Numerical solution of the three-dimensional Navier-Stokes equations
Author: Stephen Michael Richardson
Publisher:
Published: 1976
Total Pages:
ISBN-13:
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Author: Stephen Michael Richardson
Publisher:
Published: 1976
Total Pages:
ISBN-13:
DOWNLOAD EBOOKAuthor: V. Babu
Publisher:
Published: 1991
Total Pages: 286
ISBN-13:
DOWNLOAD EBOOKAuthor: James W. Thomas
Publisher:
Published: 1982
Total Pages: 13
ISBN-13:
DOWNLOAD EBOOKA 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).
Author: Stephen Michael Richardson
Publisher:
Published: 1976
Total Pages:
ISBN-13:
DOWNLOAD EBOOKAuthor: Luigi C. Berselli
Publisher: Academic Press
Published: 2021-03-10
Total Pages: 330
ISBN-13: 0128219459
DOWNLOAD EBOOKThree-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
Author: Stuart Eames Rogers
Publisher:
Published: 1986
Total Pages: 52
ISBN-13:
DOWNLOAD EBOOKAuthor: L. Quartapelle
Publisher: Springer Science & Business Media
Published: 1993-09-01
Total Pages: 312
ISBN-13: 9783764329358
DOWNLOAD EBOOKThis 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.
Author: James C. Robinson
Publisher: Cambridge University Press
Published: 2016-09-07
Total Pages: 487
ISBN-13: 1316715124
DOWNLOAD EBOOKA 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.
Author: Joe F. Thompson
Publisher:
Published: 1973
Total Pages: 50
ISBN-13:
DOWNLOAD EBOOKAuthor: Alexander Victor
Publisher:
Published: 2017
Total Pages:
ISBN-13:
DOWNLOAD EBOOKOne of the most important applications of finite difference lies in the field of computational fluid dynamics (CFD). In particular, the solution to the Navier-Stokes equation grants us insight into the behavior of many physical systems. The 2-D and 3-D incompressible Navier-Stokes equation has been studied extensively due to its analogous nature to many practical applications, and several numerical schemes have been developed to provide solutions dedicated to different environmental conditions (such as different Reynolds numbers). This research also covers the assignment of boundary conditions, starting with the simple case of driven cavity flow problem. In addition, several parts of the equations are given implicitly, which requires efficient ways of solving large systems of equations.We also considered numerical solution methods for the incompressible Navier-Stokes equations discretized on staggered grids in general coordinates. Numerical experiments are carried out on a vector computer. Robustness and efficiency of these methods are studied. It appears that good methods result from suitable combinations of multigrid methods.Numerically solving the incompressible Navier-Stokes equations is known to be time-consuming and expensive; hence this research presents some MATLAB codes for obtaining numerical solution of the Navier-Stokes equations for incompressible flow through flow cavities, using method of lines, in three-dimensional space (3-D). The code treats the laminar flow over a two-dimensional backward-facing step, and the results of the computations over the backward-facing step are in excellent agreement with experimental results.