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Zdravko Stojanovic March 20, 2001 13:39

Finite differences
Is it possible to compute 2-D problems, only with fiite differences, no finite volumes? If yes, which classes of problems can be solved?


John C. Chien March 20, 2001 14:19

Re: Finite differences
(1). You would normally learn how to use finite-difference method to solve fluid dynamics problems first. It is easier to understand based on the traditional calculus. (2). Finite-volume method is a control volume method, which controls only the global balance of mass, momentum and energy over the cell volume.

Zdravko Stojanovic March 21, 2001 05:09

Re: Finite differences
I have already been working with finite differences for some time. The reason that I am asking this is that I have been explicitly told that 2-D without control (finite) volumes, but only with finite differences, is impossible.

This is very important for me, because I have to estimate to what extent is this source reliable.


Petri Majander March 21, 2001 06:31

Re: Finite differences
It is quite possible to formulate 2-D problems with a finite volume (FV) formulation as well as 3-D problems. I'm afraid your source is not reliable on this issue ...

Petri M

Zdravko Stojanovic March 21, 2001 15:13

Re: Finite differences
Thanks to Mr.Chien and Mr. Majander for their answers.

It seems that my question was not precise enough...

Is it possible to solve 2-D problems without CV and without FEM, ONLY with finite differences?

John C. Chien March 21, 2001 15:26

Re: Finite differences
(1). Yes, finite-difference method can solve 2-D problems. You don't have to use CV or FEM to solve 2-D problems. (2). I have been using finite-difference method to solve 2-D problems. (3). I guess, some commercial CFD codes are written in 3-D form only, they don't have 2-D versions. So, in those cases, you have to model the 2-D problems in 3-D codes. (4). I hope that this is clear enough to answer your question?

Kang, Seok Koo March 21, 2001 21:55

Re: Finite differences
Why do you think FDM is not applicable to 2D problem?

You may know that many papers on numerical solution of 2D problems are based on FDM.

I think FDM, FVM and FEM have their own advantages and different ways of approximating PDEs.

First I recommend that you know the advantage and disadvantages of each method from books, and where/how they are used from papers.

FDM requires the use of a Cartesian or a structured curvilinear mesh, and directly approximates the differential operators appearing in equations. Body-fitted meshes have been widely used and are particularly well suited to the treatment of viscous flow because they readily allow the mesh to be compressed near the body surface.

In FVM, the discretisation is accomplished by dividing the domain of the flow into a large number of small subdomains, and applying conservation laws in the integral form. The use of integral form has the advantage that no assumptions of differentiability of the solution is implied, with the result that is remains a valid statement for a subdomain containing shock wave.

Whereas the FDM and FVM approximate the differential and integral operators, the FEM proceeds by inserting an approxiamte solution into the exact equations.

The FDM and FVM lead to essentially similar schemes on structured meshes.

clifford bradford March 24, 2001 23:28

Re: Finite differences
You've been talking to an ignorant person. Finite differences have been used to solve just about every type of CFD problem as have Finite volumes. There is not real advantage between them and on the basic level they are the same.

clifford bradford March 24, 2001 23:31

Re: Finite differences
you can solve any kind (dimension) of problem with any method. They are all basically the same. I'd recommend you read an introductory CFD book like the one b John Anderson.

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