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.
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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
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This short chapter is intended primarily to help bring the 'novice' up-to-speed by supplying a sufficiently-generous (but by no means complete) sampling of the relevant introductory and contemporary related literature. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
This short chapter is intended primarily to help bring the 'novice' up-to-speed by supplying a sufficiently-generous (but by no means complete) sampling of the relevant introductory and contemporary related literature. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Customer Reviews
Most Helpful Customer Reviews
1 of 2 people found the following review helpful
Format:Hardcover
I bought this book once I saw it on the internet. With the price I paid, I said I am quite dissapointed with the style the book was authored. Very obviously, there is no proper planning of the book or any attempt to try to make it very clear to the readers. I have to suffer just to read it even though the things presented are quite fundamental. The authors also included a large amount of subjective opinions and a lot of remarks that is not necessary. For example, in chapter 3, when they derived the nodal equation, they called it an element equation, which is confusing. Although badly written, this is a collection of experiences of three well-known investigators in this area. To buy, I will say no, unless you are well aquianted with finite element or at least been working in this area for at least 3 yrs.
Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com:
4.0 out of 5 stars
2 reviews
6 of 6 people found the following review helpful
4.0 out of 5 stars
Strange but useful
11 July 2000
By A Customer
- Published on Amazon.com
Format:Hardcover
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.
4.0 out of 5 stars
A must have for anyone willing to understand the subtelties of FEM
16 Nov 2009
By Rafael M. C. Neto
- Published on Amazon.com
Format:Paperback|Amazon Verified Purchase
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 !
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 !
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