The Three-Dimensional Navier–Stokes Equations
The Three-Dimensional Navier–Stokes Equations

Author: James C. Robinson

Publisher: Cambridge University Press

Published: 2016-09-07

Total Pages: 487

ISBN-13: 1316715124

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A rigorous but accessible introduction to the mathematical theory of the three-dimensional Navier–Stokes equations, this book provides self-contained proofs of some of the most significant results in the area, many of which can only be found in research papers. Highlights include the existence of global-in-time Leray–Hopf weak solutions and the local existence of strong solutions; the conditional local regularity results of Serrin and others; and the partial regularity results of Caffarelli, Kohn, and Nirenberg. Appendices provide background material and proofs of some 'standard results' that are hard to find in the literature. A substantial number of exercises are included, with full solutions given at the end of the book. As the only introductory text on the topic to treat all of the mainstream results in detail, this book is an ideal text for a graduate course of one or two semesters. It is also a useful resource for anyone working in mathematical fluid dynamics.

Numerical Solution of the Three-Dimensional Navier-Stokes Equation
Numerical Solution of the Three-Dimensional Navier-Stokes Equation

Author: James W. Thomas

Publisher:

Published: 1982

Total Pages: 13

ISBN-13:

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A three-dimensional version of the Beam-Warming scheme for solving the compressible Navier-Stokes equations was implemented on the Cray-1 computer. The scheme is implicit and second-order accurate. The code is totally vectorized, allows for complicated geometries and includes a thin layer turbulence model. Timings and comparisons are given. A preliminary discussion of the full viscous model is included. (Author).

Numerical Solution of the Three-Dimensional Navier-Stokes Equations in Integro-Differential Form: Flow About a Finite Body
Numerical Solution of the Three-Dimensional Navier-Stokes Equations in Integro-Differential Form: Flow About a Finite Body

Author: J. F Thompson (Jr)

Publisher:

Published: 1973

Total Pages: 13

ISBN-13:

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A new method of numerical solution of the incompressible Navier-Stokes equations is applied to time-dependent flow about a rectangular slab at an angle of attack. With this formulation the solition is obtained in the entire unbounded flow field, but with actual computation required only in regions of significant vorticity. This allows considerable reduction in computer storage, since only points in regions of signficant vorticity need be stored at any particular time. The computational field thus expands in time. (Modified author abstract).

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.