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Incompressible Flow and the Finite Element Method, Volume 1, Advection-Diffusion and Isothermal Laminar Flow, by P. M. Gresho, R. L. Sani
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This comprehensive two-volume reference covers the application of the finite element method to incompressible flows in fluid mechanics, addressing the theoretical background and the development of appropriate numerical methods applied to their solution.
Volume One provides extensive coverage of the prototypical fluid mechanics equation: the advection-diffusion equation. For both this equation and the equations of principal interest - the Navier-Stokes equations (covered in detail in Volume Two) - a discussion of both the continuous and discrete equations is presented, as well as explanations of how to properly march the time-dependent equations using smart implicit methods. Boundary and initial conditions, so important in applications, are carefully described and discussed, including well-posedness. The important role played by the pressure, so confusing in the past, is carefully explained.
The book explains and emphasizes consistency in six areas:
* consistent mass matrix
* consistent pressure Poisson equation
* consistent penalty methods
* consistent normal direction
* consistent heat flux
* consistent forces
Fully indexed and referenced, this book is an essential reference tool for all researchers, students and applied scientists in incompressible fluid mechanics.
- Sales Rank: #3600840 in Books
- Published on: 2000-06-09
- Original language: English
- Number of items: 1
- Dimensions: 9.65" h x .94" w x 6.65" l, 1.78 pounds
- Binding: Paperback
- 480 pages
From the Publisher
This self-contained book examines the applications of the finite element method to incompressible flows. It discusses theoretical background and methods development as well as the solution of a wide range of incompressible flows.
From the Back Cover
This comprehensive two volume reference work is devoted to the important details regarding the application of the finite element method to incompressible flows, addressing the theoretical background and the detailed development of appropriate numerical methods applied to their solution. Volume One provides extensive coverage of the prototypical fluid mechanics equation: the advection-diffusion equation. In addition, for both this equation and the equations of principal interest - the Navier-Stokes equations - (covered in detail in Volume Two), a discussion of both the continuous and discrete equations is presented. Also addressed are explanations of how to properly march the time-dependent equations using smart implicit methods. Boundary and initial conditions, so important in applications, are thoroughly described and discussed, including well-posedness. The important role played by the pressure, so confusing in the past, is carefully explained. Together, this two volume work explains and emphasizes consistency in six areas:
* consistent mass matrix
* consistent pressure Poisson equation
* consistent penalty methods
* consistent normal direction
* consistent heat flux
* consistent forces
Fully indexed and referenced
Most helpful customer reviews
6 of 6 people found the following review helpful.
Strange but useful
By A Customer
This book comprises a very thorough introduction to the Finite Element Method for diffusion-advection problems and the incompressible Navier-Stokes equations. The authors' style is strange and often very bizarre but the subject is presented with full details. Many different weak forms of the Navier-Stokes equations are presented and compared. From a practical point of view one will find a great deal of recipes on what elements to use, different strategies on mesh generation, time integration, etc. One will also find a useful discussion on the advantages/disadvantages of FEM compared to some well established finite diffrences and finite volume methods for incompressible flows.
2 of 2 people found the following review helpful.
A must have for anyone willing to understand the subtelties of FEM
By Rafael M. C. Neto
First of all, if you're looking for an "operational book" of FEM - the ones who have all the matrices and methods step-by-step - don't buy this one; choose Reddy - The finite element method in heat transfer and fluid dynamics instead. Or even Hughes - The Finite Element Method should attend your needs.
But this is a very special book, written for those who really want to understand the difficulties and advantages of the Finite Element Method. It makes very very nice comparisons to the so called Control Volume Finite Element Method (the approach currently implemented in Ansys CFX), and it does a very good job in convincing you to follow the finite element, instead of the finite volume school. It is many times funny - at least I cought myself laughing loudly about the audacity and informal way in which the author gives you arguments to shut the finite volume advocates mouth when they say that "FEM Methods aren't conservative". Get this book and you will know how to answer them !
A must have, to read in free time !
0 of 0 people found the following review helpful.
Five Stars
By Yutao Tao
Great Book!
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