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March 20, 2001, 13:39 
Finite differences

#1 
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Is it possible to compute 2D problems, only with fiite differences, no finite volumes? If yes, which classes of problems can be solved?
Thanks. 

March 20, 2001, 14:19 
Re: Finite differences

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


March 21, 2001, 05:09 
Re: Finite differences

#3 
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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 2D 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. Thanks. 

March 21, 2001, 06:31 
Re: Finite differences

#4 
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It is quite possible to formulate 2D problems with a finite volume (FV) formulation as well as 3D problems. I'm afraid your source is not reliable on this issue ...
Petri M 

March 21, 2001, 15:13 
Re: Finite differences

#5 
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Thanks to Mr.Chien and Mr. Majander for their answers.
It seems that my question was not precise enough... Is it possible to solve 2D problems without CV and without FEM, ONLY with finite differences? 

March 21, 2001, 15:26 
Re: Finite differences

#6 
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(1). Yes, finitedifference method can solve 2D problems. You don't have to use CV or FEM to solve 2D problems. (2). I have been using finitedifference method to solve 2D problems. (3). I guess, some commercial CFD codes are written in 3D form only, they don't have 2D versions. So, in those cases, you have to model the 2D problems in 3D codes. (4). I hope that this is clear enough to answer your question?


March 21, 2001, 21:55 
Re: Finite differences

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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. Bodyfitted 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. 

March 24, 2001, 23:28 
Re: Finite differences

#8 
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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.


March 24, 2001, 23:31 
Re: Finite differences

#9 
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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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