik) has sponsored the organization of a GAMM Workshop dedicated to the numerical simulation of three dimensional incompressible unsteady viscous laminar flows to test Navier-Stokes solvers. The Workshop was held in Paris from June 12th to June 14th, 1991 at the Ecole Nationale Superieure des Arts et Metiers. Two test problems were set up. The first one is the flow in a driven-lid parallelepipedic cavity at Re = 3200 . The second problem is a flow around a prolate spheroid at incidence. These problems are challenging as fully transient solutions are expected to show up. The difficulties for meaningful calculations come from both space and temporal discretizations which have to be sufficiently accurate to resol ve detailed structures like Taylor-Görtler-like vortices and the appropriate time development. Several research teams from academia and industry tackled the tests using different formulations (veloci ty-pressure, vortici ty velocity), different numerical methods (finite differences, finite volumes, finite elements), various solution algorithms (splitting, coupled ...), various solvers (direct, iterative, semi-iterative) with preconditioners or other numerical speed-up procedures. The results show some scatter and achieve different levels of efficiency. The Workshop was attended by about 25 scientists and drove much interaction between the participants. The contributions in these proceedings are presented in alphabetical order according to the first author, first for the cavi ty problem and then for the prolate spheroid problem. No definite conclusions about benchmark solutions can be drawn.

Numerical Solution of the Incompressible Navier-Stokes Equations

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Author :
Publisher : Springer Science & Business Media
ISBN 13 : 9783764329358
Total Pages : 312 pages
Book Rating : 4.3/5 (293 download)

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Book Synopsis Numerical Solution of the Incompressible Navier-Stokes Equations by : L. Quartapelle

Download or read book Numerical Solution of the Incompressible Navier-Stokes Equations written by L. Quartapelle and published by Springer Science & Business Media. This book was released on 1993-09-01 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations

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Author :
Publisher : American Mathematical Society
ISBN 13 : 1470471787
Total Pages : 235 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations by : Jacob Bedrossian

Download or read book The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations written by Jacob Bedrossian and published by American Mathematical Society. This book was released on 2022-09-22 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide beginning graduate students who completed the first two semesters of graduate-level analysis and PDE courses with a first exposure to the mathematical analysis of the incompressible Euler and Navier-Stokes equations. The book gives a concise introduction to the fundamental results in the well-posedness theory of these PDEs, leaving aside some of the technical challenges presented by bounded domains or by intricate functional spaces. Chapters 1 and 2 cover the fundamentals of the Euler theory: derivation, Eulerian and Lagrangian perspectives, vorticity, special solutions, existence theory for smooth solutions, and blowup criteria. Chapters 3, 4, and 5 cover the fundamentals of the Navier-Stokes theory: derivation, special solutions, existence theory for strong solutions, Leray theory of weak solutions, weak-strong uniqueness, existence theory of mild solutions, and Prodi-Serrin regularity criteria. Chapter 6 provides a short guide to the must-read topics, including active research directions, for an advanced graduate student working in incompressible fluids. It may be used as a roadmap for a topics course in a subsequent semester. The appendix recalls basic results from real, harmonic, and functional analysis. Each chapter concludes with exercises, making the text suitable for a one-semester graduate course. Prerequisites to this book are the first two semesters of graduate-level analysis and PDE courses.

Random Perturbation of PDEs and Fluid Dynamic Models

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Publisher : Springer
ISBN 13 : 3642182313
Total Pages : 187 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Random Perturbation of PDEs and Fluid Dynamic Models by : Franco Flandoli

Download or read book Random Perturbation of PDEs and Fluid Dynamic Models written by Franco Flandoli and published by Springer. This book was released on 2011-03-02 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with the random perturbation of PDEs which lack well-posedness, mainly because of their non-uniqueness, in some cases because of blow-up. The aim is to show that noise may restore uniqueness or prevent blow-up. This is not a general or easy-to-apply rule, and the theory presented in the book is in fact a series of examples with a few unifying ideas. The role of additive and bilinear multiplicative noise is described and a variety of examples are included, from abstract parabolic evolution equations with non-Lipschitz nonlinearities to particular fluid dynamic models, like the dyadic model, linear transport equations and motion of point vortices.

An Upwind Method for the Solution of the 3D Euler and Navier-Stokes Equations on Adaptively Meshes

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Publisher :
ISBN 13 :
Total Pages : 52 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis An Upwind Method for the Solution of the 3D Euler and Navier-Stokes Equations on Adaptively Meshes by : Michael J. Aftosmis

Download or read book An Upwind Method for the Solution of the 3D Euler and Navier-Stokes Equations on Adaptively Meshes written by Michael J. Aftosmis and published by . This book was released on 1992 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new node based upwind scheme for the solution of the 3D Navier- Stokes equations on adaptively refined meshes is presented. The method uses a second-order upwind TVD scheme to integrate the convective terms, and discretizes the viscous terms with a new compact central difference technique. Grid adaptation is achieved through directional division of hexahedral cells in response to evolving features as the solution converges. The method is advanced in time with a multistage Runge-Kutta time stepping scheme. Two- and three- dimensional examples establish the accuracy of the inviscid and viscous discretization. These investigations highlight the ability of the method to produce crisp shocks, while accurately and economically resolving viscous layers. The representation of these and other structures is shown to be comparable to that obtained by structured methods. Further 3D examples demonstrate the ability of the adaptive algorithm to effectively locate and resolve multiple scale features in complex 3D flows with many interacting, viscous, and inviscid structures.

Harmonic Analysis Method For Nonlinear Evolution Equations, I

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Author :
Publisher : World Scientific
ISBN 13 : 9814458392
Total Pages : 298 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Harmonic Analysis Method For Nonlinear Evolution Equations, I by : Baoxiang Wang

Download or read book Harmonic Analysis Method For Nonlinear Evolution Equations, I written by Baoxiang Wang and published by World Scientific. This book was released on 2011-08-10 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear Schrödinger equations, nonlinear Klein-Gordon equations, KdV equations as well as Navier-Stokes equations and Boltzmann equations. The global wellposedness to the Cauchy problem for those equations is systematically studied by using the harmonic analysis methods.This book is self-contained and may also be used as an advanced textbook by graduate students in analysis and PDE subjects and even ambitious undergraduate students.

Recent Progress in the Theory of the Euler and Navier-Stokes Equations

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Publisher : Cambridge University Press
ISBN 13 : 1107554977
Total Pages : 247 pages
Book Rating : 4.1/5 (75 download)

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Book Synopsis Recent Progress in the Theory of the Euler and Navier-Stokes Equations by : James C. Robinson

Download or read book Recent Progress in the Theory of the Euler and Navier-Stokes Equations written by James C. Robinson and published by Cambridge University Press. This book was released on 2016-01-21 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible summary of a wide range of active research topics written by leaders in their field, including exciting new results.

Intermittent Convex Integration for the 3D Euler Equations

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Publisher : Princeton University Press
ISBN 13 : 0691249547
Total Pages : 256 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis Intermittent Convex Integration for the 3D Euler Equations by : Tristan Buckmaster

Download or read book Intermittent Convex Integration for the 3D Euler Equations written by Tristan Buckmaster and published by Princeton University Press. This book was released on 2023-07-11 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new threshold for the existence of weak solutions to the incompressible Euler equations To gain insight into the nature of turbulent fluids, mathematicians start from experimental facts, translate them into mathematical properties for solutions of the fundamental fluids PDEs, and construct solutions to these PDEs that exhibit turbulent properties. This book belongs to such a program, one that has brought convex integration techniques into hydrodynamics. Convex integration techniques have been used to produce solutions with precise regularity, which are necessary for the resolution of the Onsager conjecture for the 3D Euler equations, or solutions with intermittency, which are necessary for the construction of dissipative weak solutions for the Navier-Stokes equations. In this book, weak solutions to the 3D Euler equations are constructed for the first time with both non-negligible regularity and intermittency. These solutions enjoy a spatial regularity index in L^2 that can be taken as close as desired to 1/2, thus lying at the threshold of all known convex integration methods. This property matches the measured intermittent nature of turbulent flows. The construction of such solutions requires technology specifically adapted to the inhomogeneities inherent in intermittent solutions. The main technical contribution of this book is to develop convex integration techniques at the local rather than global level. This localization procedure functions as an ad hoc wavelet decomposition of the solution, carrying information about position, amplitude, and frequency in both Lagrangian and Eulerian coordinates.

Acta Numerica 2009

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Publisher : Cambridge University Press
ISBN 13 : 9780521192118
Total Pages : 360 pages
Book Rating : 4.1/5 (921 download)

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Book Synopsis Acta Numerica 2009 by : Arieh Iserles

Download or read book Acta Numerica 2009 written by Arieh Iserles and published by Cambridge University Press. This book was released on 2009-05-28 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: A high-impact, prestigious, annual publication featuring invited surveys by subject leaders: essential reading for all practitioners and researchers.

Dynamics of Viscous Compressible Fluids

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Publisher : Oxford University Press
ISBN 13 : 9780198528388
Total Pages : 228 pages
Book Rating : 4.5/5 (283 download)

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Book Synopsis Dynamics of Viscous Compressible Fluids by : Eduard Feireisl

Download or read book Dynamics of Viscous Compressible Fluids written by Eduard Feireisl and published by Oxford University Press. This book was released on 2004 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text develops the ideas and concepts of the mathematical theory of viscous, compressible and heat conducting fluids. The material is by no means intended to be the last word on the subject but rather to indicate possible directions of future research.

Applied Mechanics Reviews

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Publisher :
ISBN 13 :
Total Pages : 1380 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Applied Mechanics Reviews by :

Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1991 with total page 1380 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Scientific and Technical Aerospace Reports

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Publisher :
ISBN 13 :
Total Pages : 892 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Scientific and Technical Aerospace Reports by :

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 892 pages. Available in PDF, EPUB and Kindle. Book excerpt:

AIAA 90-1605 - AIAA 90-1634

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Author :
Publisher :
ISBN 13 :
Total Pages : 368 pages
Book Rating : 4.0/5 ( download)

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Book Synopsis AIAA 90-1605 - AIAA 90-1634 by :

Download or read book AIAA 90-1605 - AIAA 90-1634 written by and published by . This book was released on 1990 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: