The Navier-Stokes Equations II - Theory and Numerical Methods
The Navier-Stokes Equations II - Theory and Numerical Methods

Author: John G. Heywood

Publisher: Springer

Published: 2006-11-14

Total Pages: 329

ISBN-13: 3540474986

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V.A. Solonnikov, A. Tani: Evolution free boundary problem for equations of motion of viscous compressible barotropic liquid.- W. Borchers, T. Miyakawa:On some coercive estimates for the Stokes problem in unbounded domains.- R. Farwig, H. Sohr: An approach to resolvent estimates for the Stokes equations in L(q)-spaces.- R. Rannacher: On Chorin's projection method for the incompressible Navier-Stokes equations.- E. S}li, A. Ware: Analysis of the spectral Lagrange-Galerkin method for the Navier-Stokes equations.- G. Grubb: Initial value problems for the Navier-Stokes equations with Neumann conditions.- B.J. Schmitt, W. v.Wahl: Decomposition of solenoidal fields into poloidal fields, toroidal fields and the mean flow. Applications to the Boussinesq-equations.- O. Walsh: Eddy solutions of the Navier-Stokesequations.- W. Xie: On a three-norm inequality for the Stokes operator in nonsmooth domains.

The Navier-Stokes Equations
The Navier-Stokes Equations

Author: Rodolfo Salvi

Publisher: CRC Press

Published: 2001-09-27

Total Pages: 337

ISBN-13: 0824744896

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"Contains proceedings of Varenna 2000, the international conference on theory and numerical methods of the navier-Stokes equations, held in Villa Monastero in Varenna, Lecco, Italy, surveying a wide range of topics in fluid mechanics, including compressible, incompressible, and non-newtonian fluids, the free boundary problem, and hydrodynamic potential theory."

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

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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.

Navier–Stokes Equations
Navier–Stokes Equations

Author: Roger Temam

Publisher: American Mathematical Society

Published: 2024-05-24

Total Pages: 426

ISBN-13: 1470477866

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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 and Their Applications
Navier-Stokes Equations and Their Applications

Author: Peter J. Johnson ((Editor of Nova Science Publishers))

Publisher:

Published: 2021

Total Pages: 0

ISBN-13: 9781685071622

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"In physics, Navier-Stokes equations are the partial differential equations that describe the motion of viscous fluid substances. In this book, these equations and their applications are described in detail. Chapter One analyzes the differences between kinetic monism and all-unity in Russian cosmism and Newtonian dualism of separated energies. Chapter Two presents a model for the numerical study of unsteady gas dynamic effects accompanying local heat release in the subsonic part of a nozzle for a given distribution of power of energy. Chapter Three describes a study of relationships between integrals and areas of their applicability. Lastly, Chapter Four defines the exact solutions of the Navier-Stokes equations characterizing movement in deep water and near the surface"--

Navier—Stokes Equations
Navier—Stokes Equations

Author: Roger Temam

Publisher: Elsevier

Published: 2016-06-03

Total Pages: 539

ISBN-13: 1483256855

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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.