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: 1107019664

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An accessible treatment of the main results in the mathematical theory of the Navier-Stokes equations, primarily aimed at graduate students.

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).

Three-Dimensional Navier-Stokes Equations for Turbulence
Three-Dimensional Navier-Stokes Equations for Turbulence

Author: Luigi C. Berselli

Publisher: Academic Press

Published: 2021-03-10

Total Pages: 330

ISBN-13: 0128219459

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Three-Dimensional Navier-Stokes Equations for Turbulence provides a rigorous but still accessible account of research into local and global energy dissipation, with particular emphasis on turbulence modeling. The mathematical detail is combined with coverage of physical terms such as energy balance and turbulence to make sure the reader is always in touch with the physical context. All important recent advancements in the analysis of the equations, such as rigorous bounds on structure functions and energy transfer rates in weak solutions, are addressed, and connections are made to numerical methods with many practical applications. The book is written to make this subject accessible to a range of readers, carefully tackling interdisciplinary topics where the combination of theory, numerics, and modeling can be a challenge. - Includes a comprehensive survey of modern reduced-order models, including ones for data assimilation - Includes a self-contained coverage of mathematical analysis of fluid flows, which will act as an ideal introduction to the book for readers without mathematical backgrounds - Presents methods and techniques in a practical way so they can be rapidly applied to the reader's own work

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

Author: L. Quartapelle

Publisher: Springer Science & Business Media

Published: 1993-09-01

Total Pages: 312

ISBN-13: 9783764329358

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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.

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.