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-   -   FEM,FVM,FDM (http://www.cfd-online.com/Forums/main/3852-fem-fvm-fdm.html)

hari September 4, 2001 00:25

FEM,FVM,FDM
 
will somebody,please, tell me what is the difference between FEM,FVM,FDM.

with regards, hari

S.P.Asok September 4, 2001 01:38

Re: FEM,FVM,FDM
 
Why don't you please refer to some basic CFD book before asking such broad based questions.

John C. Chien September 4, 2001 01:41

Re: FEM,FVM,FDM
 
(1). These are different methods used to convert the governing equations into algebraic equations, FEM being finite element method, FVM being finite volume method, and FDM being finite difference method. (2). You can check out a cfd text book to read more about each method. Books can be found in this forum/books section.

S.P.Asok September 4, 2001 01:47

Re: FEM,FVM,FDM
 
This is what is typical John C.Chien sincerity.Regards. If the visitor is Indian I may suggest some books available here in the local markets.

John C. Chien September 4, 2001 02:10

Re: FEM,FVM,FDM
 
(1). At the forum, the door is open to everyone interested in CFD. (2). But since the time is donated and is quite limited, it is the reader's responsibility to work harder, if he is anxious to learn more. (3). By the way, the news is saying that HP is acquiring Compaq (for 25 billions in stock), which also acquired Digital sometimes ago.

hari September 4, 2001 03:50

Re: FEM,FVM,FDM
 
where are these methods typically used?

John C. Chien September 4, 2001 05:07

Re: FEM,FVM,FDM
 
(1). Good question. (2). If you don't use these methods to solve your problem (fluid, thermal, structure,...etc.), then you will be back to 19th century using series expansion methods or something like that. (3). So, these methods were developed to transform the governing equations (in partial differential equation form) into algebraic equation form, so that the modern digital computer can handle them easily (solve the set of algebraic equations instead of partial differential equations). (4). These methods are used in CFD, Structure analysis, heat transfer analysis, Computational physics, ...etc.

hari September 4, 2001 05:55

Re: FEM,FVM,FDM
 
thank you john

Andrew Parker September 4, 2001 07:01

Re: FEM,FVM,FDM
 
I can recommend a very good book for beginners. Computational fluid dynamics-the basics with applications by John D. Anderson Jr, McGraw-Hill. It explains about how all this CFD stuff started and gives a VERY good introduction. It deals heavily with FDM, used in structured solvers, but does not talk about FVM, or FEM. If you are using Fluent for example then you will need to do some extra reading on FVM. This is a very good book-well recommended.

Andy

Axel Rohde September 4, 2001 08:53

Re: FEM,FVM,FDM
 
The bottom line is that all methods are mathematically identical at the most basic level (if you use a weight function of '1' in FEM). FEM, FVM, and FDM are different ways of looking at the same mathematical problem in a physical sense. You can transform one formulation into another by simply 'massaging' the algebraic equations. After all, each formulation has to be consistent with the original equations.

Whether you look at the Navier Stokes equations in a differential (FDM) or integral format (FVM), they are still the NS equations. The real difference is the accuracy of your numerical solution, since each method uses a slightly different spatial discretization. From a physical viewpoint, FVM is the most intuitive formulation, and often the most accurate, especially if your solution contains shocks.

To give you an example of what I mean with 'identical', take a look at page 56 of my dissertation,

www.cfd4pc.com/papers.htm

where I derive the finite difference metrics for the stress tensor from finite volume terms (volumes, areas, and surface normal vectors). Strictly speaking, equation 4.15 is only a good approximation, so things are not exactly 'identical', unless the mesh/grid is infinitely fine. But I think you will get the point here: Finite difference 'metrics' are difficult to visualize, whereas if you look at the finite volume expression, you will immediately see the interpretation of these metrics in the physical space. The only advantage of expressing the stress tensor using metrics is book-keeping when you write your code.

hari September 4, 2001 12:55

Re: FEM,FVM,FDM
 
Axel,that's the beautiful and relevant explanation.

with regards, hari

hari September 4, 2001 12:56

Re: FEM,FVM,FDM
 
thank you Andrew for responding promptly

Axel Rohde September 4, 2001 14:24

Re: FEM,FVM,FDM
 
My pleasure, Hari!

Peter liang September 4, 2001 19:34

Re: FEM,FVM,FDM
 
Alex: cfd4pc is nice site as well!

Axel Rohde September 4, 2001 22:23

Re: FEM,FVM,FDM
 
Thank you, Peter!!!


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