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Old   June 28, 2005, 04:49
Default FVM vs FDM
  #1
rajesh
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Dear friends, does Finite Difference method has any advatage over Finite volume methods. thank you.
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Old   June 28, 2005, 10:11
Default Re: FVM vs FDM
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Jonno
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No it doesn't. Its more restrictive geometry wise though. Stick to FVM.
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Old   June 28, 2005, 15:02
Default Re: FVM vs FDM
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ganesh
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Dear Rajesh,

Finite Volume Methods are popular in CFD because they satisfy the "conservation" property which FDM cannot. Thus use of FDM will lead to a lack of conservation and hence discrepancies in shock strengths and location, if we solve for transonic and supersonic compressible flows. Historically, FDM was the first step towards CFD, but as Jonno pointed out it is restrictive geometry wise since applying conventional finite differences for arbitrary geometries is difficult. However, if you would like to explore FDM in present context of CFD, you can check the paper on LSFD-U( Type this on net for more information), which is a finite difference based meshless algorithm. But in a broad scenario that exists at present, it is FVM for CFD.

Regards,

Ganesh
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Old   June 28, 2005, 17:20
Default Re: FVM vs FDM
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Mani
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Absolutely. You will find relatively few people using finite-volume methods in cases where higher-order schemes are required in order to minimize numerical dissipation. One example is the application of FDM to acoustics. If you're looking for a suitable method... it really depends on the problem you want to solve. There is no method that can do everything most efficiently and most accurately.
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Old   June 29, 2005, 08:50
Default Re: FVM vs FDM
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ag
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Actually a well-formulated finite difference method satisfies the exact same conservation equations as do finite volume methods, and yileds the same conservation characteristics. In fact, for structured grids it can be shown that using the conservative form of the NS equations can yield the same form of difference equations regardless of whether you start with FVM or FDM.
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Old   June 29, 2005, 09:25
Default Re: FVM vs FDM
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Jonno
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Too bad real engineering problems cannot be solved on structured meshes...(without severe simplification that is)
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Old   June 29, 2005, 10:18
Default Re: FVM vs FDM
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peter.zhao
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Marcel Vinokur has discussed this problem in detail in Journal of Computational Physics at 1989 and Chi-Wang shu also did so in ICASE report 97-65, you'd better read their papers.
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Old   June 29, 2005, 11:29
Default Re: FVM vs FDM
  #8
andy
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On structured grids with low order differencing (e.g. first or second order) there is little to choose between the two and, often, they produce the same set of algebraic equations.

It is easy to create high order finite difference methods on structured grids and significantly more difficult for a finite volume method.

On unstructured grids it is easy to write a finite volume method but more difficult to write a finite difference method.

As with many things, the most appropriate numerical appraoach depends on what you want to solve.
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Old   June 29, 2005, 12:52
Default Re: FVM vs FDM
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ag
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I'm not sure I would agree with this. I routinely solve for flowfields over advanced fighter aircraft using structured grids. Most of the CFD work done for the space shuttle was performed using structured grids. What do you consider real engineering problems?
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Old   July 3, 2005, 03:04
Default Re: FVM vs FDM
  #10
behzad
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Hello

dear peter zhao

these articles aren't accessible for me. I would be very grateful if you send me these articles.

with best regards behzad
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